size
int64
2
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keys
stringlengths
10
106
symbols
stringlengths
3
29
domains
stringclasses
62 values
pi
stringlengths
3
46
equation
stringlengths
10
59
name
stringclasses
19 values
n_const
int64
0
4
n_domains
int64
1
6
max_exp
int64
1
34
exp_l1
int64
2
134
complexity
float64
0
113
score
float64
-104.8
10
plausible
bool
2 classes
exponents
stringlengths
27
177
6
current,heat_capacity,length,mass,resistance,thermal_cond
m·ℓ·C·κ·i·R
em,mechanics,thermo
m·ℓ⁵·C⁻³·κ³·i⁻²·R⁻¹
m = k₀ · ℓ⁻⁵·C³·κ⁻³·i²·R
null
0
3
5
15
13.5
-4.5
false
{"mass": "1", "length": "5", "heat_capacity": "-3", "thermal_cond": "3", "current": "-2", "resistance": "-1"}
6
capacitance,current,heat_capacity,length,mass,thermal_cond
m·ℓ·C·κ·i·C_e
em,mechanics,thermo
m·ℓ⁶·C⁻⁴·κ⁴·i⁻²·C_e
m = k₀ · ℓ⁻⁶·C⁴·κ⁻⁴·i²·C_e⁻¹
null
0
3
6
18
16.1
-7.1
false
{"mass": "1", "length": "6", "heat_capacity": "-4", "thermal_cond": "4", "current": "-2", "capacitance": "1"}
6
current,heat_capacity,inductance,length,mass,thermal_cond
m·ℓ·C·κ·i·L_e
em,mechanics,thermo
m·ℓ⁴·C⁻²·κ²·i⁻²·L_e⁻¹
m = k₀ · ℓ⁻⁴·C²·κ⁻²·i²·L_e
null
0
3
4
12
10.9
-1.9
false
{"mass": "1", "length": "4", "heat_capacity": "-2", "thermal_cond": "2", "current": "-2", "inductance": "-1"}
6
current,efield,heat_capacity,length,mass,thermal_cond
m·ℓ·C·κ·i·E_f
em,mechanics,thermo
m·ℓ⁴·C⁻³·κ³·i⁻¹·E_f⁻¹
m = k₀ · ℓ⁻⁴·C³·κ⁻³·i·E_f
null
0
3
4
13
11.6
-2.6
false
{"mass": "1", "length": "4", "heat_capacity": "-3", "thermal_cond": "3", "current": "-1", "efield": "-1"}
6
bfield,current,heat_capacity,length,mass,thermal_cond
m·ℓ·C·κ·i·B
em,mechanics,thermo
m·ℓ²·C⁻²·κ²·i⁻¹·B⁻¹
m = k₀ · ℓ⁻²·C²·κ⁻²·i·B
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "2", "heat_capacity": "-2", "thermal_cond": "2", "current": "-1", "bfield": "-1"}
6
current,heat_capacity,length,mag_flux,mass,thermal_cond
m·ℓ·C·κ·i·Φ
em,mechanics,thermo
m·ℓ⁴·C⁻²·κ²·i⁻¹·Φ⁻¹
m = k₀ · ℓ⁻⁴·C²·κ⁻²·i·Φ
null
0
3
4
11
10.2
-1.2
false
{"mass": "1", "length": "4", "heat_capacity": "-2", "thermal_cond": "2", "current": "-1", "mag_flux": "-1"}
6
current,heat_capacity,length,mass,permittivity,thermal_cond
m·ℓ·C·κ·i·ε
em,mechanics,thermo
m·ℓ⁷·C⁻⁴·κ⁴·i⁻²·ε
m = k₀ · ℓ⁻⁷·C⁴·κ⁻⁴·i²·ε⁻¹
null
0
3
7
19
17.3
-8.3
false
{"mass": "1", "length": "7", "heat_capacity": "-4", "thermal_cond": "4", "current": "-2", "permittivity": "1"}
6
current,heat_capacity,length,mass,permeability,thermal_cond
m·ℓ·C·κ·i·μ₀
em,mechanics,thermo
m·ℓ³·C⁻²·κ²·i⁻²·μ₀⁻¹
m = k₀ · ℓ⁻³·C²·κ⁻²·i²·μ₀
null
0
3
3
11
9.7
-0.7
false
{"mass": "1", "length": "3", "heat_capacity": "-2", "thermal_cond": "2", "current": "-2", "permeability": "-1"}
6
conductivity,current,heat_capacity,length,mass,thermal_cond
m·ℓ·C·κ·i·σ
em,mechanics,thermo
m·ℓ⁶·C⁻³·κ³·i⁻²·σ
m = k₀ · ℓ⁻⁶·C³·κ⁻³·i²·σ⁻¹
null
0
3
6
16
14.7
-5.7
false
{"mass": "1", "length": "6", "heat_capacity": "-3", "thermal_cond": "3", "current": "-2", "conductivity": "1"}
6
current,heat_capacity,length,mass,resistivity,thermal_cond
m·ℓ·C·κ·i·ρ_e
em,mechanics,thermo
m·ℓ⁶·C⁻³·κ³·i⁻²·ρ_e⁻¹
m = k₀ · ℓ⁻⁶·C³·κ⁻³·i²·ρ_e
null
0
3
6
16
14.7
-5.7
false
{"mass": "1", "length": "6", "heat_capacity": "-3", "thermal_cond": "3", "current": "-2", "resistivity": "-1"}
6
heat_capacity,length,mass,resistance,thermal_cond,voltage
m·ℓ·C·κ·U·R
em,mechanics,thermo
m·ℓ⁵·C⁻³·κ³·U⁻²·R
m = k₀ · ℓ⁻⁵·C³·κ⁻³·U²·R⁻¹
null
0
3
5
15
13.5
-4.5
false
{"mass": "1", "length": "5", "heat_capacity": "-3", "thermal_cond": "3", "voltage": "-2", "resistance": "1"}
6
capacitance,heat_capacity,length,mass,thermal_cond,voltage
m·ℓ·C·κ·U·C_e
em,mechanics,thermo
m·ℓ⁴·C⁻²·κ²·U⁻²·C_e⁻¹
m = k₀ · ℓ⁻⁴·C²·κ⁻²·U²·C_e
null
0
3
4
12
10.9
-1.9
false
{"mass": "1", "length": "4", "heat_capacity": "-2", "thermal_cond": "2", "voltage": "-2", "capacitance": "-1"}
6
heat_capacity,inductance,length,mass,thermal_cond,voltage
m·ℓ·C·κ·U·L_e
em,mechanics,thermo
m·ℓ⁶·C⁻⁴·κ⁴·U⁻²·L_e
m = k₀ · ℓ⁻⁶·C⁴·κ⁻⁴·U²·L_e⁻¹
null
0
3
6
18
16.1
-7.1
false
{"mass": "1", "length": "6", "heat_capacity": "-4", "thermal_cond": "4", "voltage": "-2", "inductance": "1"}
6
heat_capacity,length,mass,permittivity,thermal_cond,voltage
m·ℓ·C·κ·U·ε
em,mechanics,thermo
m·ℓ³·C⁻²·κ²·U⁻²·ε⁻¹
m = k₀ · ℓ⁻³·C²·κ⁻²·U²·ε
null
0
3
3
11
9.7
-0.7
false
{"mass": "1", "length": "3", "heat_capacity": "-2", "thermal_cond": "2", "voltage": "-2", "permittivity": "-1"}
6
heat_capacity,length,mass,permeability,thermal_cond,voltage
m·ℓ·C·κ·U·μ₀
em,mechanics,thermo
m·ℓ⁷·C⁻⁴·κ⁴·U⁻²·μ₀
m = k₀ · ℓ⁻⁷·C⁴·κ⁻⁴·U²·μ₀⁻¹
null
0
3
7
19
17.3
-8.3
false
{"mass": "1", "length": "7", "heat_capacity": "-4", "thermal_cond": "4", "voltage": "-2", "permeability": "1"}
6
conductivity,heat_capacity,length,mass,thermal_cond,voltage
m·ℓ·C·κ·U·σ
em,mechanics,thermo
m·ℓ⁴·C⁻³·κ³·U⁻²·σ⁻¹
m = k₀ · ℓ⁻⁴·C³·κ⁻³·U²·σ
null
0
3
4
14
12.3
-3.3
false
{"mass": "1", "length": "4", "heat_capacity": "-3", "thermal_cond": "3", "voltage": "-2", "conductivity": "-1"}
6
heat_capacity,length,mass,resistivity,thermal_cond,voltage
m·ℓ·C·κ·U·ρ_e
em,mechanics,thermo
m·ℓ⁴·C⁻³·κ³·U⁻²·ρ_e
m = k₀ · ℓ⁻⁴·C³·κ⁻³·U²·ρ_e⁻¹
null
0
3
4
14
12.3
-3.3
false
{"mass": "1", "length": "4", "heat_capacity": "-3", "thermal_cond": "3", "voltage": "-2", "resistivity": "1"}
6
elem_charge,heat_capacity,length,mass,thermal_cond,voltage
m·ℓ·C·κ·U·e
constants,em,mechanics,thermo
m·ℓ⁴·C⁻²·κ²·U⁻¹·e⁻¹
m = k₀ · ℓ⁻⁴·C²·κ⁻²·U·e
null
1
4
4
11
10.8
-2.3
false
{"mass": "1", "length": "4", "heat_capacity": "-2", "thermal_cond": "2", "voltage": "-1", "elem_charge": "-1"}
6
efield,heat_capacity,length,mass,resistance,thermal_cond
m·ℓ·C·κ·R·E_f
em,mechanics,thermo
m·ℓ³·C⁻³·κ³·R·E_f⁻²
m = k₀ · ℓ⁻³·C³·κ⁻³·R⁻¹·E_f²
null
0
3
3
13
11.1
-2.1
false
{"mass": "1", "length": "3", "heat_capacity": "-3", "thermal_cond": "3", "resistance": "1", "efield": "-2"}
6
bfield,heat_capacity,length,mass,resistance,thermal_cond
m·ℓ·C·κ·R·B
em,mechanics,thermo
m·ℓ⁻¹·C⁻¹·κ·R·B⁻²
m = k₀ · ℓ·C·κ⁻¹·R⁻¹·B²
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "length": "-1", "heat_capacity": "-1", "thermal_cond": "1", "resistance": "1", "bfield": "-2"}
6
heat_capacity,length,mag_flux,mass,resistance,thermal_cond
m·ℓ·C·κ·R·Φ
em,mechanics,thermo
m·ℓ³·C⁻¹·κ·R·Φ⁻²
m = k₀ · ℓ⁻³·C·κ⁻¹·R⁻¹·Φ²
null
0
3
3
9
8.3
0.7
false
{"mass": "1", "length": "3", "heat_capacity": "-1", "thermal_cond": "1", "resistance": "1", "mag_flux": "-2"}
6
elem_charge,heat_capacity,length,mass,resistance,thermal_cond
m·ℓ·C·κ·R·e
constants,em,mechanics,thermo
m·ℓ³·C⁻¹·κ·R⁻¹·e⁻²
m = k₀ · ℓ⁻³·C·κ⁻¹·R·e²
null
1
4
3
9
8.9
-0.4
false
{"mass": "1", "length": "3", "heat_capacity": "-1", "thermal_cond": "1", "resistance": "-1", "elem_charge": "-2"}
6
capacitance,efield,heat_capacity,length,mass,thermal_cond
m·ℓ·C·κ·C_e·E_f
em,mechanics,thermo
m·ℓ²·C⁻²·κ²·C_e⁻¹·E_f⁻²
m = k₀ · ℓ⁻²·C²·κ⁻²·C_e·E_f²
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "length": "2", "heat_capacity": "-2", "thermal_cond": "2", "capacitance": "-1", "efield": "-2"}
6
capacitance,elem_charge,heat_capacity,length,mass,thermal_cond
m·ℓ·C·κ·C_e·e
constants,em,mechanics,thermo
m·ℓ⁴·C⁻²·κ²·C_e·e⁻²
m = k₀ · ℓ⁻⁴·C²·κ⁻²·C_e⁻¹·e²
null
1
4
4
12
11.5
-3
false
{"mass": "1", "length": "4", "heat_capacity": "-2", "thermal_cond": "2", "capacitance": "1", "elem_charge": "-2"}
6
efield,heat_capacity,inductance,length,mass,thermal_cond
m·ℓ·C·κ·L_e·E_f
em,mechanics,thermo
m·ℓ⁴·C⁻⁴·κ⁴·L_e·E_f⁻²
m = k₀ · ℓ⁻⁴·C⁴·κ⁻⁴·L_e⁻¹·E_f²
null
0
3
4
16
13.7
-4.7
false
{"mass": "1", "length": "4", "heat_capacity": "-4", "thermal_cond": "4", "inductance": "1", "efield": "-2"}
6
heat_capacity,inductance,length,mag_flux,mass,thermal_cond
m·ℓ·C·κ·L_e·Φ
em,mechanics,thermo
m·ℓ⁴·C⁻²·κ²·L_e·Φ⁻²
m = k₀ · ℓ⁻⁴·C²·κ⁻²·L_e⁻¹·Φ²
null
0
3
4
12
10.9
-1.9
false
{"mass": "1", "length": "4", "heat_capacity": "-2", "thermal_cond": "2", "inductance": "1", "mag_flux": "-2"}
6
efield,heat_capacity,length,mass,permittivity,thermal_cond
m·ℓ·C·κ·E_f·ε
em,mechanics,thermo
m·ℓ·C⁻²·κ²·E_f⁻²·ε⁻¹
m = k₀ · ℓ⁻¹·C²·κ⁻²·E_f²·ε
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "1", "heat_capacity": "-2", "thermal_cond": "2", "efield": "-2", "permittivity": "-1"}
6
efield,heat_capacity,length,mass,permeability,thermal_cond
m·ℓ·C·κ·E_f·μ₀
em,mechanics,thermo
m·ℓ⁵·C⁻⁴·κ⁴·E_f⁻²·μ₀
m = k₀ · ℓ⁻⁵·C⁴·κ⁻⁴·E_f²·μ₀⁻¹
null
0
3
5
17
14.9
-5.9
false
{"mass": "1", "length": "5", "heat_capacity": "-4", "thermal_cond": "4", "efield": "-2", "permeability": "1"}
6
conductivity,efield,heat_capacity,length,mass,thermal_cond
m·ℓ·C·κ·E_f·σ
em,mechanics,thermo
m·ℓ²·C⁻³·κ³·E_f⁻²·σ⁻¹
m = k₀ · ℓ⁻²·C³·κ⁻³·E_f²·σ
null
0
3
3
12
10.4
-1.4
false
{"mass": "1", "length": "2", "heat_capacity": "-3", "thermal_cond": "3", "efield": "-2", "conductivity": "-1"}
6
efield,heat_capacity,length,mass,resistivity,thermal_cond
m·ℓ·C·κ·E_f·ρ_e
em,mechanics,thermo
m·ℓ²·C⁻³·κ³·E_f⁻²·ρ_e
m = k₀ · ℓ⁻²·C³·κ⁻³·E_f²·ρ_e⁻¹
null
0
3
3
12
10.4
-1.4
false
{"mass": "1", "length": "2", "heat_capacity": "-3", "thermal_cond": "3", "efield": "-2", "resistivity": "1"}
6
efield,elem_charge,heat_capacity,length,mass,thermal_cond
m·ℓ·C·κ·E_f·e
constants,em,mechanics,thermo
m·ℓ³·C⁻²·κ²·E_f⁻¹·e⁻¹
m = k₀ · ℓ⁻³·C²·κ⁻²·E_f·e
null
1
4
3
10
9.6
-1.1
false
{"mass": "1", "length": "3", "heat_capacity": "-2", "thermal_cond": "2", "efield": "-1", "elem_charge": "-1"}
6
bfield,heat_capacity,length,mass,permeability,thermal_cond
m·ℓ·C·κ·B·μ₀
em,mechanics,thermo
m·ℓ·C⁻²·κ²·B⁻²·μ₀
m = k₀ · ℓ⁻¹·C²·κ⁻²·B²·μ₀⁻¹
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "1", "heat_capacity": "-2", "thermal_cond": "2", "bfield": "-2", "permeability": "1"}
6
bfield,conductivity,heat_capacity,length,mass,thermal_cond
m·ℓ·C·κ·B·σ
em,mechanics,thermo
m·ℓ⁻²·C⁻¹·κ·B⁻²·σ⁻¹
m = k₀ · ℓ²·C·κ⁻¹·B²·σ
null
0
3
2
8
7.1
1.9
false
{"mass": "1", "length": "-2", "heat_capacity": "-1", "thermal_cond": "1", "bfield": "-2", "conductivity": "-1"}
6
bfield,heat_capacity,length,mass,resistivity,thermal_cond
m·ℓ·C·κ·B·ρ_e
em,mechanics,thermo
m·ℓ⁻²·C⁻¹·κ·B⁻²·ρ_e
m = k₀ · ℓ²·C·κ⁻¹·B²·ρ_e⁻¹
null
0
3
2
8
7.1
1.9
false
{"mass": "1", "length": "-2", "heat_capacity": "-1", "thermal_cond": "1", "bfield": "-2", "resistivity": "1"}
6
bfield,elem_charge,heat_capacity,length,mass,thermal_cond
m·ℓ·C·κ·B·e
constants,em,mechanics,thermo
m·ℓ·C⁻¹·κ·B⁻¹·e⁻¹
m = k₀ · ℓ⁻¹·C·κ⁻¹·B·e
null
1
4
1
6
5.8
2.7
false
{"mass": "1", "length": "1", "heat_capacity": "-1", "thermal_cond": "1", "bfield": "-1", "elem_charge": "-1"}
6
heat_capacity,length,mag_flux,mass,permeability,thermal_cond
m·ℓ·C·κ·Φ·μ₀
em,mechanics,thermo
m·ℓ⁵·C⁻²·κ²·Φ⁻²·μ₀
m = k₀ · ℓ⁻⁵·C²·κ⁻²·Φ²·μ₀⁻¹
null
0
3
5
13
12.1
-3.1
false
{"mass": "1", "length": "5", "heat_capacity": "-2", "thermal_cond": "2", "mag_flux": "-2", "permeability": "1"}
6
conductivity,heat_capacity,length,mag_flux,mass,thermal_cond
m·ℓ·C·κ·Φ·σ
em,mechanics,thermo
m·ℓ²·C⁻¹·κ·Φ⁻²·σ⁻¹
m = k₀ · ℓ⁻²·C·κ⁻¹·Φ²·σ
null
0
3
2
8
7.1
1.9
false
{"mass": "1", "length": "2", "heat_capacity": "-1", "thermal_cond": "1", "mag_flux": "-2", "conductivity": "-1"}
6
heat_capacity,length,mag_flux,mass,resistivity,thermal_cond
m·ℓ·C·κ·Φ·ρ_e
em,mechanics,thermo
m·ℓ²·C⁻¹·κ·Φ⁻²·ρ_e
m = k₀ · ℓ⁻²·C·κ⁻¹·Φ²·ρ_e⁻¹
null
0
3
2
8
7.1
1.9
false
{"mass": "1", "length": "2", "heat_capacity": "-1", "thermal_cond": "1", "mag_flux": "-2", "resistivity": "1"}
6
elem_charge,heat_capacity,length,mag_flux,mass,thermal_cond
m·ℓ·C·κ·Φ·e
constants,em,mechanics,thermo
m·ℓ³·C⁻¹·κ·Φ⁻¹·e⁻¹
m = k₀ · ℓ⁻³·C·κ⁻¹·Φ·e
null
1
4
3
8
8.2
0.3
false
{"mass": "1", "length": "3", "heat_capacity": "-1", "thermal_cond": "1", "mag_flux": "-1", "elem_charge": "-1"}
6
elem_charge,heat_capacity,length,mass,permittivity,thermal_cond
m·ℓ·C·κ·ε·e
constants,em,mechanics,thermo
m·ℓ⁵·C⁻²·κ²·ε·e⁻²
m = k₀ · ℓ⁻⁵·C²·κ⁻²·ε⁻¹·e²
null
1
4
5
13
12.7
-4.2
false
{"mass": "1", "length": "5", "heat_capacity": "-2", "thermal_cond": "2", "permittivity": "1", "elem_charge": "-2"}
6
conductivity,elem_charge,heat_capacity,length,mass,thermal_cond
m·ℓ·C·κ·σ·e
constants,em,mechanics,thermo
m·ℓ⁴·C⁻¹·κ·σ·e⁻²
m = k₀ · ℓ⁻⁴·C·κ⁻¹·σ⁻¹·e²
null
1
4
4
10
10.1
-1.6
false
{"mass": "1", "length": "4", "heat_capacity": "-1", "thermal_cond": "1", "conductivity": "1", "elem_charge": "-2"}
6
elem_charge,heat_capacity,length,mass,resistivity,thermal_cond
m·ℓ·C·κ·ρ_e·e
constants,em,mechanics,thermo
m·ℓ⁴·C⁻¹·κ·ρ_e⁻¹·e⁻²
m = k₀ · ℓ⁻⁴·C·κ⁻¹·ρ_e·e²
null
1
4
4
10
10.1
-1.6
false
{"mass": "1", "length": "4", "heat_capacity": "-1", "thermal_cond": "1", "resistivity": "-1", "elem_charge": "-2"}
6
amount,heat_capacity,length,mass,molar_energy,thermal_cond
m·ℓ·C·κ·n·E_m
chemistry,mechanics,thermo
m·ℓ⁴·C⁻²·κ²·n⁻¹·E_m⁻¹
m = k₀ · ℓ⁻⁴·C²·κ⁻²·n·E_m
null
0
3
4
11
10.2
-1.2
false
{"mass": "1", "length": "4", "heat_capacity": "-2", "thermal_cond": "2", "amount": "-1", "molar_energy": "-1"}
6
cat_activity,heat_capacity,length,mass,molar_mass,thermal_cond
m·ℓ·C·κ·M_m·z
chemistry,mechanics,thermo
m·ℓ·C⁻¹·κ·M_m⁻¹·z⁻¹
m = k₀ · ℓ⁻¹·C·κ⁻¹·M_m·z
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "length": "1", "heat_capacity": "-1", "thermal_cond": "1", "molar_mass": "-1", "cat_activity": "-1"}
6
concentration,heat_capacity,length,mass,molar_energy,thermal_cond
m·ℓ·C·κ·c_n·E_m
chemistry,mechanics,thermo
m·ℓ·C⁻²·κ²·c_n⁻¹·E_m⁻¹
m = k₀ · ℓ⁻¹·C²·κ⁻²·c_n·E_m
null
0
3
2
8
7.1
1.9
false
{"mass": "1", "length": "1", "heat_capacity": "-2", "thermal_cond": "2", "concentration": "-1", "molar_energy": "-1"}
6
gas_constant,heat_capacity,length,mass,molar_energy,thermal_cond
m·ℓ·C·κ·E_m·R
chemistry,mechanics,thermo
m·ℓ⁴·C⁻³·κ²·E_m⁻¹·R
m = k₀ · ℓ⁻⁴·C³·κ⁻²·E_m·R⁻¹
null
0
3
4
12
10.9
-1.9
false
{"mass": "1", "length": "4", "heat_capacity": "-3", "thermal_cond": "2", "molar_energy": "-1", "gas_constant": "1"}
6
cat_activity,heat_capacity,length,mass,molar_energy,thermal_cond
m·ℓ·C·κ·E_m·z
chemistry,mechanics,thermo
m·ℓ⁵·C⁻³·κ³·E_m⁻¹·z⁻¹
m = k₀ · ℓ⁻⁵·C³·κ⁻³·E_m·z
null
0
3
5
14
12.8
-3.8
false
{"mass": "1", "length": "5", "heat_capacity": "-3", "thermal_cond": "3", "molar_energy": "-1", "cat_activity": "-1"}
6
avogadro,heat_capacity,length,mass,molar_energy,thermal_cond
m·ℓ·C·κ·E_m·N_A
chemistry,constants,mechanics,thermo
m·ℓ⁴·C⁻²·κ²·E_m⁻¹·N_A
m = k₀ · ℓ⁻⁴·C²·κ⁻²·E_m·N_A⁻¹
null
1
4
4
11
10.8
-2.3
false
{"mass": "1", "length": "4", "heat_capacity": "-2", "thermal_cond": "2", "molar_energy": "-1", "avogadro": "1"}
5
grav_const,heat_capacity,length,mass,thermal_cond
m·ℓ·C·κ·G
constants,mechanics,thermo
m·ℓ⁻⁵·C²·κ⁻²·G
m = k₀ · ℓ⁵·C⁻²·κ²·G⁻¹
null
1
3
5
11
10.4
-1.4
false
{"mass": "1", "length": "-5", "heat_capacity": "2", "thermal_cond": "-2", "grav_const": "1"}
5
heat_capacity,length,mass,planck,thermal_cond
m·ℓ·C·κ·h
constants,mechanics,thermo
m·ℓ³·C⁻¹·κ·h⁻¹
m = k₀ · ℓ⁻³·C·κ⁻¹·h
null
1
3
3
7
6.6
2.4
false
{"mass": "1", "length": "3", "heat_capacity": "-1", "thermal_cond": "1", "planck": "-1"}
5
expansion,heat_capacity,length,mass,thermal_diff
m·ℓ·C·α·β
mechanics,thermo
m·ℓ⁻²·C⁻¹·α²·β
m = k₀ · ℓ²·C·α⁻²·β⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "-2", "heat_capacity": "-1", "thermal_diff": "2", "expansion": "1"}
6
gas_constant,heat_capacity,length,mass,molar_energy,thermal_diff
m·ℓ·C·α·E_m·R
chemistry,mechanics,thermo
m·ℓ⁻²·C⁻¹·α²·E_m⁻¹·R
m = k₀ · ℓ²·C·α⁻²·E_m·R⁻¹
null
0
3
2
8
7.1
1.9
false
{"mass": "1", "length": "-2", "heat_capacity": "-1", "thermal_diff": "2", "molar_energy": "-1", "gas_constant": "1"}
6
charge,current,expansion,heat_capacity,length,mass
m·ℓ·C·β·q·i
em,mechanics,thermo
m·ℓ²·C⁻¹·β·q⁻²·i²
m = k₀ · ℓ⁻²·C·β⁻¹·q²·i⁻²
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "2", "heat_capacity": "-1", "expansion": "1", "charge": "-2", "current": "2"}
6
charge,expansion,heat_capacity,length,mass,resistance
m·ℓ·C·β·q·R
em,mechanics,thermo
m·ℓ²·C·β⁻¹·q⁻⁴·R⁻²
m = k₀ · ℓ⁻²·C⁻¹·β·q⁴·R²
null
0
3
4
11
10.2
-1.2
false
{"mass": "1", "length": "2", "heat_capacity": "1", "expansion": "-1", "charge": "-4", "resistance": "-2"}
6
bfield,charge,expansion,heat_capacity,length,mass
m·ℓ·C·β·q·B
em,mechanics,thermo
m·ℓ⁻²·C·β⁻¹·q⁻²·B⁻²
m = k₀ · ℓ²·C⁻¹·β·q²·B²
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "-2", "heat_capacity": "1", "expansion": "-1", "charge": "-2", "bfield": "-2"}
6
charge,expansion,heat_capacity,length,mag_flux,mass
m·ℓ·C·β·q·Φ
em,mechanics,thermo
m·ℓ²·C·β⁻¹·q⁻²·Φ⁻²
m = k₀ · ℓ⁻²·C⁻¹·β·q²·Φ²
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "2", "heat_capacity": "1", "expansion": "-1", "charge": "-2", "mag_flux": "-2"}
6
charge,conductivity,expansion,heat_capacity,length,mass
m·ℓ·C·β·q·σ
em,mechanics,thermo
m·ℓ⁴·C·β⁻¹·q⁻⁴·σ²
m = k₀ · ℓ⁻⁴·C⁻¹·β·q⁴·σ⁻²
null
0
3
4
13
11.6
-2.6
false
{"mass": "1", "length": "4", "heat_capacity": "1", "expansion": "-1", "charge": "-4", "conductivity": "2"}
6
charge,expansion,heat_capacity,length,mass,resistivity
m·ℓ·C·β·q·ρ_e
em,mechanics,thermo
m·ℓ⁴·C·β⁻¹·q⁻⁴·ρ_e⁻²
m = k₀ · ℓ⁻⁴·C⁻¹·β·q⁴·ρ_e²
null
0
3
4
13
11.6
-2.6
false
{"mass": "1", "length": "4", "heat_capacity": "1", "expansion": "-1", "charge": "-4", "resistivity": "-2"}
6
current,expansion,heat_capacity,length,mass,voltage
m·ℓ·C·β·i·U
em,mechanics,thermo
m·ℓ²·C⁻³·β³·i²·U²
m = k₀ · ℓ⁻²·C³·β⁻³·i⁻²·U⁻²
null
0
3
3
13
11.1
-2.1
false
{"mass": "1", "length": "2", "heat_capacity": "-3", "expansion": "3", "current": "2", "voltage": "2"}
6
current,expansion,heat_capacity,length,mass,resistance
m·ℓ·C·β·i·R
em,mechanics,thermo
m·ℓ²·C⁻³·β³·i⁴·R²
m = k₀ · ℓ⁻²·C³·β⁻³·i⁻⁴·R⁻²
null
0
3
4
15
13
-4
false
{"mass": "1", "length": "2", "heat_capacity": "-3", "expansion": "3", "current": "4", "resistance": "2"}
6
capacitance,current,expansion,heat_capacity,length,mass
m·ℓ·C·β·i·C_e
em,mechanics,thermo
m·ℓ²·C⁻²·β²·i²·C_e⁻¹
m = k₀ · ℓ⁻²·C²·β⁻²·i⁻²·C_e
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "length": "2", "heat_capacity": "-2", "expansion": "2", "current": "2", "capacitance": "-1"}
6
current,efield,expansion,heat_capacity,length,mass
m·ℓ·C·β·i·E_f
em,mechanics,thermo
m·ℓ⁴·C⁻³·β³·i²·E_f²
m = k₀ · ℓ⁻⁴·C³·β⁻³·i⁻²·E_f⁻²
null
0
3
4
15
13
-4
false
{"mass": "1", "length": "4", "heat_capacity": "-3", "expansion": "3", "current": "2", "efield": "2"}
6
current,expansion,heat_capacity,length,mass,permittivity
m·ℓ·C·β·i·ε
em,mechanics,thermo
m·ℓ·C⁻²·β²·i²·ε⁻¹
m = k₀ · ℓ⁻¹·C²·β⁻²·i⁻²·ε
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "1", "heat_capacity": "-2", "expansion": "2", "current": "2", "permittivity": "-1"}
6
current,elem_charge,expansion,heat_capacity,length,mass
m·ℓ·C·β·i·e
constants,em,mechanics,thermo
m·ℓ²·C⁻¹·β·i²·e⁻²
m = k₀ · ℓ⁻²·C·β⁻¹·i⁻²·e²
null
1
4
2
9
8.4
0.1
false
{"mass": "1", "length": "2", "heat_capacity": "-1", "expansion": "1", "current": "2", "elem_charge": "-2"}
6
expansion,heat_capacity,length,mass,resistance,voltage
m·ℓ·C·β·U·R
em,mechanics,thermo
m·ℓ²·C⁻³·β³·U⁴·R⁻²
m = k₀ · ℓ⁻²·C³·β⁻³·U⁻⁴·R²
null
0
3
4
15
13
-4
false
{"mass": "1", "length": "2", "heat_capacity": "-3", "expansion": "3", "voltage": "4", "resistance": "-2"}
6
expansion,heat_capacity,inductance,length,mass,voltage
m·ℓ·C·β·U·L_e
em,mechanics,thermo
m·ℓ²·C⁻²·β²·U²·L_e⁻¹
m = k₀ · ℓ⁻²·C²·β⁻²·U⁻²·L_e
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "length": "2", "heat_capacity": "-2", "expansion": "2", "voltage": "2", "inductance": "-1"}
6
bfield,expansion,heat_capacity,length,mass,voltage
m·ℓ·C·β·U·B
em,mechanics,thermo
m·ℓ⁻²·C⁻¹·β·U²·B⁻²
m = k₀ · ℓ²·C·β⁻¹·U⁻²·B²
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "-2", "heat_capacity": "-1", "expansion": "1", "voltage": "2", "bfield": "-2"}
6
expansion,heat_capacity,length,mag_flux,mass,voltage
m·ℓ·C·β·U·Φ
em,mechanics,thermo
m·ℓ²·C⁻¹·β·U²·Φ⁻²
m = k₀ · ℓ⁻²·C·β⁻¹·U⁻²·Φ²
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "2", "heat_capacity": "-1", "expansion": "1", "voltage": "2", "mag_flux": "-2"}
6
expansion,heat_capacity,length,mass,permeability,voltage
m·ℓ·C·β·U·μ₀
em,mechanics,thermo
m·ℓ·C⁻²·β²·U²·μ₀⁻¹
m = k₀ · ℓ⁻¹·C²·β⁻²·U⁻²·μ₀
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "1", "heat_capacity": "-2", "expansion": "2", "voltage": "2", "permeability": "-1"}
6
conductivity,expansion,heat_capacity,length,mass,voltage
m·ℓ·C·β·U·σ
em,mechanics,thermo
m·ℓ⁴·C⁻³·β³·U⁴·σ²
m = k₀ · ℓ⁻⁴·C³·β⁻³·U⁻⁴·σ⁻²
null
0
3
4
17
14.4
-5.4
false
{"mass": "1", "length": "4", "heat_capacity": "-3", "expansion": "3", "voltage": "4", "conductivity": "2"}
6
expansion,heat_capacity,length,mass,resistivity,voltage
m·ℓ·C·β·U·ρ_e
em,mechanics,thermo
m·ℓ⁴·C⁻³·β³·U⁴·ρ_e⁻²
m = k₀ · ℓ⁻⁴·C³·β⁻³·U⁻⁴·ρ_e²
null
0
3
4
17
14.4
-5.4
false
{"mass": "1", "length": "4", "heat_capacity": "-3", "expansion": "3", "voltage": "4", "resistivity": "-2"}
6
capacitance,expansion,heat_capacity,length,mass,resistance
m·ℓ·C·β·R·C_e
em,mechanics,thermo
m·ℓ²·C⁻¹·β·R⁻²·C_e⁻²
m = k₀ · ℓ⁻²·C·β⁻¹·R²·C_e²
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "2", "heat_capacity": "-1", "expansion": "1", "resistance": "-2", "capacitance": "-2"}
6
expansion,heat_capacity,inductance,length,mass,resistance
m·ℓ·C·β·R·L_e
em,mechanics,thermo
m·ℓ²·C⁻¹·β·R²·L_e⁻²
m = k₀ · ℓ⁻²·C·β⁻¹·R⁻²·L_e²
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "2", "heat_capacity": "-1", "expansion": "1", "resistance": "2", "inductance": "-2"}
6
efield,expansion,heat_capacity,length,mass,resistance
m·ℓ·C·β·R·E_f
em,mechanics,thermo
m·ℓ⁶·C⁻³·β³·R⁻²·E_f⁴
m = k₀ · ℓ⁻⁶·C³·β⁻³·R²·E_f⁻⁴
null
0
3
6
19
16.8
-7.8
false
{"mass": "1", "length": "6", "heat_capacity": "-3", "expansion": "3", "resistance": "-2", "efield": "4"}
6
bfield,expansion,heat_capacity,length,mass,resistance
m·ℓ·C·β·R·B
em,mechanics,thermo
m·ℓ⁻⁶·C·β⁻¹·R²·B⁻⁴
m = k₀ · ℓ⁶·C⁻¹·β·R⁻²·B⁴
null
0
3
6
15
14
-5
false
{"mass": "1", "length": "-6", "heat_capacity": "1", "expansion": "-1", "resistance": "2", "bfield": "-4"}
6
expansion,heat_capacity,length,mag_flux,mass,resistance
m·ℓ·C·β·R·Φ
em,mechanics,thermo
m·ℓ²·C·β⁻¹·R²·Φ⁻⁴
m = k₀ · ℓ⁻²·C⁻¹·β·R⁻²·Φ⁴
null
0
3
4
11
10.2
-1.2
false
{"mass": "1", "length": "2", "heat_capacity": "1", "expansion": "-1", "resistance": "2", "mag_flux": "-4"}
6
elem_charge,expansion,heat_capacity,length,mass,resistance
m·ℓ·C·β·R·e
constants,em,mechanics,thermo
m·ℓ²·C·β⁻¹·R⁻²·e⁻⁴
m = k₀ · ℓ⁻²·C⁻¹·β·R²·e⁴
null
1
4
4
11
10.8
-2.3
false
{"mass": "1", "length": "2", "heat_capacity": "1", "expansion": "-1", "resistance": "-2", "elem_charge": "-4"}
6
capacitance,expansion,heat_capacity,inductance,length,mass
m·ℓ·C·β·C_e·L_e
em,mechanics,thermo
m·ℓ²·C⁻¹·β·C_e⁻¹·L_e⁻¹
m = k₀ · ℓ⁻²·C·β⁻¹·C_e·L_e
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "length": "2", "heat_capacity": "-1", "expansion": "1", "capacitance": "-1", "inductance": "-1"}
6
capacitance,expansion,heat_capacity,length,mass,permeability
m·ℓ·C·β·C_e·μ₀
em,mechanics,thermo
m·ℓ·C⁻¹·β·C_e⁻¹·μ₀⁻¹
m = k₀ · ℓ⁻¹·C·β⁻¹·C_e·μ₀
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "length": "1", "heat_capacity": "-1", "expansion": "1", "capacitance": "-1", "permeability": "-1"}
6
capacitance,conductivity,expansion,heat_capacity,length,mass
m·ℓ·C·β·C_e·σ
em,mechanics,thermo
m·ℓ⁴·C⁻¹·β·C_e⁻²·σ²
m = k₀ · ℓ⁻⁴·C·β⁻¹·C_e²·σ⁻²
null
0
3
4
11
10.2
-1.2
false
{"mass": "1", "length": "4", "heat_capacity": "-1", "expansion": "1", "capacitance": "-2", "conductivity": "2"}
6
capacitance,expansion,heat_capacity,length,mass,resistivity
m·ℓ·C·β·C_e·ρ_e
em,mechanics,thermo
m·ℓ⁴·C⁻¹·β·C_e⁻²·ρ_e⁻²
m = k₀ · ℓ⁻⁴·C·β⁻¹·C_e²·ρ_e²
null
0
3
4
11
10.2
-1.2
false
{"mass": "1", "length": "4", "heat_capacity": "-1", "expansion": "1", "capacitance": "-2", "resistivity": "-2"}
6
efield,expansion,heat_capacity,inductance,length,mass
m·ℓ·C·β·L_e·E_f
em,mechanics,thermo
m·ℓ⁴·C⁻²·β²·L_e⁻¹·E_f²
m = k₀ · ℓ⁻⁴·C²·β⁻²·L_e·E_f⁻²
null
0
3
4
12
10.9
-1.9
false
{"mass": "1", "length": "4", "heat_capacity": "-2", "expansion": "2", "inductance": "-1", "efield": "2"}
6
expansion,heat_capacity,inductance,length,mass,permittivity
m·ℓ·C·β·L_e·ε
em,mechanics,thermo
m·ℓ·C⁻¹·β·L_e⁻¹·ε⁻¹
m = k₀ · ℓ⁻¹·C·β⁻¹·L_e·ε
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "length": "1", "heat_capacity": "-1", "expansion": "1", "inductance": "-1", "permittivity": "-1"}
6
efield,expansion,heat_capacity,length,mag_flux,mass
m·ℓ·C·β·E_f·Φ
em,mechanics,thermo
m·ℓ⁴·C⁻¹·β·E_f²·Φ⁻²
m = k₀ · ℓ⁻⁴·C·β⁻¹·E_f⁻²·Φ²
null
0
3
4
11
10.2
-1.2
false
{"mass": "1", "length": "4", "heat_capacity": "-1", "expansion": "1", "efield": "2", "mag_flux": "-2"}
6
efield,expansion,heat_capacity,length,mass,permeability
m·ℓ·C·β·E_f·μ₀
em,mechanics,thermo
m·ℓ³·C⁻²·β²·E_f²·μ₀⁻¹
m = k₀ · ℓ⁻³·C²·β⁻²·E_f⁻²·μ₀
null
0
3
3
11
9.7
-0.7
false
{"mass": "1", "length": "3", "heat_capacity": "-2", "expansion": "2", "efield": "2", "permeability": "-1"}
6
conductivity,efield,expansion,heat_capacity,length,mass
m·ℓ·C·β·E_f·σ
em,mechanics,thermo
m·ℓ⁸·C⁻³·β³·E_f⁴·σ²
m = k₀ · ℓ⁻⁸·C³·β⁻³·E_f⁻⁴·σ⁻²
null
0
3
8
21
19.2
-10.2
false
{"mass": "1", "length": "8", "heat_capacity": "-3", "expansion": "3", "efield": "4", "conductivity": "2"}
6
efield,expansion,heat_capacity,length,mass,resistivity
m·ℓ·C·β·E_f·ρ_e
em,mechanics,thermo
m·ℓ⁸·C⁻³·β³·E_f⁴·ρ_e⁻²
m = k₀ · ℓ⁻⁸·C³·β⁻³·E_f⁻⁴·ρ_e²
null
0
3
8
21
19.2
-10.2
false
{"mass": "1", "length": "8", "heat_capacity": "-3", "expansion": "3", "efield": "4", "resistivity": "-2"}
6
bfield,conductivity,expansion,heat_capacity,length,mass
m·ℓ·C·β·B·σ
em,mechanics,thermo
m·ℓ⁻⁸·C·β⁻¹·B⁻⁴·σ⁻²
m = k₀ · ℓ⁸·C⁻¹·β·B⁴·σ²
null
0
3
8
17
16.4
-7.4
false
{"mass": "1", "length": "-8", "heat_capacity": "1", "expansion": "-1", "bfield": "-4", "conductivity": "-2"}
6
bfield,expansion,heat_capacity,length,mass,resistivity
m·ℓ·C·β·B·ρ_e
em,mechanics,thermo
m·ℓ⁻⁸·C·β⁻¹·B⁻⁴·ρ_e²
m = k₀ · ℓ⁸·C⁻¹·β·B⁴·ρ_e⁻²
null
0
3
8
17
16.4
-7.4
false
{"mass": "1", "length": "-8", "heat_capacity": "1", "expansion": "-1", "bfield": "-4", "resistivity": "2"}
6
bfield,elem_charge,expansion,heat_capacity,length,mass
m·ℓ·C·β·B·e
constants,em,mechanics,thermo
m·ℓ⁻²·C·β⁻¹·B⁻²·e⁻²
m = k₀ · ℓ²·C⁻¹·β·B²·e²
null
1
4
2
9
8.4
0.1
false
{"mass": "1", "length": "-2", "heat_capacity": "1", "expansion": "-1", "bfield": "-2", "elem_charge": "-2"}
6
elem_charge,expansion,heat_capacity,length,mag_flux,mass
m·ℓ·C·β·Φ·e
constants,em,mechanics,thermo
m·ℓ²·C·β⁻¹·Φ⁻²·e⁻²
m = k₀ · ℓ⁻²·C⁻¹·β·Φ²·e²
null
1
4
2
9
8.4
0.1
false
{"mass": "1", "length": "2", "heat_capacity": "1", "expansion": "-1", "mag_flux": "-2", "elem_charge": "-2"}
6
conductivity,expansion,heat_capacity,length,mass,permittivity
m·ℓ·C·β·ε·σ
em,mechanics,thermo
m·ℓ²·C⁻¹·β·ε⁻²·σ²
m = k₀ · ℓ⁻²·C·β⁻¹·ε²·σ⁻²
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "2", "heat_capacity": "-1", "expansion": "1", "permittivity": "-2", "conductivity": "2"}
6
expansion,heat_capacity,length,mass,permittivity,resistivity
m·ℓ·C·β·ε·ρ_e
em,mechanics,thermo
m·ℓ²·C⁻¹·β·ε⁻²·ρ_e⁻²
m = k₀ · ℓ⁻²·C·β⁻¹·ε²·ρ_e²
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "2", "heat_capacity": "-1", "expansion": "1", "permittivity": "-2", "resistivity": "-2"}
6
conductivity,expansion,heat_capacity,length,mass,permeability
m·ℓ·C·β·μ₀·σ
em,mechanics,thermo
m·ℓ⁻²·C⁻¹·β·μ₀⁻²·σ⁻²
m = k₀ · ℓ²·C·β⁻¹·μ₀²·σ²
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "-2", "heat_capacity": "-1", "expansion": "1", "permeability": "-2", "conductivity": "-2"}
6
expansion,heat_capacity,length,mass,permeability,resistivity
m·ℓ·C·β·μ₀·ρ_e
em,mechanics,thermo
m·ℓ⁻²·C⁻¹·β·μ₀⁻²·ρ_e²
m = k₀ · ℓ²·C·β⁻¹·μ₀²·ρ_e⁻²
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "-2", "heat_capacity": "-1", "expansion": "1", "permeability": "-2", "resistivity": "2"}
6
conductivity,elem_charge,expansion,heat_capacity,length,mass
m·ℓ·C·β·σ·e
constants,em,mechanics,thermo
m·ℓ⁴·C·β⁻¹·σ²·e⁻⁴
m = k₀ · ℓ⁻⁴·C⁻¹·β·σ⁻²·e⁴
null
1
4
4
13
12.2
-3.7
false
{"mass": "1", "length": "4", "heat_capacity": "1", "expansion": "-1", "conductivity": "2", "elem_charge": "-4"}
6
elem_charge,expansion,heat_capacity,length,mass,resistivity
m·ℓ·C·β·ρ_e·e
constants,em,mechanics,thermo
m·ℓ⁴·C·β⁻¹·ρ_e⁻²·e⁻⁴
m = k₀ · ℓ⁻⁴·C⁻¹·β·ρ_e²·e⁴
null
1
4
4
13
12.2
-3.7
false
{"mass": "1", "length": "4", "heat_capacity": "1", "expansion": "-1", "resistivity": "-2", "elem_charge": "-4"}
6
amount,cat_activity,expansion,heat_capacity,length,mass
m·ℓ·C·β·n·z
chemistry,mechanics,thermo
m·ℓ²·C⁻¹·β·n⁻²·z²
m = k₀ · ℓ⁻²·C·β⁻¹·n²·z⁻²
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "2", "heat_capacity": "-1", "expansion": "1", "amount": "-2", "cat_activity": "2"}
6
cat_activity,expansion,heat_capacity,length,mass,molar_mass
m·ℓ·C·β·M_m·z
chemistry,mechanics,thermo
m·ℓ⁻²·C·β⁻¹·M_m⁻²·z⁻²
m = k₀ · ℓ²·C⁻¹·β·M_m²·z²
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "-2", "heat_capacity": "1", "expansion": "-1", "molar_mass": "-2", "cat_activity": "-2"}
6
cat_activity,concentration,expansion,heat_capacity,length,mass
m·ℓ·C·β·c_n·z
chemistry,mechanics,thermo
m·ℓ⁻⁴·C⁻¹·β·c_n⁻²·z²
m = k₀ · ℓ⁴·C·β⁻¹·c_n²·z⁻²
null
0
3
4
11
10.2
-1.2
false
{"mass": "1", "length": "-4", "heat_capacity": "-1", "expansion": "1", "concentration": "-2", "cat_activity": "2"}