size
int64
2
8
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
5
current,elem_charge,length,mass,planck
m·ℓ·i·h·e
constants,em,mechanics
m·ℓ²·i·h⁻¹·e⁻¹
m = k₀ · ℓ⁻²·i⁻¹·h·e
null
2
3
2
6
6.4
1.1
false
{"mass": "1", "length": "2", "current": "1", "planck": "-1", "elem_charge": "-1"}
5
capacitance,length,mass,resistance,voltage
m·ℓ·U·R·C_e
em,mechanics
m·ℓ²·U⁻²·R⁻²·C_e⁻³
m = k₀ · ℓ⁻²·U²·R²·C_e³
null
0
2
3
10
8.1
1.4
false
{"mass": "1", "length": "2", "voltage": "-2", "resistance": "-2", "capacitance": "-3"}
5
inductance,length,mass,resistance,voltage
m·ℓ·U·R·L_e
em,mechanics
m·ℓ²·U⁻²·R⁴·L_e⁻³
m = k₀ · ℓ⁻²·U²·R⁻⁴·L_e³
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "2", "voltage": "-2", "resistance": "4", "inductance": "-3"}
5
bfield,length,mass,resistance,voltage
m·ℓ·U·R·B
em,mechanics
m·ℓ⁻⁴·U·R·B⁻³
m = k₀ · ℓ⁴·U⁻¹·R⁻¹·B³
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "-4", "voltage": "1", "resistance": "1", "bfield": "-3"}
5
length,mag_flux,mass,resistance,voltage
m·ℓ·U·R·Φ
em,mechanics
m·ℓ²·U·R·Φ⁻³
m = k₀ · ℓ⁻²·U⁻¹·R⁻¹·Φ³
null
0
2
3
8
6.7
2.8
true
{"mass": "1", "length": "2", "voltage": "1", "resistance": "1", "mag_flux": "-3"}
5
length,mass,permittivity,resistance,voltage
m·ℓ·U·R·ε
em,mechanics
m·ℓ⁻¹·U⁻²·R⁻²·ε⁻³
m = k₀ · ℓ·U²·R²·ε³
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "-1", "voltage": "-2", "resistance": "-2", "permittivity": "-3"}
5
length,mass,permeability,resistance,voltage
m·ℓ·U·R·μ₀
em,mechanics
m·ℓ⁻¹·U⁻²·R⁴·μ₀⁻³
m = k₀ · ℓ·U²·R⁻⁴·μ₀³
null
0
2
4
11
9.3
0.2
false
{"mass": "1", "length": "-1", "voltage": "-2", "resistance": "4", "permeability": "-3"}
6
amount,length,mass,molar_energy,resistance,voltage
m·ℓ·U·R·n·E_m
chemistry,em,mechanics
m·ℓ²·U⁴·R⁻²·n⁻³·E_m⁻³
m = k₀ · ℓ⁻²·U⁻⁴·R²·n³·E_m³
null
0
3
4
15
13
-4
false
{"mass": "1", "length": "2", "voltage": "4", "resistance": "-2", "amount": "-3", "molar_energy": "-3"}
6
amount,cat_activity,length,mass,resistance,voltage
m·ℓ·U·R·n·z
chemistry,em,mechanics
m·ℓ²·U⁻²·R·n⁻³·z³
m = k₀ · ℓ⁻²·U²·R⁻¹·n³·z⁻³
null
0
3
3
12
10.4
-1.4
false
{"mass": "1", "length": "2", "voltage": "-2", "resistance": "1", "amount": "-3", "cat_activity": "3"}
6
length,mass,molar_energy,molar_mass,resistance,voltage
m·ℓ·U·R·M_m·E_m
chemistry,em,mechanics
m²·ℓ⁻²·U⁻⁴·R²·M_m⁻³·E_m³
m = k₀ · ℓ·U²·R⁻¹·M_m³ᐟ²·E_m⁻³ᐟ²
null
0
3
4
16
13.7
-4.7
false
{"mass": "2", "length": "-2", "voltage": "-4", "resistance": "2", "molar_mass": "-3", "molar_energy": "3"}
6
cat_activity,length,mass,molar_mass,resistance,voltage
m·ℓ·U·R·M_m·z
chemistry,em,mechanics
m²·ℓ⁻²·U²·R⁻¹·M_m⁻³·z⁻³
R = k₀ · m²·ℓ⁻²·U²·M_m⁻³·z⁻³
null
0
3
3
13
11.1
-2.1
false
{"mass": "2", "length": "-2", "voltage": "2", "resistance": "-1", "molar_mass": "-3", "cat_activity": "-3"}
6
concentration,length,mass,molar_energy,resistance,voltage
m·ℓ·U·R·c_n·E_m
chemistry,em,mechanics
m·ℓ⁻⁷·U⁴·R⁻²·c_n⁻³·E_m⁻³
m = k₀ · ℓ⁷·U⁻⁴·R²·c_n³·E_m³
null
0
3
7
20
18
-9
false
{"mass": "1", "length": "-7", "voltage": "4", "resistance": "-2", "concentration": "-3", "molar_energy": "-3"}
6
cat_activity,concentration,length,mass,resistance,voltage
m·ℓ·U·R·c_n·z
chemistry,em,mechanics
m·ℓ⁻⁷·U⁻²·R·c_n⁻³·z³
m = k₀ · ℓ⁷·U²·R⁻¹·c_n³·z⁻³
null
0
3
7
17
15.9
-6.9
false
{"mass": "1", "length": "-7", "voltage": "-2", "resistance": "1", "concentration": "-3", "cat_activity": "3"}
7
boltzmann,gas_constant,length,mass,molar_energy,resistance,voltage
m·ℓ·U·R·E_m·R·k_B
chemistry,constants,em,mechanics
m·ℓ²·U⁴·R⁻²·E_m⁻³·R³·k_B⁻³
m = k₀ · ℓ⁻²·U⁻⁴·R²·E_m³·R⁻³·k_B³
null
1
4
4
18
16
-7.5
false
{"mass": "1", "length": "2", "voltage": "4", "resistance": "-2", "molar_energy": "-3", "gas_constant": "3", "boltzmann": "-3"}
6
avogadro,length,mass,molar_energy,resistance,voltage
m·ℓ·U·R·E_m·N_A
chemistry,constants,em,mechanics
m·ℓ²·U⁴·R⁻²·E_m⁻³·N_A³
m = k₀ · ℓ⁻²·U⁻⁴·R²·E_m³·N_A⁻³
null
1
4
4
15
13.6
-5.1
false
{"mass": "1", "length": "2", "voltage": "4", "resistance": "-2", "molar_energy": "-3", "avogadro": "3"}
7
boltzmann,cat_activity,gas_constant,length,mass,resistance,voltage
m·ℓ·U·R·R·z·k_B
chemistry,constants,em,mechanics
m·ℓ²·U⁻²·R·R³·z³·k_B⁻³
m = k₀ · ℓ⁻²·U²·R⁻¹·R⁻³·z⁻³·k_B³
null
1
4
3
15
13.4
-4.9
false
{"mass": "1", "length": "2", "voltage": "-2", "resistance": "1", "gas_constant": "3", "cat_activity": "3", "boltzmann": "-3"}
6
avogadro,cat_activity,length,mass,resistance,voltage
m·ℓ·U·R·z·N_A
chemistry,constants,em,mechanics
m·ℓ²·U⁻²·R·z³·N_A³
m = k₀ · ℓ⁻²·U²·R⁻¹·z⁻³·N_A⁻³
null
1
4
3
12
11
-2.5
false
{"mass": "1", "length": "2", "voltage": "-2", "resistance": "1", "cat_activity": "3", "avogadro": "3"}
5
length,light_speed,mass,resistance,voltage
m·ℓ·U·R·c₀
constants,em,mechanics
m·ℓ⁻¹·U⁻²·R·c₀³
m = k₀ · ℓ·U²·R⁻¹·c₀⁻³
null
1
3
3
8
7.3
1.7
false
{"mass": "1", "length": "-1", "voltage": "-2", "resistance": "1", "light_speed": "3"}
5
grav_const,length,mass,resistance,voltage
m·ℓ·U·R·G
constants,em,mechanics
m⁵·ℓ⁻⁵·U⁻⁴·R²·G³
R = k₀ · m⁻⁵ᐟ²·ℓ⁵ᐟ²·U²·G⁻³ᐟ²
null
1
3
5
19
16
-7
false
{"mass": "5", "length": "-5", "voltage": "-4", "resistance": "2", "grav_const": "3"}
5
length,mass,planck,resistance,voltage
m·ℓ·U·R·h
constants,em,mechanics
m²·ℓ⁴·U²·R⁻¹·h⁻³
R = k₀ · m²·ℓ⁴·U²·h⁻³
null
1
3
4
12
10.6
-1.6
false
{"mass": "2", "length": "4", "voltage": "2", "resistance": "-1", "planck": "-3"}
5
elem_charge,length,mass,resistance,voltage
m·ℓ·U·R·e
constants,em,mechanics
m·ℓ²·U·R⁻²·e⁻³
m = k₀ · ℓ⁻²·U⁻¹·R²·e³
null
1
3
3
9
8
1
false
{"mass": "1", "length": "2", "voltage": "1", "resistance": "-2", "elem_charge": "-3"}
5
capacitance,inductance,length,mass,voltage
m·ℓ·U·C_e·L_e
em,mechanics
m·ℓ²·U⁻²·C_e⁻²·L_e⁻¹
m = k₀ · ℓ⁻²·U²·C_e²·L_e
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "voltage": "-2", "capacitance": "-2", "inductance": "-1"}
5
capacitance,length,mass,permeability,voltage
m·ℓ·U·C_e·μ₀
em,mechanics
m·ℓ·U⁻²·C_e⁻²·μ₀⁻¹
m = k₀ · ℓ⁻¹·U²·C_e²·μ₀
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "1", "voltage": "-2", "capacitance": "-2", "permeability": "-1"}
5
capacitance,conductivity,length,mass,voltage
m·ℓ·U·C_e·σ
em,mechanics
m·ℓ⁴·U⁻²·C_e⁻³·σ²
m = k₀ · ℓ⁻⁴·U²·C_e³·σ⁻²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "4", "voltage": "-2", "capacitance": "-3", "conductivity": "2"}
5
capacitance,length,mass,resistivity,voltage
m·ℓ·U·C_e·ρ_e
em,mechanics
m·ℓ⁴·U⁻²·C_e⁻³·ρ_e⁻²
m = k₀ · ℓ⁻⁴·U²·C_e³·ρ_e²
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "4", "voltage": "-2", "capacitance": "-3", "resistivity": "-2"}
6
amount,capacitance,cat_activity,length,mass,voltage
m·ℓ·U·C_e·n·z
chemistry,em,mechanics
m·ℓ²·U⁻²·C_e⁻¹·n⁻²·z²
m = k₀ · ℓ⁻²·U²·C_e·n²·z⁻²
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "length": "2", "voltage": "-2", "capacitance": "-1", "amount": "-2", "cat_activity": "2"}
6
capacitance,cat_activity,length,mass,molar_mass,voltage
m·ℓ·U·C_e·M_m·z
chemistry,em,mechanics
m·ℓ⁻²·U²·C_e·M_m⁻²·z⁻²
m = k₀ · ℓ²·U⁻²·C_e⁻¹·M_m²·z²
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "length": "-2", "voltage": "2", "capacitance": "1", "molar_mass": "-2", "cat_activity": "-2"}
6
capacitance,cat_activity,concentration,length,mass,voltage
m·ℓ·U·C_e·c_n·z
chemistry,em,mechanics
m·ℓ⁻⁴·U⁻²·C_e⁻¹·c_n⁻²·z²
m = k₀ · ℓ⁴·U²·C_e·c_n²·z⁻²
null
0
3
4
12
10.9
-1.9
false
{"mass": "1", "length": "-4", "voltage": "-2", "capacitance": "-1", "concentration": "-2", "cat_activity": "2"}
6
capacitance,cat_activity,length,mass,molar_energy,voltage
m·ℓ·U·C_e·E_m·z
chemistry,em,mechanics
m·ℓ²·U⁻⁶·C_e⁻³·E_m²·z²
m = k₀ · ℓ⁻²·U⁶·C_e³·E_m⁻²·z⁻²
null
0
3
6
16
14.7
-5.7
false
{"mass": "1", "length": "2", "voltage": "-6", "capacitance": "-3", "molar_energy": "2", "cat_activity": "2"}
7
boltzmann,capacitance,cat_activity,gas_constant,length,mass,voltage
m·ℓ·U·C_e·R·z·k_B
chemistry,constants,em,mechanics
m·ℓ²·U⁻²·C_e⁻¹·R²·z²·k_B⁻²
m = k₀ · ℓ⁻²·U²·C_e·R⁻²·z⁻²·k_B²
null
1
4
2
12
10.8
-2.3
false
{"mass": "1", "length": "2", "voltage": "-2", "capacitance": "-1", "gas_constant": "2", "cat_activity": "2", "boltzmann": "-2"}
6
avogadro,capacitance,cat_activity,length,mass,voltage
m·ℓ·U·C_e·z·N_A
chemistry,constants,em,mechanics
m·ℓ²·U⁻²·C_e⁻¹·z²·N_A²
m = k₀ · ℓ⁻²·U²·C_e·z⁻²·N_A⁻²
null
1
4
2
10
9.1
-0.6
false
{"mass": "1", "length": "2", "voltage": "-2", "capacitance": "-1", "cat_activity": "2", "avogadro": "2"}
5
capacitance,grav_const,length,mass,voltage
m·ℓ·U·C_e·G
constants,em,mechanics
m²·ℓ⁻¹·U⁻²·C_e⁻¹·G
ℓ = k₀ · m²·U⁻²·C_e⁻¹·G
null
1
3
2
7
6.1
2.9
false
{"mass": "2", "length": "-1", "voltage": "-2", "capacitance": "-1", "grav_const": "1"}
5
capacitance,length,mass,planck,voltage
m·ℓ·U·C_e·h
constants,em,mechanics
m·ℓ²·U²·C_e·h⁻²
m = k₀ · ℓ⁻²·U⁻²·C_e⁻¹·h²
null
1
3
2
8
6.8
2.2
false
{"mass": "1", "length": "2", "voltage": "2", "capacitance": "1", "planck": "-2"}
5
bfield,inductance,length,mass,voltage
m·ℓ·U·L_e·B
em,mechanics
m·ℓ⁻⁶·U²·L_e·B⁻⁴
m = k₀ · ℓ⁶·U⁻²·L_e⁻¹·B⁴
null
0
2
6
14
12.4
-2.9
false
{"mass": "1", "length": "-6", "voltage": "2", "inductance": "1", "bfield": "-4"}
5
inductance,length,mag_flux,mass,voltage
m·ℓ·U·L_e·Φ
em,mechanics
m·ℓ²·U²·L_e·Φ⁻⁴
m = k₀ · ℓ⁻²·U⁻²·L_e⁻¹·Φ⁴
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "2", "voltage": "2", "inductance": "1", "mag_flux": "-4"}
5
conductivity,inductance,length,mass,voltage
m·ℓ·U·L_e·σ
em,mechanics
m·ℓ⁻²·U⁻²·L_e⁻³·σ⁻⁴
m = k₀ · ℓ²·U²·L_e³·σ⁴
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "-2", "voltage": "-2", "inductance": "-3", "conductivity": "-4"}
5
inductance,length,mass,resistivity,voltage
m·ℓ·U·L_e·ρ_e
em,mechanics
m·ℓ⁻²·U⁻²·L_e⁻³·ρ_e⁴
m = k₀ · ℓ²·U²·L_e³·ρ_e⁻⁴
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "-2", "voltage": "-2", "inductance": "-3", "resistivity": "4"}
6
amount,inductance,length,mass,molar_energy,voltage
m·ℓ·U·L_e·n·E_m
chemistry,em,mechanics
m·ℓ²·U²·L_e⁻¹·n⁻²·E_m⁻²
m = k₀ · ℓ⁻²·U⁻²·L_e·n²·E_m²
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "length": "2", "voltage": "2", "inductance": "-1", "amount": "-2", "molar_energy": "-2"}
6
amount,cat_activity,inductance,length,mass,voltage
m·ℓ·U·L_e·n·z
chemistry,em,mechanics
m·ℓ²·U⁻²·L_e·n⁻⁴·z⁴
m = k₀ · ℓ⁻²·U²·L_e⁻¹·n⁴·z⁻⁴
null
0
3
4
14
12.3
-3.3
false
{"mass": "1", "length": "2", "voltage": "-2", "inductance": "1", "amount": "-4", "cat_activity": "4"}
6
inductance,length,mass,molar_energy,molar_mass,voltage
m·ℓ·U·L_e·M_m·E_m
chemistry,em,mechanics
m·ℓ⁻²·U⁻²·L_e·M_m⁻²·E_m²
m = k₀ · ℓ²·U²·L_e⁻¹·M_m²·E_m⁻²
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "length": "-2", "voltage": "-2", "inductance": "1", "molar_mass": "-2", "molar_energy": "2"}
6
cat_activity,inductance,length,mass,molar_mass,voltage
m·ℓ·U·L_e·M_m·z
chemistry,em,mechanics
m³·ℓ⁻²·U²·L_e⁻¹·M_m⁻⁴·z⁻⁴
L_e = k₀ · m³·ℓ⁻²·U²·M_m⁻⁴·z⁻⁴
null
0
3
4
16
13.7
-4.7
false
{"mass": "3", "length": "-2", "voltage": "2", "inductance": "-1", "molar_mass": "-4", "cat_activity": "-4"}
6
concentration,inductance,length,mass,molar_energy,voltage
m·ℓ·U·L_e·c_n·E_m
chemistry,em,mechanics
m·ℓ⁻⁴·U²·L_e⁻¹·c_n⁻²·E_m⁻²
m = k₀ · ℓ⁴·U⁻²·L_e·c_n²·E_m²
null
0
3
4
12
10.9
-1.9
false
{"mass": "1", "length": "-4", "voltage": "2", "inductance": "-1", "concentration": "-2", "molar_energy": "-2"}
6
cat_activity,concentration,inductance,length,mass,voltage
m·ℓ·U·L_e·c_n·z
chemistry,em,mechanics
m·ℓ⁻¹⁰·U⁻²·L_e·c_n⁻⁴·z⁴
m = k₀ · ℓ¹⁰·U²·L_e⁻¹·c_n⁴·z⁻⁴
null
0
3
10
22
20.9
-11.9
false
{"mass": "1", "length": "-10", "voltage": "-2", "inductance": "1", "concentration": "-4", "cat_activity": "4"}
7
boltzmann,gas_constant,inductance,length,mass,molar_energy,voltage
m·ℓ·U·L_e·E_m·R·k_B
chemistry,constants,em,mechanics
m·ℓ²·U²·L_e⁻¹·E_m⁻²·R²·k_B⁻²
m = k₀ · ℓ⁻²·U⁻²·L_e·E_m²·R⁻²·k_B²
null
1
4
2
12
10.8
-2.3
false
{"mass": "1", "length": "2", "voltage": "2", "inductance": "-1", "molar_energy": "-2", "gas_constant": "2", "boltzmann": "-2"}
6
cat_activity,inductance,length,mass,molar_energy,voltage
m·ℓ·U·L_e·E_m·z
chemistry,em,mechanics
m·ℓ²·U⁶·L_e⁻³·E_m⁻⁴·z⁻⁴
m = k₀ · ℓ⁻²·U⁻⁶·L_e³·E_m⁴·z⁴
null
0
3
6
20
17.5
-8.5
false
{"mass": "1", "length": "2", "voltage": "6", "inductance": "-3", "molar_energy": "-4", "cat_activity": "-4"}
6
avogadro,inductance,length,mass,molar_energy,voltage
m·ℓ·U·L_e·E_m·N_A
chemistry,constants,em,mechanics
m·ℓ²·U²·L_e⁻¹·E_m⁻²·N_A²
m = k₀ · ℓ⁻²·U⁻²·L_e·E_m²·N_A⁻²
null
1
4
2
10
9.1
-0.6
false
{"mass": "1", "length": "2", "voltage": "2", "inductance": "-1", "molar_energy": "-2", "avogadro": "2"}
7
boltzmann,cat_activity,gas_constant,inductance,length,mass,voltage
m·ℓ·U·L_e·R·z·k_B
chemistry,constants,em,mechanics
m·ℓ²·U⁻²·L_e·R⁴·z⁴·k_B⁻⁴
m = k₀ · ℓ⁻²·U²·L_e⁻¹·R⁻⁴·z⁻⁴·k_B⁴
null
1
4
4
18
16
-7.5
false
{"mass": "1", "length": "2", "voltage": "-2", "inductance": "1", "gas_constant": "4", "cat_activity": "4", "boltzmann": "-4"}
6
avogadro,cat_activity,inductance,length,mass,voltage
m·ℓ·U·L_e·z·N_A
chemistry,constants,em,mechanics
m·ℓ²·U⁻²·L_e·z⁴·N_A⁴
m = k₀ · ℓ⁻²·U²·L_e⁻¹·z⁻⁴·N_A⁻⁴
null
1
4
4
14
12.9
-4.4
false
{"mass": "1", "length": "2", "voltage": "-2", "inductance": "1", "cat_activity": "4", "avogadro": "4"}
5
inductance,length,light_speed,mass,voltage
m·ℓ·U·L_e·c₀
constants,em,mechanics
m·ℓ⁻²·U⁻²·L_e·c₀⁴
m = k₀ · ℓ²·U²·L_e⁻¹·c₀⁻⁴
null
1
3
4
10
9.2
-0.2
false
{"mass": "1", "length": "-2", "voltage": "-2", "inductance": "1", "light_speed": "4"}
5
grav_const,inductance,length,mass,voltage
m·ℓ·U·L_e·G
constants,em,mechanics
m³·ℓ⁻⁴·U⁻²·L_e·G²
L_e = k₀ · m⁻³·ℓ⁴·U²·G⁻²
null
1
3
4
12
10.6
-1.6
false
{"mass": "3", "length": "-4", "voltage": "-2", "inductance": "1", "grav_const": "2"}
5
inductance,length,mass,planck,voltage
m·ℓ·U·L_e·h
constants,em,mechanics
m³·ℓ⁶·U²·L_e⁻¹·h⁻⁴
L_e = k₀ · m³·ℓ⁶·U²·h⁻⁴
null
1
3
6
16
14.4
-5.4
false
{"mass": "3", "length": "6", "voltage": "2", "inductance": "-1", "planck": "-4"}
5
bfield,length,mass,permeability,voltage
m·ℓ·U·B·μ₀
em,mechanics
m·ℓ⁻⁵·U²·B⁻⁴·μ₀
m = k₀ · ℓ⁵·U⁻²·B⁴·μ₀⁻¹
null
0
2
5
13
11.2
-1.7
false
{"mass": "1", "length": "-5", "voltage": "2", "bfield": "-4", "permeability": "1"}
5
bfield,conductivity,length,mass,voltage
m·ℓ·U·B·σ
em,mechanics
m·ℓ⁻⁵·U·B⁻³·σ⁻¹
m = k₀ · ℓ⁵·U⁻¹·B³·σ
null
0
2
5
11
9.8
-0.3
false
{"mass": "1", "length": "-5", "voltage": "1", "bfield": "-3", "conductivity": "-1"}
5
bfield,length,mass,resistivity,voltage
m·ℓ·U·B·ρ_e
em,mechanics
m·ℓ⁻⁵·U·B⁻³·ρ_e
m = k₀ · ℓ⁵·U⁻¹·B³·ρ_e⁻¹
null
0
2
5
11
9.8
-0.3
false
{"mass": "1", "length": "-5", "voltage": "1", "bfield": "-3", "resistivity": "1"}
6
amount,bfield,length,mass,molar_energy,voltage
m·ℓ·U·B·n·E_m
chemistry,em,mechanics
m·ℓ⁻²·U²·B⁻²·n⁻¹·E_m⁻¹
m = k₀ · ℓ²·U⁻²·B²·n·E_m
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "-2", "voltage": "2", "bfield": "-2", "amount": "-1", "molar_energy": "-1"}
6
bfield,cat_activity,length,mass,molar_mass,voltage
m·ℓ·U·B·M_m·z
chemistry,em,mechanics
m·ℓ⁻²·U·B⁻¹·M_m⁻¹·z⁻¹
m = k₀ · ℓ²·U⁻¹·B·M_m·z
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "length": "-2", "voltage": "1", "bfield": "-1", "molar_mass": "-1", "cat_activity": "-1"}
6
bfield,concentration,length,mass,molar_energy,voltage
m·ℓ·U·B·c_n·E_m
chemistry,em,mechanics
m·ℓ⁻⁵·U²·B⁻²·c_n⁻¹·E_m⁻¹
m = k₀ · ℓ⁵·U⁻²·B²·c_n·E_m
null
0
3
5
12
11.4
-2.4
false
{"mass": "1", "length": "-5", "voltage": "2", "bfield": "-2", "concentration": "-1", "molar_energy": "-1"}
7
bfield,boltzmann,gas_constant,length,mass,molar_energy,voltage
m·ℓ·U·B·E_m·R·k_B
chemistry,constants,em,mechanics
m·ℓ⁻²·U²·B⁻²·E_m⁻¹·R·k_B⁻¹
m = k₀ · ℓ²·U⁻²·B²·E_m·R⁻¹·k_B
null
1
4
2
10
9.4
-0.9
false
{"mass": "1", "length": "-2", "voltage": "2", "bfield": "-2", "molar_energy": "-1", "gas_constant": "1", "boltzmann": "-1"}
6
bfield,cat_activity,length,mass,molar_energy,voltage
m·ℓ·U·B·E_m·z
chemistry,em,mechanics
m·ℓ⁻⁴·U³·B⁻³·E_m⁻¹·z⁻¹
m = k₀ · ℓ⁴·U⁻³·B³·E_m·z
null
0
3
4
13
11.6
-2.6
false
{"mass": "1", "length": "-4", "voltage": "3", "bfield": "-3", "molar_energy": "-1", "cat_activity": "-1"}
6
avogadro,bfield,length,mass,molar_energy,voltage
m·ℓ·U·B·E_m·N_A
chemistry,constants,em,mechanics
m·ℓ⁻²·U²·B⁻²·E_m⁻¹·N_A
m = k₀ · ℓ²·U⁻²·B²·E_m·N_A⁻¹
null
1
4
2
9
8.4
0.1
false
{"mass": "1", "length": "-2", "voltage": "2", "bfield": "-2", "molar_energy": "-1", "avogadro": "1"}
5
bfield,grav_const,length,mass,voltage
m·ℓ·U·B·G
constants,em,mechanics
m·ℓ·U⁻²·B²·G
m = k₀ · ℓ⁻¹·U²·B⁻²·G⁻¹
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "1", "voltage": "-2", "bfield": "2", "grav_const": "1"}
5
bfield,elem_charge,length,mass,voltage
m·ℓ·U·B·e
constants,em,mechanics
m·ℓ⁻²·U·B⁻²·e⁻¹
m = k₀ · ℓ²·U⁻¹·B²·e
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "-2", "voltage": "1", "bfield": "-2", "elem_charge": "-1"}
5
length,mag_flux,mass,permeability,voltage
m·ℓ·U·Φ·μ₀
em,mechanics
m·ℓ³·U²·Φ⁻⁴·μ₀
m = k₀ · ℓ⁻³·U⁻²·Φ⁴·μ₀⁻¹
null
0
2
4
11
9.3
0.2
false
{"mass": "1", "length": "3", "voltage": "2", "mag_flux": "-4", "permeability": "1"}
5
conductivity,length,mag_flux,mass,voltage
m·ℓ·U·Φ·σ
em,mechanics
m·ℓ·U·Φ⁻³·σ⁻¹
m = k₀ · ℓ⁻¹·U⁻¹·Φ³·σ
null
0
2
3
7
6
3.5
true
{"mass": "1", "length": "1", "voltage": "1", "mag_flux": "-3", "conductivity": "-1"}
5
length,mag_flux,mass,resistivity,voltage
m·ℓ·U·Φ·ρ_e
em,mechanics
m·ℓ·U·Φ⁻³·ρ_e
m = k₀ · ℓ⁻¹·U⁻¹·Φ³·ρ_e⁻¹
null
0
2
3
7
6
3.5
true
{"mass": "1", "length": "1", "voltage": "1", "mag_flux": "-3", "resistivity": "1"}
6
amount,length,mag_flux,mass,molar_energy,voltage
m·ℓ·U·Φ·n·E_m
chemistry,em,mechanics
m·ℓ²·U²·Φ⁻²·n⁻¹·E_m⁻¹
m = k₀ · ℓ⁻²·U⁻²·Φ²·n·E_m
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "2", "voltage": "2", "mag_flux": "-2", "amount": "-1", "molar_energy": "-1"}
6
concentration,length,mag_flux,mass,molar_energy,voltage
m·ℓ·U·Φ·c_n·E_m
chemistry,em,mechanics
m·ℓ⁻¹·U²·Φ⁻²·c_n⁻¹·E_m⁻¹
m = k₀ · ℓ·U⁻²·Φ²·c_n·E_m
null
0
3
2
8
7.1
1.9
false
{"mass": "1", "length": "-1", "voltage": "2", "mag_flux": "-2", "concentration": "-1", "molar_energy": "-1"}
7
boltzmann,gas_constant,length,mag_flux,mass,molar_energy,voltage
m·ℓ·U·Φ·E_m·R·k_B
chemistry,constants,em,mechanics
m·ℓ²·U²·Φ⁻²·E_m⁻¹·R·k_B⁻¹
m = k₀ · ℓ⁻²·U⁻²·Φ²·E_m·R⁻¹·k_B
null
1
4
2
10
9.4
-0.9
false
{"mass": "1", "length": "2", "voltage": "2", "mag_flux": "-2", "molar_energy": "-1", "gas_constant": "1", "boltzmann": "-1"}
6
cat_activity,length,mag_flux,mass,molar_energy,voltage
m·ℓ·U·Φ·E_m·z
chemistry,em,mechanics
m·ℓ²·U³·Φ⁻³·E_m⁻¹·z⁻¹
m = k₀ · ℓ⁻²·U⁻³·Φ³·E_m·z
null
0
3
3
11
9.7
-0.7
false
{"mass": "1", "length": "2", "voltage": "3", "mag_flux": "-3", "molar_energy": "-1", "cat_activity": "-1"}
6
avogadro,length,mag_flux,mass,molar_energy,voltage
m·ℓ·U·Φ·E_m·N_A
chemistry,constants,em,mechanics
m·ℓ²·U²·Φ⁻²·E_m⁻¹·N_A
m = k₀ · ℓ⁻²·U⁻²·Φ²·E_m·N_A⁻¹
null
1
4
2
9
8.4
0.1
false
{"mass": "1", "length": "2", "voltage": "2", "mag_flux": "-2", "molar_energy": "-1", "avogadro": "1"}
5
grav_const,length,mag_flux,mass,voltage
m·ℓ·U·Φ·G
constants,em,mechanics
m·ℓ⁻³·U⁻²·Φ²·G
m = k₀ · ℓ³·U²·Φ⁻²·G⁻¹
null
1
3
3
9
8
1
false
{"mass": "1", "length": "-3", "voltage": "-2", "mag_flux": "2", "grav_const": "1"}
5
length,mag_flux,mass,planck,voltage
m·ℓ·U·Φ·h
constants,em,mechanics
m·ℓ²·U·Φ⁻¹·h⁻¹
m = k₀ · ℓ⁻²·U⁻¹·Φ·h
null
1
3
2
6
5.4
3.6
false
{"mass": "1", "length": "2", "voltage": "1", "mag_flux": "-1", "planck": "-1"}
5
elem_charge,length,mag_flux,mass,voltage
m·ℓ·U·Φ·e
constants,em,mechanics
m·ℓ²·U·Φ⁻²·e⁻¹
m = k₀ · ℓ⁻²·U⁻¹·Φ²·e
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "2", "voltage": "1", "mag_flux": "-2", "elem_charge": "-1"}
5
length,mass,permeability,permittivity,voltage
m·ℓ·U·ε·μ₀
em,mechanics
m·ℓ⁻¹·U⁻²·ε⁻²·μ₀⁻¹
m = k₀ · ℓ·U²·ε²·μ₀
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "-1", "voltage": "-2", "permittivity": "-2", "permeability": "-1"}
5
conductivity,length,mass,permittivity,voltage
m·ℓ·U·ε·σ
em,mechanics
m·ℓ·U⁻²·ε⁻³·σ²
m = k₀ · ℓ⁻¹·U²·ε³·σ⁻²
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "1", "voltage": "-2", "permittivity": "-3", "conductivity": "2"}
5
length,mass,permittivity,resistivity,voltage
m·ℓ·U·ε·ρ_e
em,mechanics
m·ℓ·U⁻²·ε⁻³·ρ_e⁻²
m = k₀ · ℓ⁻¹·U²·ε³·ρ_e²
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "1", "voltage": "-2", "permittivity": "-3", "resistivity": "-2"}
6
amount,cat_activity,length,mass,permittivity,voltage
m·ℓ·U·ε·n·z
chemistry,em,mechanics
m·ℓ·U⁻²·ε⁻¹·n⁻²·z²
m = k₀ · ℓ⁻¹·U²·ε·n²·z⁻²
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "1", "voltage": "-2", "permittivity": "-1", "amount": "-2", "cat_activity": "2"}
6
length,mass,molar_energy,molar_mass,permittivity,voltage
m·ℓ·U·ε·M_m·E_m
chemistry,em,mechanics
m·ℓ⁻¹·U⁻²·ε⁻¹·M_m⁻¹·E_m
m = k₀ · ℓ·U²·ε·M_m·E_m⁻¹
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "length": "-1", "voltage": "-2", "permittivity": "-1", "molar_mass": "-1", "molar_energy": "1"}
6
cat_activity,length,mass,molar_mass,permittivity,voltage
m·ℓ·U·ε·M_m·z
chemistry,em,mechanics
m·ℓ⁻¹·U²·ε·M_m⁻²·z⁻²
m = k₀ · ℓ·U⁻²·ε⁻¹·M_m²·z²
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "-1", "voltage": "2", "permittivity": "1", "molar_mass": "-2", "cat_activity": "-2"}
6
cat_activity,concentration,length,mass,permittivity,voltage
m·ℓ·U·ε·c_n·z
chemistry,em,mechanics
m·ℓ⁻⁵·U⁻²·ε⁻¹·c_n⁻²·z²
m = k₀ · ℓ⁵·U²·ε·c_n²·z⁻²
null
0
3
5
13
12.1
-3.1
false
{"mass": "1", "length": "-5", "voltage": "-2", "permittivity": "-1", "concentration": "-2", "cat_activity": "2"}
6
cat_activity,length,mass,molar_energy,permittivity,voltage
m·ℓ·U·ε·E_m·z
chemistry,em,mechanics
m·ℓ⁻¹·U⁻⁶·ε⁻³·E_m²·z²
m = k₀ · ℓ·U⁶·ε³·E_m⁻²·z⁻²
null
0
3
6
15
14
-5
false
{"mass": "1", "length": "-1", "voltage": "-6", "permittivity": "-3", "molar_energy": "2", "cat_activity": "2"}
7
boltzmann,cat_activity,gas_constant,length,mass,permittivity,voltage
m·ℓ·U·ε·R·z·k_B
chemistry,constants,em,mechanics
m·ℓ·U⁻²·ε⁻¹·R²·z²·k_B⁻²
m = k₀ · ℓ⁻¹·U²·ε·R⁻²·z⁻²·k_B²
null
1
4
2
11
10.1
-1.6
false
{"mass": "1", "length": "1", "voltage": "-2", "permittivity": "-1", "gas_constant": "2", "cat_activity": "2", "boltzmann": "-2"}
6
avogadro,cat_activity,length,mass,permittivity,voltage
m·ℓ·U·ε·z·N_A
chemistry,constants,em,mechanics
m·ℓ·U⁻²·ε⁻¹·z²·N_A²
m = k₀ · ℓ⁻¹·U²·ε·z⁻²·N_A⁻²
null
1
4
2
9
8.4
0.1
false
{"mass": "1", "length": "1", "voltage": "-2", "permittivity": "-1", "cat_activity": "2", "avogadro": "2"}
5
length,light_speed,mass,permittivity,voltage
m·ℓ·U·ε·c₀
constants,em,mechanics
m·ℓ⁻¹·U⁻²·ε⁻¹·c₀²
m = k₀ · ℓ·U²·ε·c₀⁻²
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "-1", "voltage": "-2", "permittivity": "-1", "light_speed": "2"}
5
grav_const,length,mass,permittivity,voltage
m·ℓ·U·ε·G
constants,em,mechanics
m²·ℓ⁻²·U⁻²·ε⁻¹·G
ε = k₀ · m²·ℓ⁻²·U⁻²·G
null
1
3
2
8
6.8
2.2
false
{"mass": "2", "length": "-2", "voltage": "-2", "permittivity": "-1", "grav_const": "1"}
5
length,mass,permittivity,planck,voltage
m·ℓ·U·ε·h
constants,em,mechanics
m·ℓ³·U²·ε·h⁻²
m = k₀ · ℓ⁻³·U⁻²·ε⁻¹·h²
null
1
3
3
9
8
1
false
{"mass": "1", "length": "3", "voltage": "2", "permittivity": "1", "planck": "-2"}
5
conductivity,length,mass,permeability,voltage
m·ℓ·U·μ₀·σ
em,mechanics
m·ℓ⁻⁵·U⁻²·μ₀⁻³·σ⁻⁴
m = k₀ · ℓ⁵·U²·μ₀³·σ⁴
null
0
2
5
15
12.6
-3.1
false
{"mass": "1", "length": "-5", "voltage": "-2", "permeability": "-3", "conductivity": "-4"}
5
length,mass,permeability,resistivity,voltage
m·ℓ·U·μ₀·ρ_e
em,mechanics
m·ℓ⁻⁵·U⁻²·μ₀⁻³·ρ_e⁴
m = k₀ · ℓ⁵·U²·μ₀³·ρ_e⁻⁴
null
0
2
5
15
12.6
-3.1
false
{"mass": "1", "length": "-5", "voltage": "-2", "permeability": "-3", "resistivity": "4"}
6
amount,length,mass,molar_energy,permeability,voltage
m·ℓ·U·μ₀·n·E_m
chemistry,em,mechanics
m·ℓ·U²·μ₀⁻¹·n⁻²·E_m⁻²
m = k₀ · ℓ⁻¹·U⁻²·μ₀·n²·E_m²
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "1", "voltage": "2", "permeability": "-1", "amount": "-2", "molar_energy": "-2"}
6
amount,cat_activity,length,mass,permeability,voltage
m·ℓ·U·μ₀·n·z
chemistry,em,mechanics
m·ℓ³·U⁻²·μ₀·n⁻⁴·z⁴
m = k₀ · ℓ⁻³·U²·μ₀⁻¹·n⁴·z⁻⁴
null
0
3
4
15
13
-4
false
{"mass": "1", "length": "3", "voltage": "-2", "permeability": "1", "amount": "-4", "cat_activity": "4"}
6
length,mass,molar_energy,molar_mass,permeability,voltage
m·ℓ·U·μ₀·M_m·E_m
chemistry,em,mechanics
m·ℓ⁻¹·U⁻²·μ₀·M_m⁻²·E_m²
m = k₀ · ℓ·U²·μ₀⁻¹·M_m²·E_m⁻²
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "-1", "voltage": "-2", "permeability": "1", "molar_mass": "-2", "molar_energy": "2"}
6
cat_activity,length,mass,molar_mass,permeability,voltage
m·ℓ·U·μ₀·M_m·z
chemistry,em,mechanics
m³·ℓ⁻³·U²·μ₀⁻¹·M_m⁻⁴·z⁻⁴
μ₀ = k₀ · m³·ℓ⁻³·U²·M_m⁻⁴·z⁻⁴
null
0
3
4
17
14.4
-5.4
false
{"mass": "3", "length": "-3", "voltage": "2", "permeability": "-1", "molar_mass": "-4", "cat_activity": "-4"}
6
concentration,length,mass,molar_energy,permeability,voltage
m·ℓ·U·μ₀·c_n·E_m
chemistry,em,mechanics
m·ℓ⁻⁵·U²·μ₀⁻¹·c_n⁻²·E_m⁻²
m = k₀ · ℓ⁵·U⁻²·μ₀·c_n²·E_m²
null
0
3
5
13
12.1
-3.1
false
{"mass": "1", "length": "-5", "voltage": "2", "permeability": "-1", "concentration": "-2", "molar_energy": "-2"}
6
cat_activity,concentration,length,mass,permeability,voltage
m·ℓ·U·μ₀·c_n·z
chemistry,em,mechanics
m·ℓ⁻⁹·U⁻²·μ₀·c_n⁻⁴·z⁴
m = k₀ · ℓ⁹·U²·μ₀⁻¹·c_n⁴·z⁻⁴
null
0
3
9
21
19.7
-10.7
false
{"mass": "1", "length": "-9", "voltage": "-2", "permeability": "1", "concentration": "-4", "cat_activity": "4"}
7
boltzmann,gas_constant,length,mass,molar_energy,permeability,voltage
m·ℓ·U·μ₀·E_m·R·k_B
chemistry,constants,em,mechanics
m·ℓ·U²·μ₀⁻¹·E_m⁻²·R²·k_B⁻²
m = k₀ · ℓ⁻¹·U⁻²·μ₀·E_m²·R⁻²·k_B²
null
1
4
2
11
10.1
-1.6
false
{"mass": "1", "length": "1", "voltage": "2", "permeability": "-1", "molar_energy": "-2", "gas_constant": "2", "boltzmann": "-2"}
6
cat_activity,length,mass,molar_energy,permeability,voltage
m·ℓ·U·μ₀·E_m·z
chemistry,em,mechanics
m·ℓ⁻¹·U⁶·μ₀⁻³·E_m⁻⁴·z⁻⁴
m = k₀ · ℓ·U⁻⁶·μ₀³·E_m⁴·z⁴
null
0
3
6
19
16.8
-7.8
false
{"mass": "1", "length": "-1", "voltage": "6", "permeability": "-3", "molar_energy": "-4", "cat_activity": "-4"}
6
avogadro,length,mass,molar_energy,permeability,voltage
m·ℓ·U·μ₀·E_m·N_A
chemistry,constants,em,mechanics
m·ℓ·U²·μ₀⁻¹·E_m⁻²·N_A²
m = k₀ · ℓ⁻¹·U⁻²·μ₀·E_m²·N_A⁻²
null
1
4
2
9
8.4
0.1
false
{"mass": "1", "length": "1", "voltage": "2", "permeability": "-1", "molar_energy": "-2", "avogadro": "2"}
7
boltzmann,cat_activity,gas_constant,length,mass,permeability,voltage
m·ℓ·U·μ₀·R·z·k_B
chemistry,constants,em,mechanics
m·ℓ³·U⁻²·μ₀·R⁴·z⁴·k_B⁻⁴
m = k₀ · ℓ⁻³·U²·μ₀⁻¹·R⁻⁴·z⁻⁴·k_B⁴
null
1
4
4
19
16.7
-8.2
false
{"mass": "1", "length": "3", "voltage": "-2", "permeability": "1", "gas_constant": "4", "cat_activity": "4", "boltzmann": "-4"}
6
avogadro,cat_activity,length,mass,permeability,voltage
m·ℓ·U·μ₀·z·N_A
chemistry,constants,em,mechanics
m·ℓ³·U⁻²·μ₀·z⁴·N_A⁴
m = k₀ · ℓ⁻³·U²·μ₀⁻¹·z⁻⁴·N_A⁻⁴
null
1
4
4
15
13.6
-5.1
false
{"mass": "1", "length": "3", "voltage": "-2", "permeability": "1", "cat_activity": "4", "avogadro": "4"}
5
length,light_speed,mass,permeability,voltage
m·ℓ·U·μ₀·c₀
constants,em,mechanics
m·ℓ⁻¹·U⁻²·μ₀·c₀⁴
m = k₀ · ℓ·U²·μ₀⁻¹·c₀⁻⁴
null
1
3
4
9
8.5
0.5
false
{"mass": "1", "length": "-1", "voltage": "-2", "permeability": "1", "light_speed": "4"}