Datasets:
RANDMEDIATION
/
PhysicsBabel

Dataset card Data Studio Files
xet
 Community
1
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
elem_charge,length,mass,permittivity,resistance
m·ℓ·R·ε·e
constants,em,mechanics
m·ℓ·R⁻²·ε⁻¹·e⁻²
m = k₀ · ℓ⁻¹·R²·ε·e²
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "1", "resistance": "-2", "permittivity": "-1", "elem_charge": "-2"}
6
cat_activity,length,mass,molar_mass,permeability,resistance
m·ℓ·R·μ₀·M_m·z
chemistry,em,mechanics
m·ℓ⁻¹·R·μ₀⁻¹·M_m⁻¹·z⁻¹
m = k₀ · ℓ·R⁻¹·μ₀·M_m·z
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "length": "-1", "resistance": "1", "permeability": "-1", "molar_mass": "-1", "cat_activity": "-1"}
6
concentration,length,mass,molar_energy,permeability,resistance
m·ℓ·R·μ₀·c_n·E_m
chemistry,em,mechanics
m·ℓ⁻³·R²·μ₀⁻²·c_n⁻¹·E_m⁻¹
m = k₀ · ℓ³·R⁻²·μ₀²·c_n·E_m
null
0
3
3
10
9
0
false
{"mass": "1", "length": "-3", "resistance": "2", "permeability": "-2", "concentration": "-1", "molar_energy": "-1"}
6
cat_activity,length,mass,molar_energy,permeability,resistance
m·ℓ·R·μ₀·E_m·z
chemistry,em,mechanics
m·ℓ⁻¹·R³·μ₀⁻³·E_m⁻¹·z⁻¹
m = k₀ · ℓ·R⁻³·μ₀³·E_m·z
null
0
3
3
10
9
0
false
{"mass": "1", "length": "-1", "resistance": "3", "permeability": "-3", "molar_energy": "-1", "cat_activity": "-1"}
5
grav_const,length,mass,permeability,resistance
m·ℓ·R·μ₀·G
constants,em,mechanics
m·ℓ⁻¹·R⁻²·μ₀²·G
m = k₀ · ℓ·R²·μ₀⁻²·G⁻¹
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "-1", "resistance": "-2", "permeability": "2", "grav_const": "1"}
5
length,mass,permeability,planck,resistance
m·ℓ·R·μ₀·h
constants,em,mechanics
m·ℓ·R·μ₀⁻¹·h⁻¹
m = k₀ · ℓ⁻¹·R⁻¹·μ₀·h
null
1
3
1
5
4.2
4.8
false
{"mass": "1", "length": "1", "resistance": "1", "permeability": "-1", "planck": "-1"}
6
amount,elem_charge,length,mass,molar_energy,resistance
m·ℓ·R·n·E_m·e
chemistry,constants,em,mechanics
m·ℓ²·R⁻²·n·E_m·e⁻⁴
m = k₀ · ℓ⁻²·R²·n⁻¹·E_m⁻¹·e⁴
null
1
4
4
11
10.8
-2.3
false
{"mass": "1", "length": "2", "resistance": "-2", "amount": "1", "molar_energy": "1", "elem_charge": "-4"}
6
amount,cat_activity,elem_charge,length,mass,resistance
m·ℓ·R·n·z·e
chemistry,constants,em,mechanics
m·ℓ²·R⁻¹·n⁻¹·z·e⁻²
m = k₀ · ℓ⁻²·R·n·z⁻¹·e²
null
1
4
2
8
7.7
0.8
false
{"mass": "1", "length": "2", "resistance": "-1", "amount": "-1", "cat_activity": "1", "elem_charge": "-2"}
6
elem_charge,length,mass,molar_energy,molar_mass,resistance
m·ℓ·R·M_m·E_m·e
chemistry,constants,em,mechanics
m²·ℓ²·R⁻²·M_m⁻¹·E_m·e⁻⁴
M_m = k₀ · m²·ℓ²·R⁻²·E_m·e⁻⁴
null
1
4
4
12
11.5
-3
false
{"mass": "2", "length": "2", "resistance": "-2", "molar_mass": "-1", "molar_energy": "1", "elem_charge": "-4"}
6
concentration,elem_charge,length,mass,molar_energy,resistance
m·ℓ·R·c_n·E_m·e
chemistry,constants,em,mechanics
m·ℓ⁵·R⁻²·c_n·E_m·e⁻⁴
m = k₀ · ℓ⁻⁵·R²·c_n⁻¹·E_m⁻¹·e⁴
null
1
4
5
14
13.4
-4.9
false
{"mass": "1", "length": "5", "resistance": "-2", "concentration": "1", "molar_energy": "1", "elem_charge": "-4"}
6
cat_activity,concentration,elem_charge,length,mass,resistance
m·ℓ·R·c_n·z·e
chemistry,constants,em,mechanics
m·ℓ⁻¹·R⁻¹·c_n⁻¹·z·e⁻²
m = k₀ · ℓ·R·c_n·z⁻¹·e²
null
1
4
2
7
7
1.5
false
{"mass": "1", "length": "-1", "resistance": "-1", "concentration": "-1", "cat_activity": "1", "elem_charge": "-2"}
7
boltzmann,elem_charge,gas_constant,length,mass,molar_energy,resistance
m·ℓ·R·E_m·R·k_B·e
chemistry,constants,em,mechanics
m·ℓ²·R⁻²·E_m·R⁻¹·k_B·e⁻⁴
m = k₀ · ℓ⁻²·R²·E_m⁻¹·R·k_B⁻¹·e⁴
null
2
4
4
12
12.8
-5.8
false
{"mass": "1", "length": "2", "resistance": "-2", "molar_energy": "1", "gas_constant": "-1", "boltzmann": "1", "elem_charge": "-4"}
6
cat_activity,elem_charge,length,mass,molar_energy,resistance
m·ℓ·R·E_m·z·e
chemistry,constants,em,mechanics
m²·ℓ⁴·R⁻³·E_m·z·e⁻⁶
E_m = k₀ · m⁻²·ℓ⁻⁴·R³·z⁻¹·e⁶
null
1
4
6
17
16
-7.5
false
{"mass": "2", "length": "4", "resistance": "-3", "molar_energy": "1", "cat_activity": "1", "elem_charge": "-6"}
6
avogadro,elem_charge,length,mass,molar_energy,resistance
m·ℓ·R·E_m·e·N_A
chemistry,constants,em,mechanics
m·ℓ²·R⁻²·E_m·e⁻⁴·N_A⁻¹
m = k₀ · ℓ⁻²·R²·E_m⁻¹·e⁴·N_A
null
2
4
4
11
11.8
-4.8
false
{"mass": "1", "length": "2", "resistance": "-2", "molar_energy": "1", "elem_charge": "-4", "avogadro": "-1"}
7
boltzmann,cat_activity,elem_charge,gas_constant,length,mass,resistance
m·ℓ·R·R·z·k_B·e
chemistry,constants,em,mechanics
m·ℓ²·R⁻¹·R·z·k_B⁻¹·e⁻²
m = k₀ · ℓ⁻²·R·R⁻¹·z⁻¹·k_B·e²
null
2
4
2
9
9.7
-2.7
false
{"mass": "1", "length": "2", "resistance": "-1", "gas_constant": "1", "cat_activity": "1", "boltzmann": "-1", "elem_charge": "-2"}
6
avogadro,cat_activity,elem_charge,length,mass,resistance
m·ℓ·R·z·e·N_A
chemistry,constants,em,mechanics
m·ℓ²·R⁻¹·z·e⁻²·N_A
m = k₀ · ℓ⁻²·R·z⁻¹·e²·N_A⁻¹
null
2
4
2
8
8.7
-1.7
false
{"mass": "1", "length": "2", "resistance": "-1", "cat_activity": "1", "elem_charge": "-2", "avogadro": "1"}
5
elem_charge,length,light_speed,mass,resistance
m·ℓ·R·c₀·e
constants,em,mechanics
m·ℓ·R⁻¹·c₀·e⁻²
m = k₀ · ℓ⁻¹·R·c₀⁻¹·e²
null
2
3
2
6
6.4
1.1
false
{"mass": "1", "length": "1", "resistance": "-1", "light_speed": "1", "elem_charge": "-2"}
5
elem_charge,grav_const,length,mass,resistance
m·ℓ·R·G·e
constants,em,mechanics
m³·ℓ·R⁻²·G·e⁻⁴
ℓ = k₀ · m⁻³·R²·G⁻¹·e⁴
null
2
3
4
11
10.9
-3.4
false
{"mass": "3", "length": "1", "resistance": "-2", "grav_const": "1", "elem_charge": "-4"}
6
amount,capacitance,inductance,length,mass,molar_energy
m·ℓ·C_e·L_e·n·E_m
chemistry,em,mechanics
m·ℓ²·C_e⁻¹·L_e⁻¹·n⁻¹·E_m⁻¹
m = k₀ · ℓ⁻²·C_e·L_e·n·E_m
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "length": "2", "capacitance": "-1", "inductance": "-1", "amount": "-1", "molar_energy": "-1"}
6
capacitance,concentration,inductance,length,mass,molar_energy
m·ℓ·C_e·L_e·c_n·E_m
chemistry,em,mechanics
m·ℓ⁻¹·C_e⁻¹·L_e⁻¹·c_n⁻¹·E_m⁻¹
m = k₀ · ℓ·C_e·L_e·c_n·E_m
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "length": "-1", "capacitance": "-1", "inductance": "-1", "concentration": "-1", "molar_energy": "-1"}
7
boltzmann,capacitance,gas_constant,inductance,length,mass,molar_energy
m·ℓ·C_e·L_e·E_m·R·k_B
chemistry,constants,em,mechanics
m·ℓ²·C_e⁻¹·L_e⁻¹·E_m⁻¹·R·k_B⁻¹
m = k₀ · ℓ⁻²·C_e·L_e·E_m·R⁻¹·k_B
null
1
4
2
8
8
0.5
false
{"mass": "1", "length": "2", "capacitance": "-1", "inductance": "-1", "molar_energy": "-1", "gas_constant": "1", "boltzmann": "-1"}
6
capacitance,cat_activity,inductance,length,mass,molar_energy
m·ℓ·C_e·L_e·E_m·z
chemistry,em,mechanics
m²·ℓ⁴·C_e⁻³·L_e⁻³·E_m⁻²·z⁻²
m = k₀ · ℓ⁻²·C_e³ᐟ²·L_e³ᐟ²·E_m·z
null
0
3
4
16
13.7
-4.7
false
{"mass": "2", "length": "4", "capacitance": "-3", "inductance": "-3", "molar_energy": "-2", "cat_activity": "-2"}
6
avogadro,capacitance,inductance,length,mass,molar_energy
m·ℓ·C_e·L_e·E_m·N_A
chemistry,constants,em,mechanics
m·ℓ²·C_e⁻¹·L_e⁻¹·E_m⁻¹·N_A
m = k₀ · ℓ⁻²·C_e·L_e·E_m·N_A⁻¹
null
1
4
2
7
7
1.5
false
{"mass": "1", "length": "2", "capacitance": "-1", "inductance": "-1", "molar_energy": "-1", "avogadro": "1"}
5
capacitance,grav_const,inductance,length,mass
m·ℓ·C_e·L_e·G
constants,em,mechanics
m·ℓ⁻³·C_e·L_e·G
m = k₀ · ℓ³·C_e⁻¹·L_e⁻¹·G⁻¹
null
1
3
3
7
6.6
2.4
false
{"mass": "1", "length": "-3", "capacitance": "1", "inductance": "1", "grav_const": "1"}
5
capacitance,inductance,length,mass,planck
m·ℓ·C_e·L_e·h
constants,em,mechanics
m²·ℓ⁴·C_e⁻¹·L_e⁻¹·h⁻²
C_e = k₀ · m²·ℓ⁴·L_e⁻¹·h⁻²
null
1
3
4
10
9.2
-0.2
false
{"mass": "2", "length": "4", "capacitance": "-1", "inductance": "-1", "planck": "-2"}
5
capacitance,efield,length,mass,permeability
m·ℓ·C_e·E_f·μ₀
em,mechanics
m·ℓ⁻¹·C_e⁻²·E_f⁻²·μ₀⁻¹
m = k₀ · ℓ·C_e²·E_f²·μ₀
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "-1", "capacitance": "-2", "efield": "-2", "permeability": "-1"}
5
capacitance,conductivity,efield,length,mass
m·ℓ·C_e·E_f·σ
em,mechanics
m·ℓ²·C_e⁻³·E_f⁻²·σ²
m = k₀ · ℓ⁻²·C_e³·E_f²·σ⁻²
null
0
2
3
10
8.1
1.4
false
{"mass": "1", "length": "2", "capacitance": "-3", "efield": "-2", "conductivity": "2"}
5
capacitance,efield,length,mass,resistivity
m·ℓ·C_e·E_f·ρ_e
em,mechanics
m·ℓ²·C_e⁻³·E_f⁻²·ρ_e⁻²
m = k₀ · ℓ⁻²·C_e³·E_f²·ρ_e²
null
0
2
3
10
8.1
1.4
false
{"mass": "1", "length": "2", "capacitance": "-3", "efield": "-2", "resistivity": "-2"}
6
capacitance,efield,length,mass,molar_energy,molar_mass
m·ℓ·C_e·E_f·M_m·E_m
chemistry,em,mechanics
m·ℓ⁻²·C_e⁻¹·E_f⁻²·M_m⁻¹·E_m
m = k₀ · ℓ²·C_e·E_f²·M_m·E_m⁻¹
null
0
3
2
8
7.1
1.9
false
{"mass": "1", "length": "-2", "capacitance": "-1", "efield": "-2", "molar_mass": "-1", "molar_energy": "1"}
6
capacitance,cat_activity,concentration,efield,length,mass
m·ℓ·C_e·E_f·c_n·z
chemistry,em,mechanics
m·ℓ⁻⁶·C_e⁻¹·E_f⁻²·c_n⁻²·z²
m = k₀ · ℓ⁶·C_e·E_f²·c_n²·z⁻²
null
0
3
6
14
13.3
-4.3
false
{"mass": "1", "length": "-6", "capacitance": "-1", "efield": "-2", "concentration": "-2", "cat_activity": "2"}
6
capacitance,cat_activity,efield,length,mass,molar_energy
m·ℓ·C_e·E_f·E_m·z
chemistry,em,mechanics
m·ℓ⁻⁴·C_e⁻³·E_f⁻⁶·E_m²·z²
m = k₀ · ℓ⁴·C_e³·E_f⁶·E_m⁻²·z⁻²
null
0
3
6
18
16.1
-7.1
false
{"mass": "1", "length": "-4", "capacitance": "-3", "efield": "-6", "molar_energy": "2", "cat_activity": "2"}
5
capacitance,efield,length,light_speed,mass
m·ℓ·C_e·E_f·c₀
constants,em,mechanics
m·ℓ⁻²·C_e⁻¹·E_f⁻²·c₀²
m = k₀ · ℓ²·C_e·E_f²·c₀⁻²
null
1
3
2
8
6.8
2.2
false
{"mass": "1", "length": "-2", "capacitance": "-1", "efield": "-2", "light_speed": "2"}
5
capacitance,efield,grav_const,length,mass
m·ℓ·C_e·E_f·G
constants,em,mechanics
m²·ℓ⁻³·C_e⁻¹·E_f⁻²·G
C_e = k₀ · m²·ℓ⁻³·E_f⁻²·G
null
1
3
3
9
8
1
false
{"mass": "2", "length": "-3", "capacitance": "-1", "efield": "-2", "grav_const": "1"}
5
capacitance,efield,length,mass,planck
m·ℓ·C_e·E_f·h
constants,em,mechanics
m·ℓ⁴·C_e·E_f²·h⁻²
m = k₀ · ℓ⁻⁴·C_e⁻¹·E_f⁻²·h²
null
1
3
4
10
9.2
-0.2
false
{"mass": "1", "length": "4", "capacitance": "1", "efield": "2", "planck": "-2"}
4
bfield,capacitance,length,mass
m·ℓ·C_e·B
em,mechanics
m·ℓ⁻²·C_e⁻¹·B⁻²
m = k₀ · ℓ²·C_e·B²
null
0
2
2
6
4.5
5
true
{"mass": "1", "length": "-2", "capacitance": "-1", "bfield": "-2"}
4
capacitance,length,mag_flux,mass
m·ℓ·C_e·Φ
em,mechanics
m·ℓ²·C_e⁻¹·Φ⁻²
m = k₀ · ℓ⁻²·C_e·Φ²
null
0
2
2
6
4.5
5
true
{"mass": "1", "length": "2", "capacitance": "-1", "mag_flux": "-2"}
6
amount,capacitance,length,mass,molar_energy,permeability
m·ℓ·C_e·μ₀·n·E_m
chemistry,em,mechanics
m·ℓ·C_e⁻¹·μ₀⁻¹·n⁻¹·E_m⁻¹
m = k₀ · ℓ⁻¹·C_e·μ₀·n·E_m
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "length": "1", "capacitance": "-1", "permeability": "-1", "amount": "-1", "molar_energy": "-1"}
6
capacitance,cat_activity,length,mass,molar_mass,permeability
m·ℓ·C_e·μ₀·M_m·z
chemistry,em,mechanics
m²·ℓ⁻¹·C_e⁻¹·μ₀⁻¹·M_m⁻²·z⁻²
ℓ = k₀ · m²·C_e⁻¹·μ₀⁻¹·M_m⁻²·z⁻²
null
0
3
2
9
7.8
1.2
false
{"mass": "2", "length": "-1", "capacitance": "-1", "permeability": "-1", "molar_mass": "-2", "cat_activity": "-2"}
6
capacitance,concentration,length,mass,molar_energy,permeability
m·ℓ·C_e·μ₀·c_n·E_m
chemistry,em,mechanics
m·ℓ⁻²·C_e⁻¹·μ₀⁻¹·c_n⁻¹·E_m⁻¹
m = k₀ · ℓ²·C_e·μ₀·c_n·E_m
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "length": "-2", "capacitance": "-1", "permeability": "-1", "concentration": "-1", "molar_energy": "-1"}
7
boltzmann,capacitance,gas_constant,length,mass,molar_energy,permeability
m·ℓ·C_e·μ₀·E_m·R·k_B
chemistry,constants,em,mechanics
m·ℓ·C_e⁻¹·μ₀⁻¹·E_m⁻¹·R·k_B⁻¹
m = k₀ · ℓ⁻¹·C_e·μ₀·E_m·R⁻¹·k_B
null
1
4
1
7
6.8
1.7
false
{"mass": "1", "length": "1", "capacitance": "-1", "permeability": "-1", "molar_energy": "-1", "gas_constant": "1", "boltzmann": "-1"}
6
capacitance,cat_activity,length,mass,molar_energy,permeability
m·ℓ·C_e·μ₀·E_m·z
chemistry,em,mechanics
m²·ℓ·C_e⁻³·μ₀⁻³·E_m⁻²·z⁻²
ℓ = k₀ · m⁻²·C_e³·μ₀³·E_m²·z²
null
0
3
3
13
11.1
-2.1
false
{"mass": "2", "length": "1", "capacitance": "-3", "permeability": "-3", "molar_energy": "-2", "cat_activity": "-2"}
6
avogadro,capacitance,length,mass,molar_energy,permeability
m·ℓ·C_e·μ₀·E_m·N_A
chemistry,constants,em,mechanics
m·ℓ·C_e⁻¹·μ₀⁻¹·E_m⁻¹·N_A
m = k₀ · ℓ⁻¹·C_e·μ₀·E_m·N_A⁻¹
null
1
4
1
6
5.8
2.7
false
{"mass": "1", "length": "1", "capacitance": "-1", "permeability": "-1", "molar_energy": "-1", "avogadro": "1"}
5
capacitance,grav_const,length,mass,permeability
m·ℓ·C_e·μ₀·G
constants,em,mechanics
m·ℓ⁻²·C_e·μ₀·G
m = k₀ · ℓ²·C_e⁻¹·μ₀⁻¹·G⁻¹
null
1
3
2
6
5.4
3.6
false
{"mass": "1", "length": "-2", "capacitance": "1", "permeability": "1", "grav_const": "1"}
5
capacitance,length,mass,permeability,planck
m·ℓ·C_e·μ₀·h
constants,em,mechanics
m²·ℓ³·C_e⁻¹·μ₀⁻¹·h⁻²
C_e = k₀ · m²·ℓ³·μ₀⁻¹·h⁻²
null
1
3
3
9
8
1
false
{"mass": "2", "length": "3", "capacitance": "-1", "permeability": "-1", "planck": "-2"}
6
amount,capacitance,conductivity,length,mass,molar_energy
m·ℓ·C_e·σ·n·E_m
chemistry,em,mechanics
m·ℓ⁴·C_e⁻²·σ²·n⁻¹·E_m⁻¹
m = k₀ · ℓ⁻⁴·C_e²·σ⁻²·n·E_m
null
0
3
4
11
10.2
-1.2
false
{"mass": "1", "length": "4", "capacitance": "-2", "conductivity": "2", "amount": "-1", "molar_energy": "-1"}
6
capacitance,cat_activity,conductivity,length,mass,molar_mass
m·ℓ·C_e·σ·M_m·z
chemistry,em,mechanics
m·ℓ·C_e⁻¹·σ·M_m⁻¹·z⁻¹
m = k₀ · ℓ⁻¹·C_e·σ⁻¹·M_m·z
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "length": "1", "capacitance": "-1", "conductivity": "1", "molar_mass": "-1", "cat_activity": "-1"}
6
capacitance,concentration,conductivity,length,mass,molar_energy
m·ℓ·C_e·σ·c_n·E_m
chemistry,em,mechanics
m·ℓ·C_e⁻²·σ²·c_n⁻¹·E_m⁻¹
m = k₀ · ℓ⁻¹·C_e²·σ⁻²·c_n·E_m
null
0
3
2
8
7.1
1.9
false
{"mass": "1", "length": "1", "capacitance": "-2", "conductivity": "2", "concentration": "-1", "molar_energy": "-1"}
7
boltzmann,capacitance,conductivity,gas_constant,length,mass,molar_energy
m·ℓ·C_e·σ·E_m·R·k_B
chemistry,constants,em,mechanics
m·ℓ⁴·C_e⁻²·σ²·E_m⁻¹·R·k_B⁻¹
m = k₀ · ℓ⁻⁴·C_e²·σ⁻²·E_m·R⁻¹·k_B
null
1
4
4
12
11.8
-3.3
false
{"mass": "1", "length": "4", "capacitance": "-2", "conductivity": "2", "molar_energy": "-1", "gas_constant": "1", "boltzmann": "-1"}
6
capacitance,cat_activity,conductivity,length,mass,molar_energy
m·ℓ·C_e·σ·E_m·z
chemistry,em,mechanics
m·ℓ⁵·C_e⁻³·σ³·E_m⁻¹·z⁻¹
m = k₀ · ℓ⁻⁵·C_e³·σ⁻³·E_m·z
null
0
3
5
14
12.8
-3.8
false
{"mass": "1", "length": "5", "capacitance": "-3", "conductivity": "3", "molar_energy": "-1", "cat_activity": "-1"}
6
avogadro,capacitance,conductivity,length,mass,molar_energy
m·ℓ·C_e·σ·E_m·N_A
chemistry,constants,em,mechanics
m·ℓ⁴·C_e⁻²·σ²·E_m⁻¹·N_A
m = k₀ · ℓ⁻⁴·C_e²·σ⁻²·E_m·N_A⁻¹
null
1
4
4
11
10.8
-2.3
false
{"mass": "1", "length": "4", "capacitance": "-2", "conductivity": "2", "molar_energy": "-1", "avogadro": "1"}
5
capacitance,conductivity,grav_const,length,mass
m·ℓ·C_e·σ·G
constants,em,mechanics
m·ℓ⁻⁵·C_e²·σ⁻²·G
m = k₀ · ℓ⁵·C_e⁻²·σ²·G⁻¹
null
1
3
5
11
10.4
-1.4
false
{"mass": "1", "length": "-5", "capacitance": "2", "conductivity": "-2", "grav_const": "1"}
5
capacitance,conductivity,length,mass,planck
m·ℓ·C_e·σ·h
constants,em,mechanics
m·ℓ³·C_e⁻¹·σ·h⁻¹
m = k₀ · ℓ⁻³·C_e·σ⁻¹·h
null
1
3
3
7
6.6
2.4
false
{"mass": "1", "length": "3", "capacitance": "-1", "conductivity": "1", "planck": "-1"}
5
capacitance,conductivity,elem_charge,length,mass
m·ℓ·C_e·σ·e
constants,em,mechanics
m·ℓ⁴·C_e⁻¹·σ²·e⁻²
m = k₀ · ℓ⁻⁴·C_e·σ⁻²·e²
null
1
3
4
10
9.2
-0.2
false
{"mass": "1", "length": "4", "capacitance": "-1", "conductivity": "2", "elem_charge": "-2"}
6
amount,capacitance,length,mass,molar_energy,resistivity
m·ℓ·C_e·ρ_e·n·E_m
chemistry,em,mechanics
m·ℓ⁴·C_e⁻²·ρ_e⁻²·n⁻¹·E_m⁻¹
m = k₀ · ℓ⁻⁴·C_e²·ρ_e²·n·E_m
null
0
3
4
11
10.2
-1.2
false
{"mass": "1", "length": "4", "capacitance": "-2", "resistivity": "-2", "amount": "-1", "molar_energy": "-1"}
6
capacitance,cat_activity,length,mass,molar_mass,resistivity
m·ℓ·C_e·ρ_e·M_m·z
chemistry,em,mechanics
m·ℓ·C_e⁻¹·ρ_e⁻¹·M_m⁻¹·z⁻¹
m = k₀ · ℓ⁻¹·C_e·ρ_e·M_m·z
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "length": "1", "capacitance": "-1", "resistivity": "-1", "molar_mass": "-1", "cat_activity": "-1"}
6
capacitance,concentration,length,mass,molar_energy,resistivity
m·ℓ·C_e·ρ_e·c_n·E_m
chemistry,em,mechanics
m·ℓ·C_e⁻²·ρ_e⁻²·c_n⁻¹·E_m⁻¹
m = k₀ · ℓ⁻¹·C_e²·ρ_e²·c_n·E_m
null
0
3
2
8
7.1
1.9
false
{"mass": "1", "length": "1", "capacitance": "-2", "resistivity": "-2", "concentration": "-1", "molar_energy": "-1"}
7
boltzmann,capacitance,gas_constant,length,mass,molar_energy,resistivity
m·ℓ·C_e·ρ_e·E_m·R·k_B
chemistry,constants,em,mechanics
m·ℓ⁴·C_e⁻²·ρ_e⁻²·E_m⁻¹·R·k_B⁻¹
m = k₀ · ℓ⁻⁴·C_e²·ρ_e²·E_m·R⁻¹·k_B
null
1
4
4
12
11.8
-3.3
false
{"mass": "1", "length": "4", "capacitance": "-2", "resistivity": "-2", "molar_energy": "-1", "gas_constant": "1", "boltzmann": "-1"}
6
capacitance,cat_activity,length,mass,molar_energy,resistivity
m·ℓ·C_e·ρ_e·E_m·z
chemistry,em,mechanics
m·ℓ⁵·C_e⁻³·ρ_e⁻³·E_m⁻¹·z⁻¹
m = k₀ · ℓ⁻⁵·C_e³·ρ_e³·E_m·z
null
0
3
5
14
12.8
-3.8
false
{"mass": "1", "length": "5", "capacitance": "-3", "resistivity": "-3", "molar_energy": "-1", "cat_activity": "-1"}
6
avogadro,capacitance,length,mass,molar_energy,resistivity
m·ℓ·C_e·ρ_e·E_m·N_A
chemistry,constants,em,mechanics
m·ℓ⁴·C_e⁻²·ρ_e⁻²·E_m⁻¹·N_A
m = k₀ · ℓ⁻⁴·C_e²·ρ_e²·E_m·N_A⁻¹
null
1
4
4
11
10.8
-2.3
false
{"mass": "1", "length": "4", "capacitance": "-2", "resistivity": "-2", "molar_energy": "-1", "avogadro": "1"}
5
capacitance,grav_const,length,mass,resistivity
m·ℓ·C_e·ρ_e·G
constants,em,mechanics
m·ℓ⁻⁵·C_e²·ρ_e²·G
m = k₀ · ℓ⁵·C_e⁻²·ρ_e⁻²·G⁻¹
null
1
3
5
11
10.4
-1.4
false
{"mass": "1", "length": "-5", "capacitance": "2", "resistivity": "2", "grav_const": "1"}
5
capacitance,length,mass,planck,resistivity
m·ℓ·C_e·ρ_e·h
constants,em,mechanics
m·ℓ³·C_e⁻¹·ρ_e⁻¹·h⁻¹
m = k₀ · ℓ⁻³·C_e·ρ_e·h
null
1
3
3
7
6.6
2.4
false
{"mass": "1", "length": "3", "capacitance": "-1", "resistivity": "-1", "planck": "-1"}
5
capacitance,elem_charge,length,mass,resistivity
m·ℓ·C_e·ρ_e·e
constants,em,mechanics
m·ℓ⁴·C_e⁻¹·ρ_e⁻²·e⁻²
m = k₀ · ℓ⁻⁴·C_e·ρ_e²·e²
null
1
3
4
10
9.2
-0.2
false
{"mass": "1", "length": "4", "capacitance": "-1", "resistivity": "-2", "elem_charge": "-2"}
6
amount,capacitance,cat_activity,elem_charge,length,mass
m·ℓ·C_e·n·z·e
chemistry,constants,em,mechanics
m·ℓ²·C_e·n⁻²·z²·e⁻²
m = k₀ · ℓ⁻²·C_e⁻¹·n²·z⁻²·e²
null
1
4
2
10
9.1
-0.6
false
{"mass": "1", "length": "2", "capacitance": "1", "amount": "-2", "cat_activity": "2", "elem_charge": "-2"}
6
capacitance,cat_activity,elem_charge,length,mass,molar_mass
m·ℓ·C_e·M_m·z·e
chemistry,constants,em,mechanics
m·ℓ⁻²·C_e⁻¹·M_m⁻²·z⁻²·e²
m = k₀ · ℓ²·C_e·M_m²·z²·e⁻²
null
1
4
2
10
9.1
-0.6
false
{"mass": "1", "length": "-2", "capacitance": "-1", "molar_mass": "-2", "cat_activity": "-2", "elem_charge": "2"}
6
capacitance,cat_activity,concentration,elem_charge,length,mass
m·ℓ·C_e·c_n·z·e
chemistry,constants,em,mechanics
m·ℓ⁻⁴·C_e·c_n⁻²·z²·e⁻²
m = k₀ · ℓ⁴·C_e⁻¹·c_n²·z⁻²·e²
null
1
4
4
12
11.5
-3
false
{"mass": "1", "length": "-4", "capacitance": "1", "concentration": "-2", "cat_activity": "2", "elem_charge": "-2"}
6
capacitance,cat_activity,elem_charge,length,mass,molar_energy
m·ℓ·C_e·E_m·z·e
chemistry,constants,em,mechanics
m·ℓ²·C_e³·E_m²·z²·e⁻⁶
m = k₀ · ℓ⁻²·C_e⁻³·E_m⁻²·z⁻²·e⁶
null
1
4
6
16
15.3
-6.8
false
{"mass": "1", "length": "2", "capacitance": "3", "molar_energy": "2", "cat_activity": "2", "elem_charge": "-6"}
7
boltzmann,capacitance,cat_activity,elem_charge,gas_constant,length,mass
m·ℓ·C_e·R·z·k_B·e
chemistry,constants,em,mechanics
m·ℓ²·C_e·R²·z²·k_B⁻²·e⁻²
m = k₀ · ℓ⁻²·C_e⁻¹·R⁻²·z⁻²·k_B²·e²
null
2
4
2
12
11.8
-4.8
false
{"mass": "1", "length": "2", "capacitance": "1", "gas_constant": "2", "cat_activity": "2", "boltzmann": "-2", "elem_charge": "-2"}
6
avogadro,capacitance,cat_activity,elem_charge,length,mass
m·ℓ·C_e·z·e·N_A
chemistry,constants,em,mechanics
m·ℓ²·C_e·z²·e⁻²·N_A²
m = k₀ · ℓ⁻²·C_e⁻¹·z⁻²·e²·N_A⁻²
null
2
4
2
10
10.1
-3.1
false
{"mass": "1", "length": "2", "capacitance": "1", "cat_activity": "2", "elem_charge": "-2", "avogadro": "2"}
5
capacitance,elem_charge,grav_const,length,mass
m·ℓ·C_e·G·e
constants,em,mechanics
m²·ℓ⁻¹·C_e·G·e⁻²
ℓ = k₀ · m²·C_e·G·e⁻²
null
2
3
2
7
7.1
0.4
false
{"mass": "2", "length": "-1", "capacitance": "1", "grav_const": "1", "elem_charge": "-2"}
5
capacitance,elem_charge,length,mass,planck
m·ℓ·C_e·h·e
constants,em,mechanics
m·ℓ²·C_e⁻¹·h⁻²·e²
m = k₀ · ℓ⁻²·C_e·h²·e⁻²
null
2
3
2
8
7.8
-0.3
false
{"mass": "1", "length": "2", "capacitance": "-1", "planck": "-2", "elem_charge": "2"}
5
bfield,efield,inductance,length,mass
m·ℓ·L_e·E_f·B
em,mechanics
m·ℓ⁻⁴·L_e·E_f²·B⁻⁴
m = k₀ · ℓ⁴·L_e⁻¹·E_f⁻²·B⁴
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "-4", "inductance": "1", "efield": "2", "bfield": "-4"}
5
efield,inductance,length,mag_flux,mass
m·ℓ·L_e·E_f·Φ
em,mechanics
m·ℓ⁴·L_e·E_f²·Φ⁻⁴
m = k₀ · ℓ⁻⁴·L_e⁻¹·E_f⁻²·Φ⁴
null
0
2
4
12
10
-0.5
false
{"mass": "1", "length": "4", "inductance": "1", "efield": "2", "mag_flux": "-4"}
5
efield,inductance,length,mass,permittivity
m·ℓ·L_e·E_f·ε
em,mechanics
m·ℓ⁻²·L_e⁻¹·E_f⁻²·ε⁻²
m = k₀ · ℓ²·L_e·E_f²·ε²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "inductance": "-1", "efield": "-2", "permittivity": "-2"}
5
conductivity,efield,inductance,length,mass
m·ℓ·L_e·E_f·σ
em,mechanics
m·ℓ⁻⁴·L_e⁻³·E_f⁻²·σ⁻⁴
m = k₀ · ℓ⁴·L_e³·E_f²·σ⁴
null
0
2
4
14
11.4
-1.9
false
{"mass": "1", "length": "-4", "inductance": "-3", "efield": "-2", "conductivity": "-4"}
5
efield,inductance,length,mass,resistivity
m·ℓ·L_e·E_f·ρ_e
em,mechanics
m·ℓ⁻⁴·L_e⁻³·E_f⁻²·ρ_e⁴
m = k₀ · ℓ⁴·L_e³·E_f²·ρ_e⁻⁴
null
0
2
4
14
11.4
-1.9
false
{"mass": "1", "length": "-4", "inductance": "-3", "efield": "-2", "resistivity": "4"}
6
amount,efield,inductance,length,mass,molar_energy
m·ℓ·L_e·E_f·n·E_m
chemistry,em,mechanics
m·ℓ⁴·L_e⁻¹·E_f²·n⁻²·E_m⁻²
m = k₀ · ℓ⁻⁴·L_e·E_f⁻²·n²·E_m²
null
0
3
4
12
10.9
-1.9
false
{"mass": "1", "length": "4", "inductance": "-1", "efield": "2", "amount": "-2", "molar_energy": "-2"}
6
efield,inductance,length,mass,molar_energy,molar_mass
m·ℓ·L_e·E_f·M_m·E_m
chemistry,em,mechanics
m·ℓ⁻⁴·L_e·E_f⁻²·M_m⁻²·E_m²
m = k₀ · ℓ⁴·L_e⁻¹·E_f²·M_m²·E_m⁻²
null
0
3
4
12
10.9
-1.9
false
{"mass": "1", "length": "-4", "inductance": "1", "efield": "-2", "molar_mass": "-2", "molar_energy": "2"}
6
concentration,efield,inductance,length,mass,molar_energy
m·ℓ·L_e·E_f·c_n·E_m
chemistry,em,mechanics
m·ℓ⁻²·L_e⁻¹·E_f²·c_n⁻²·E_m⁻²
m = k₀ · ℓ²·L_e·E_f⁻²·c_n²·E_m²
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "length": "-2", "inductance": "-1", "efield": "2", "concentration": "-2", "molar_energy": "-2"}
6
cat_activity,concentration,efield,inductance,length,mass
m·ℓ·L_e·E_f·c_n·z
chemistry,em,mechanics
m·ℓ⁻¹²·L_e·E_f⁻²·c_n⁻⁴·z⁴
m = k₀ · ℓ¹²·L_e⁻¹·E_f²·c_n⁴·z⁻⁴
null
0
3
12
24
23.3
-14.3
false
{"mass": "1", "length": "-12", "inductance": "1", "efield": "-2", "concentration": "-4", "cat_activity": "4"}
7
boltzmann,efield,gas_constant,inductance,length,mass,molar_energy
m·ℓ·L_e·E_f·E_m·R·k_B
chemistry,constants,em,mechanics
m·ℓ⁴·L_e⁻¹·E_f²·E_m⁻²·R²·k_B⁻²
m = k₀ · ℓ⁻⁴·L_e·E_f⁻²·E_m²·R⁻²·k_B²
null
1
4
4
14
13.2
-4.7
false
{"mass": "1", "length": "4", "inductance": "-1", "efield": "2", "molar_energy": "-2", "gas_constant": "2", "boltzmann": "-2"}
6
cat_activity,efield,inductance,length,mass,molar_energy
m·ℓ·L_e·E_f·E_m·z
chemistry,em,mechanics
m·ℓ⁸·L_e⁻³·E_f⁶·E_m⁻⁴·z⁻⁴
m = k₀ · ℓ⁻⁸·L_e³·E_f⁻⁶·E_m⁴·z⁴
null
0
3
8
26
22.7
-13.7
false
{"mass": "1", "length": "8", "inductance": "-3", "efield": "6", "molar_energy": "-4", "cat_activity": "-4"}
6
avogadro,efield,inductance,length,mass,molar_energy
m·ℓ·L_e·E_f·E_m·N_A
chemistry,constants,em,mechanics
m·ℓ⁴·L_e⁻¹·E_f²·E_m⁻²·N_A²
m = k₀ · ℓ⁻⁴·L_e·E_f⁻²·E_m²·N_A⁻²
null
1
4
4
12
11.5
-3
false
{"mass": "1", "length": "4", "inductance": "-1", "efield": "2", "molar_energy": "-2", "avogadro": "2"}
5
efield,inductance,length,light_speed,mass
m·ℓ·L_e·E_f·c₀
constants,em,mechanics
m·ℓ⁻⁴·L_e·E_f⁻²·c₀⁴
m = k₀ · ℓ⁴·L_e⁻¹·E_f²·c₀⁻⁴
null
1
3
4
12
10.6
-1.6
false
{"mass": "1", "length": "-4", "inductance": "1", "efield": "-2", "light_speed": "4"}
5
efield,grav_const,inductance,length,mass
m·ℓ·L_e·E_f·G
constants,em,mechanics
m³·ℓ⁻⁶·L_e·E_f⁻²·G²
L_e = k₀ · m⁻³·ℓ⁶·E_f²·G⁻²
null
1
3
6
14
13
-4
false
{"mass": "3", "length": "-6", "inductance": "1", "efield": "-2", "grav_const": "2"}
5
efield,inductance,length,mass,planck
m·ℓ·L_e·E_f·h
constants,em,mechanics
m³·ℓ⁸·L_e⁻¹·E_f²·h⁻⁴
L_e = k₀ · m³·ℓ⁸·E_f²·h⁻⁴
null
1
3
8
18
16.8
-7.8
false
{"mass": "3", "length": "8", "inductance": "-1", "efield": "2", "planck": "-4"}
5
bfield,conductivity,inductance,length,mass
m·ℓ·L_e·B·σ
em,mechanics
m·ℓ⁻⁴·L_e⁻¹·B⁻²·σ⁻²
m = k₀ · ℓ⁴·L_e·B²·σ²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "-4", "inductance": "-1", "bfield": "-2", "conductivity": "-2"}
5
bfield,inductance,length,mass,resistivity
m·ℓ·L_e·B·ρ_e
em,mechanics
m·ℓ⁻⁴·L_e⁻¹·B⁻²·ρ_e²
m = k₀ · ℓ⁴·L_e·B²·ρ_e⁻²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "-4", "inductance": "-1", "bfield": "-2", "resistivity": "2"}
6
amount,bfield,cat_activity,inductance,length,mass
m·ℓ·L_e·B·n·z
chemistry,em,mechanics
m·ℓ⁻²·L_e·B⁻²·n⁻²·z²
m = k₀ · ℓ²·L_e⁻¹·B²·n²·z⁻²
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "length": "-2", "inductance": "1", "bfield": "-2", "amount": "-2", "cat_activity": "2"}
6
bfield,inductance,length,mass,molar_energy,molar_mass
m·ℓ·L_e·B·M_m·E_m
chemistry,em,mechanics
m·ℓ⁻⁴·L_e·B⁻²·M_m⁻¹·E_m
m = k₀ · ℓ⁴·L_e⁻¹·B²·M_m·E_m⁻¹
null
0
3
4
10
9.5
-0.5
false
{"mass": "1", "length": "-4", "inductance": "1", "bfield": "-2", "molar_mass": "-1", "molar_energy": "1"}
6
bfield,cat_activity,inductance,length,mass,molar_mass
m·ℓ·L_e·B·M_m·z
chemistry,em,mechanics
m·ℓ²·L_e⁻¹·B²·M_m⁻²·z⁻²
m = k₀ · ℓ⁻²·L_e·B⁻²·M_m²·z²
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "length": "2", "inductance": "-1", "bfield": "2", "molar_mass": "-2", "cat_activity": "-2"}
6
bfield,cat_activity,concentration,inductance,length,mass
m·ℓ·L_e·B·c_n·z
chemistry,em,mechanics
m·ℓ⁻⁸·L_e·B⁻²·c_n⁻²·z²
m = k₀ · ℓ⁸·L_e⁻¹·B²·c_n²·z⁻²
null
0
3
8
16
15.7
-6.7
false
{"mass": "1", "length": "-8", "inductance": "1", "bfield": "-2", "concentration": "-2", "cat_activity": "2"}
6
bfield,cat_activity,inductance,length,mass,molar_energy
m·ℓ·L_e·B·E_m·z
chemistry,em,mechanics
m·ℓ⁻¹⁰·L_e³·B⁻⁶·E_m²·z²
m = k₀ · ℓ¹⁰·L_e⁻³·B⁶·E_m⁻²·z⁻²
null
0
3
10
24
22.3
-13.3
false
{"mass": "1", "length": "-10", "inductance": "3", "bfield": "-6", "molar_energy": "2", "cat_activity": "2"}
7
bfield,boltzmann,cat_activity,gas_constant,inductance,length,mass
m·ℓ·L_e·B·R·z·k_B
chemistry,constants,em,mechanics
m·ℓ⁻²·L_e·B⁻²·R²·z²·k_B⁻²
m = k₀ · ℓ²·L_e⁻¹·B²·R⁻²·z⁻²·k_B²
null
1
4
2
12
10.8
-2.3
false
{"mass": "1", "length": "-2", "inductance": "1", "bfield": "-2", "gas_constant": "2", "cat_activity": "2", "boltzmann": "-2"}
6
avogadro,bfield,cat_activity,inductance,length,mass
m·ℓ·L_e·B·z·N_A
chemistry,constants,em,mechanics
m·ℓ⁻²·L_e·B⁻²·z²·N_A²
m = k₀ · ℓ²·L_e⁻¹·B²·z⁻²·N_A⁻²
null
1
4
2
10
9.1
-0.6
false
{"mass": "1", "length": "-2", "inductance": "1", "bfield": "-2", "cat_activity": "2", "avogadro": "2"}
5
bfield,inductance,length,light_speed,mass
m·ℓ·L_e·B·c₀
constants,em,mechanics
m·ℓ⁻⁴·L_e·B⁻²·c₀²
m = k₀ · ℓ⁴·L_e⁻¹·B²·c₀⁻²
null
1
3
4
10
9.2
-0.2
false
{"mass": "1", "length": "-4", "inductance": "1", "bfield": "-2", "light_speed": "2"}
5
bfield,grav_const,inductance,length,mass
m·ℓ·L_e·B·G
constants,em,mechanics
m²·ℓ⁻⁵·L_e·B⁻²·G
L_e = k₀ · m⁻²·ℓ⁵·B²·G⁻¹
null
1
3
5
11
10.4
-1.4
false
{"mass": "2", "length": "-5", "inductance": "1", "bfield": "-2", "grav_const": "1"}
5
bfield,inductance,length,mass,planck
m·ℓ·L_e·B·h
constants,em,mechanics
m·ℓ⁶·L_e⁻¹·B²·h⁻²
m = k₀ · ℓ⁻⁶·L_e·B⁻²·h²
null
1
3
6
12
11.6
-2.6
false
{"mass": "1", "length": "6", "inductance": "-1", "bfield": "2", "planck": "-2"}
6
amount,cat_activity,inductance,length,mag_flux,mass
m·ℓ·L_e·Φ·n·z
chemistry,em,mechanics
m·ℓ²·L_e·Φ⁻²·n⁻²·z²
m = k₀ · ℓ⁻²·L_e⁻¹·Φ²·n²·z⁻²
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "length": "2", "inductance": "1", "mag_flux": "-2", "amount": "-2", "cat_activity": "2"}
6
cat_activity,inductance,length,mag_flux,mass,molar_mass
m·ℓ·L_e·Φ·M_m·z
chemistry,em,mechanics
m·ℓ⁻²·L_e⁻¹·Φ²·M_m⁻²·z⁻²
m = k₀ · ℓ²·L_e·Φ⁻²·M_m²·z²
null
0
3
2
10
8.5
0.5
false
{"mass": "1", "length": "-2", "inductance": "-1", "mag_flux": "2", "molar_mass": "-2", "cat_activity": "-2"}
6
cat_activity,concentration,inductance,length,mag_flux,mass
m·ℓ·L_e·Φ·c_n·z
chemistry,em,mechanics
m·ℓ⁻⁴·L_e·Φ⁻²·c_n⁻²·z²
m = k₀ · ℓ⁴·L_e⁻¹·Φ²·c_n²·z⁻²
null
0
3
4
12
10.9
-1.9
false
{"mass": "1", "length": "-4", "inductance": "1", "mag_flux": "-2", "concentration": "-2", "cat_activity": "2"}