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
length,mass,permeability,permittivity,planck
m·ℓ·ε·μ₀·h
constants,em,mechanics
m²·ℓ²·ε⁻¹·μ₀⁻¹·h⁻²
ε = k₀ · m²·ℓ²·μ₀⁻¹·h⁻²
null
1
3
2
8
6.8
2.2
false
{"mass": "2", "length": "2", "permittivity": "-1", "permeability": "-1", "planck": "-2"}
6
amount,conductivity,length,mass,molar_energy,permittivity
m·ℓ·ε·σ·n·E_m
chemistry,em,mechanics
m·ℓ²·ε⁻²·σ²·n⁻¹·E_m⁻¹
m = k₀ · ℓ⁻²·ε²·σ⁻²·n·E_m
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "2", "permittivity": "-2", "conductivity": "2", "amount": "-1", "molar_energy": "-1"}
6
concentration,conductivity,length,mass,molar_energy,permittivity
m·ℓ·ε·σ·c_n·E_m
chemistry,em,mechanics
m·ℓ⁻¹·ε⁻²·σ²·c_n⁻¹·E_m⁻¹
m = k₀ · ℓ·ε²·σ⁻²·c_n·E_m
null
0
3
2
8
7.1
1.9
false
{"mass": "1", "length": "-1", "permittivity": "-2", "conductivity": "2", "concentration": "-1", "molar_energy": "-1"}
7
boltzmann,conductivity,gas_constant,length,mass,molar_energy,permittivity
m·ℓ·ε·σ·E_m·R·k_B
chemistry,constants,em,mechanics
m·ℓ²·ε⁻²·σ²·E_m⁻¹·R·k_B⁻¹
m = k₀ · ℓ⁻²·ε²·σ⁻²·E_m·R⁻¹·k_B
null
1
4
2
10
9.4
-0.9
false
{"mass": "1", "length": "2", "permittivity": "-2", "conductivity": "2", "molar_energy": "-1", "gas_constant": "1", "boltzmann": "-1"}
6
cat_activity,conductivity,length,mass,molar_energy,permittivity
m·ℓ·ε·σ·E_m·z
chemistry,em,mechanics
m·ℓ²·ε⁻³·σ³·E_m⁻¹·z⁻¹
m = k₀ · ℓ⁻²·ε³·σ⁻³·E_m·z
null
0
3
3
11
9.7
-0.7
false
{"mass": "1", "length": "2", "permittivity": "-3", "conductivity": "3", "molar_energy": "-1", "cat_activity": "-1"}
6
avogadro,conductivity,length,mass,molar_energy,permittivity
m·ℓ·ε·σ·E_m·N_A
chemistry,constants,em,mechanics
m·ℓ²·ε⁻²·σ²·E_m⁻¹·N_A
m = k₀ · ℓ⁻²·ε²·σ⁻²·E_m·N_A⁻¹
null
1
4
2
9
8.4
0.1
false
{"mass": "1", "length": "2", "permittivity": "-2", "conductivity": "2", "molar_energy": "-1", "avogadro": "1"}
5
conductivity,grav_const,length,mass,permittivity
m·ℓ·ε·σ·G
constants,em,mechanics
m·ℓ⁻³·ε²·σ⁻²·G
m = k₀ · ℓ³·ε⁻²·σ²·G⁻¹
null
1
3
3
9
8
1
false
{"mass": "1", "length": "-3", "permittivity": "2", "conductivity": "-2", "grav_const": "1"}
5
conductivity,length,mass,permittivity,planck
m·ℓ·ε·σ·h
constants,em,mechanics
m·ℓ²·ε⁻¹·σ·h⁻¹
m = k₀ · ℓ⁻²·ε·σ⁻¹·h
null
1
3
2
6
5.4
3.6
false
{"mass": "1", "length": "2", "permittivity": "-1", "conductivity": "1", "planck": "-1"}
5
conductivity,elem_charge,length,mass,permittivity
m·ℓ·ε·σ·e
constants,em,mechanics
m·ℓ³·ε⁻¹·σ²·e⁻²
m = k₀ · ℓ⁻³·ε·σ⁻²·e²
null
1
3
3
9
8
1
false
{"mass": "1", "length": "3", "permittivity": "-1", "conductivity": "2", "elem_charge": "-2"}
6
amount,length,mass,molar_energy,permittivity,resistivity
m·ℓ·ε·ρ_e·n·E_m
chemistry,em,mechanics
m·ℓ²·ε⁻²·ρ_e⁻²·n⁻¹·E_m⁻¹
m = k₀ · ℓ⁻²·ε²·ρ_e²·n·E_m
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "2", "permittivity": "-2", "resistivity": "-2", "amount": "-1", "molar_energy": "-1"}
6
concentration,length,mass,molar_energy,permittivity,resistivity
m·ℓ·ε·ρ_e·c_n·E_m
chemistry,em,mechanics
m·ℓ⁻¹·ε⁻²·ρ_e⁻²·c_n⁻¹·E_m⁻¹
m = k₀ · ℓ·ε²·ρ_e²·c_n·E_m
null
0
3
2
8
7.1
1.9
false
{"mass": "1", "length": "-1", "permittivity": "-2", "resistivity": "-2", "concentration": "-1", "molar_energy": "-1"}
7
boltzmann,gas_constant,length,mass,molar_energy,permittivity,resistivity
m·ℓ·ε·ρ_e·E_m·R·k_B
chemistry,constants,em,mechanics
m·ℓ²·ε⁻²·ρ_e⁻²·E_m⁻¹·R·k_B⁻¹
m = k₀ · ℓ⁻²·ε²·ρ_e²·E_m·R⁻¹·k_B
null
1
4
2
10
9.4
-0.9
false
{"mass": "1", "length": "2", "permittivity": "-2", "resistivity": "-2", "molar_energy": "-1", "gas_constant": "1", "boltzmann": "-1"}
6
cat_activity,length,mass,molar_energy,permittivity,resistivity
m·ℓ·ε·ρ_e·E_m·z
chemistry,em,mechanics
m·ℓ²·ε⁻³·ρ_e⁻³·E_m⁻¹·z⁻¹
m = k₀ · ℓ⁻²·ε³·ρ_e³·E_m·z
null
0
3
3
11
9.7
-0.7
false
{"mass": "1", "length": "2", "permittivity": "-3", "resistivity": "-3", "molar_energy": "-1", "cat_activity": "-1"}
6
avogadro,length,mass,molar_energy,permittivity,resistivity
m·ℓ·ε·ρ_e·E_m·N_A
chemistry,constants,em,mechanics
m·ℓ²·ε⁻²·ρ_e⁻²·E_m⁻¹·N_A
m = k₀ · ℓ⁻²·ε²·ρ_e²·E_m·N_A⁻¹
null
1
4
2
9
8.4
0.1
false
{"mass": "1", "length": "2", "permittivity": "-2", "resistivity": "-2", "molar_energy": "-1", "avogadro": "1"}
5
grav_const,length,mass,permittivity,resistivity
m·ℓ·ε·ρ_e·G
constants,em,mechanics
m·ℓ⁻³·ε²·ρ_e²·G
m = k₀ · ℓ³·ε⁻²·ρ_e⁻²·G⁻¹
null
1
3
3
9
8
1
false
{"mass": "1", "length": "-3", "permittivity": "2", "resistivity": "2", "grav_const": "1"}
5
length,mass,permittivity,planck,resistivity
m·ℓ·ε·ρ_e·h
constants,em,mechanics
m·ℓ²·ε⁻¹·ρ_e⁻¹·h⁻¹
m = k₀ · ℓ⁻²·ε·ρ_e·h
null
1
3
2
6
5.4
3.6
false
{"mass": "1", "length": "2", "permittivity": "-1", "resistivity": "-1", "planck": "-1"}
5
elem_charge,length,mass,permittivity,resistivity
m·ℓ·ε·ρ_e·e
constants,em,mechanics
m·ℓ³·ε⁻¹·ρ_e⁻²·e⁻²
m = k₀ · ℓ⁻³·ε·ρ_e²·e²
null
1
3
3
9
8
1
false
{"mass": "1", "length": "3", "permittivity": "-1", "resistivity": "-2", "elem_charge": "-2"}
6
amount,cat_activity,elem_charge,length,mass,permittivity
m·ℓ·ε·n·z·e
chemistry,constants,em,mechanics
m·ℓ³·ε·n⁻²·z²·e⁻²
m = k₀ · ℓ⁻³·ε⁻¹·n²·z⁻²·e²
null
1
4
3
11
10.3
-1.8
false
{"mass": "1", "length": "3", "permittivity": "1", "amount": "-2", "cat_activity": "2", "elem_charge": "-2"}
6
elem_charge,length,mass,molar_energy,molar_mass,permittivity
m·ℓ·ε·M_m·E_m·e
chemistry,constants,em,mechanics
m·ℓ·ε·M_m⁻¹·E_m·e⁻²
m = k₀ · ℓ⁻¹·ε⁻¹·M_m·E_m⁻¹·e²
null
1
4
2
7
7
1.5
false
{"mass": "1", "length": "1", "permittivity": "1", "molar_mass": "-1", "molar_energy": "1", "elem_charge": "-2"}
6
cat_activity,elem_charge,length,mass,molar_mass,permittivity
m·ℓ·ε·M_m·z·e
chemistry,constants,em,mechanics
m·ℓ⁻³·ε⁻¹·M_m⁻²·z⁻²·e²
m = k₀ · ℓ³·ε·M_m²·z²·e⁻²
null
1
4
3
11
10.3
-1.8
false
{"mass": "1", "length": "-3", "permittivity": "-1", "molar_mass": "-2", "cat_activity": "-2", "elem_charge": "2"}
6
cat_activity,concentration,elem_charge,length,mass,permittivity
m·ℓ·ε·c_n·z·e
chemistry,constants,em,mechanics
m·ℓ⁻³·ε·c_n⁻²·z²·e⁻²
m = k₀ · ℓ³·ε⁻¹·c_n²·z⁻²·e²
null
1
4
3
11
10.3
-1.8
false
{"mass": "1", "length": "-3", "permittivity": "1", "concentration": "-2", "cat_activity": "2", "elem_charge": "-2"}
6
cat_activity,elem_charge,length,mass,molar_energy,permittivity
m·ℓ·ε·E_m·z·e
chemistry,constants,em,mechanics
m·ℓ⁵·ε³·E_m²·z²·e⁻⁶
m = k₀ · ℓ⁻⁵·ε⁻³·E_m⁻²·z⁻²·e⁶
null
1
4
6
19
17.4
-8.9
false
{"mass": "1", "length": "5", "permittivity": "3", "molar_energy": "2", "cat_activity": "2", "elem_charge": "-6"}
7
boltzmann,cat_activity,elem_charge,gas_constant,length,mass,permittivity
m·ℓ·ε·R·z·k_B·e
chemistry,constants,em,mechanics
m·ℓ³·ε·R²·z²·k_B⁻²·e⁻²
m = k₀ · ℓ⁻³·ε⁻¹·R⁻²·z⁻²·k_B²·e²
null
2
4
3
13
13
-6
false
{"mass": "1", "length": "3", "permittivity": "1", "gas_constant": "2", "cat_activity": "2", "boltzmann": "-2", "elem_charge": "-2"}
6
avogadro,cat_activity,elem_charge,length,mass,permittivity
m·ℓ·ε·z·e·N_A
chemistry,constants,em,mechanics
m·ℓ³·ε·z²·e⁻²·N_A²
m = k₀ · ℓ⁻³·ε⁻¹·z⁻²·e²·N_A⁻²
null
2
4
3
11
11.3
-4.3
false
{"mass": "1", "length": "3", "permittivity": "1", "cat_activity": "2", "elem_charge": "-2", "avogadro": "2"}
5
elem_charge,length,light_speed,mass,permittivity
m·ℓ·ε·c₀·e
constants,em,mechanics
m·ℓ·ε·c₀²·e⁻²
m = k₀ · ℓ⁻¹·ε⁻¹·c₀⁻²·e²
null
2
3
2
7
7.1
0.4
false
{"mass": "1", "length": "1", "permittivity": "1", "light_speed": "2", "elem_charge": "-2"}
5
elem_charge,length,mass,permittivity,planck
m·ℓ·ε·h·e
constants,em,mechanics
m·ℓ·ε⁻¹·h⁻²·e²
m = k₀ · ℓ⁻¹·ε·h²·e⁻²
null
2
3
2
7
7.1
0.4
false
{"mass": "1", "length": "1", "permittivity": "-1", "planck": "-2", "elem_charge": "2"}
6
amount,conductivity,length,mass,molar_energy,permeability
m·ℓ·μ₀·σ·n·E_m
chemistry,em,mechanics
m·ℓ⁻²·μ₀⁻²·σ⁻²·n⁻¹·E_m⁻¹
m = k₀ · ℓ²·μ₀²·σ²·n·E_m
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "-2", "permeability": "-2", "conductivity": "-2", "amount": "-1", "molar_energy": "-1"}
6
cat_activity,conductivity,length,mass,molar_mass,permeability
m·ℓ·μ₀·σ·M_m·z
chemistry,em,mechanics
m·ℓ⁻²·μ₀⁻¹·σ⁻¹·M_m⁻¹·z⁻¹
m = k₀ · ℓ²·μ₀·σ·M_m·z
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "length": "-2", "permeability": "-1", "conductivity": "-1", "molar_mass": "-1", "cat_activity": "-1"}
6
concentration,conductivity,length,mass,molar_energy,permeability
m·ℓ·μ₀·σ·c_n·E_m
chemistry,em,mechanics
m·ℓ⁻⁵·μ₀⁻²·σ⁻²·c_n⁻¹·E_m⁻¹
m = k₀ · ℓ⁵·μ₀²·σ²·c_n·E_m
null
0
3
5
12
11.4
-2.4
false
{"mass": "1", "length": "-5", "permeability": "-2", "conductivity": "-2", "concentration": "-1", "molar_energy": "-1"}
7
boltzmann,conductivity,gas_constant,length,mass,molar_energy,permeability
m·ℓ·μ₀·σ·E_m·R·k_B
chemistry,constants,em,mechanics
m·ℓ⁻²·μ₀⁻²·σ⁻²·E_m⁻¹·R·k_B⁻¹
m = k₀ · ℓ²·μ₀²·σ²·E_m·R⁻¹·k_B
null
1
4
2
10
9.4
-0.9
false
{"mass": "1", "length": "-2", "permeability": "-2", "conductivity": "-2", "molar_energy": "-1", "gas_constant": "1", "boltzmann": "-1"}
6
cat_activity,conductivity,length,mass,molar_energy,permeability
m·ℓ·μ₀·σ·E_m·z
chemistry,em,mechanics
m·ℓ⁻⁴·μ₀⁻³·σ⁻³·E_m⁻¹·z⁻¹
m = k₀ · ℓ⁴·μ₀³·σ³·E_m·z
null
0
3
4
13
11.6
-2.6
false
{"mass": "1", "length": "-4", "permeability": "-3", "conductivity": "-3", "molar_energy": "-1", "cat_activity": "-1"}
6
avogadro,conductivity,length,mass,molar_energy,permeability
m·ℓ·μ₀·σ·E_m·N_A
chemistry,constants,em,mechanics
m·ℓ⁻²·μ₀⁻²·σ⁻²·E_m⁻¹·N_A
m = k₀ · ℓ²·μ₀²·σ²·E_m·N_A⁻¹
null
1
4
2
9
8.4
0.1
false
{"mass": "1", "length": "-2", "permeability": "-2", "conductivity": "-2", "molar_energy": "-1", "avogadro": "1"}
5
conductivity,grav_const,length,mass,permeability
m·ℓ·μ₀·σ·G
constants,em,mechanics
m·ℓ·μ₀²·σ²·G
m = k₀ · ℓ⁻¹·μ₀⁻²·σ⁻²·G⁻¹
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "1", "permeability": "2", "conductivity": "2", "grav_const": "1"}
6
amount,length,mass,molar_energy,permeability,resistivity
m·ℓ·μ₀·ρ_e·n·E_m
chemistry,em,mechanics
m·ℓ⁻²·μ₀⁻²·ρ_e²·n⁻¹·E_m⁻¹
m = k₀ · ℓ²·μ₀²·ρ_e⁻²·n·E_m
null
0
3
2
9
7.8
1.2
false
{"mass": "1", "length": "-2", "permeability": "-2", "resistivity": "2", "amount": "-1", "molar_energy": "-1"}
6
cat_activity,length,mass,molar_mass,permeability,resistivity
m·ℓ·μ₀·ρ_e·M_m·z
chemistry,em,mechanics
m·ℓ⁻²·μ₀⁻¹·ρ_e·M_m⁻¹·z⁻¹
m = k₀ · ℓ²·μ₀·ρ_e⁻¹·M_m·z
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "length": "-2", "permeability": "-1", "resistivity": "1", "molar_mass": "-1", "cat_activity": "-1"}
6
concentration,length,mass,molar_energy,permeability,resistivity
m·ℓ·μ₀·ρ_e·c_n·E_m
chemistry,em,mechanics
m·ℓ⁻⁵·μ₀⁻²·ρ_e²·c_n⁻¹·E_m⁻¹
m = k₀ · ℓ⁵·μ₀²·ρ_e⁻²·c_n·E_m
null
0
3
5
12
11.4
-2.4
false
{"mass": "1", "length": "-5", "permeability": "-2", "resistivity": "2", "concentration": "-1", "molar_energy": "-1"}
7
boltzmann,gas_constant,length,mass,molar_energy,permeability,resistivity
m·ℓ·μ₀·ρ_e·E_m·R·k_B
chemistry,constants,em,mechanics
m·ℓ⁻²·μ₀⁻²·ρ_e²·E_m⁻¹·R·k_B⁻¹
m = k₀ · ℓ²·μ₀²·ρ_e⁻²·E_m·R⁻¹·k_B
null
1
4
2
10
9.4
-0.9
false
{"mass": "1", "length": "-2", "permeability": "-2", "resistivity": "2", "molar_energy": "-1", "gas_constant": "1", "boltzmann": "-1"}
6
cat_activity,length,mass,molar_energy,permeability,resistivity
m·ℓ·μ₀·ρ_e·E_m·z
chemistry,em,mechanics
m·ℓ⁻⁴·μ₀⁻³·ρ_e³·E_m⁻¹·z⁻¹
m = k₀ · ℓ⁴·μ₀³·ρ_e⁻³·E_m·z
null
0
3
4
13
11.6
-2.6
false
{"mass": "1", "length": "-4", "permeability": "-3", "resistivity": "3", "molar_energy": "-1", "cat_activity": "-1"}
6
avogadro,length,mass,molar_energy,permeability,resistivity
m·ℓ·μ₀·ρ_e·E_m·N_A
chemistry,constants,em,mechanics
m·ℓ⁻²·μ₀⁻²·ρ_e²·E_m⁻¹·N_A
m = k₀ · ℓ²·μ₀²·ρ_e⁻²·E_m·N_A⁻¹
null
1
4
2
9
8.4
0.1
false
{"mass": "1", "length": "-2", "permeability": "-2", "resistivity": "2", "molar_energy": "-1", "avogadro": "1"}
5
grav_const,length,mass,permeability,resistivity
m·ℓ·μ₀·ρ_e·G
constants,em,mechanics
m·ℓ·μ₀²·ρ_e⁻²·G
m = k₀ · ℓ⁻¹·μ₀⁻²·ρ_e²·G⁻¹
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "1", "permeability": "2", "resistivity": "-2", "grav_const": "1"}
4
elem_charge,length,mass,permeability
m·ℓ·μ₀·e
constants,em,mechanics
m·ℓ·μ₀⁻¹·e⁻²
m = k₀ · ℓ⁻¹·μ₀·e²
null
1
3
2
5
4.4
4.6
false
{"mass": "1", "length": "1", "permeability": "-1", "elem_charge": "-2"}
6
amount,conductivity,elem_charge,length,mass,molar_energy
m·ℓ·σ·n·E_m·e
chemistry,constants,em,mechanics
m·ℓ⁴·σ²·n·E_m·e⁻⁴
m = k₀ · ℓ⁻⁴·σ⁻²·n⁻¹·E_m⁻¹·e⁴
null
1
4
4
13
12.2
-3.7
false
{"mass": "1", "length": "4", "conductivity": "2", "amount": "1", "molar_energy": "1", "elem_charge": "-4"}
6
amount,cat_activity,conductivity,elem_charge,length,mass
m·ℓ·σ·n·z·e
chemistry,constants,em,mechanics
m·ℓ³·σ·n⁻¹·z·e⁻²
m = k₀ · ℓ⁻³·σ⁻¹·n·z⁻¹·e²
null
1
4
3
9
8.9
-0.4
false
{"mass": "1", "length": "3", "conductivity": "1", "amount": "-1", "cat_activity": "1", "elem_charge": "-2"}
6
conductivity,elem_charge,length,mass,molar_energy,molar_mass
m·ℓ·σ·M_m·E_m·e
chemistry,constants,em,mechanics
m²·ℓ⁴·σ²·M_m⁻¹·E_m·e⁻⁴
M_m = k₀ · m²·ℓ⁴·σ²·E_m·e⁻⁴
null
1
4
4
14
12.9
-4.4
false
{"mass": "2", "length": "4", "conductivity": "2", "molar_mass": "-1", "molar_energy": "1", "elem_charge": "-4"}
6
concentration,conductivity,elem_charge,length,mass,molar_energy
m·ℓ·σ·c_n·E_m·e
chemistry,constants,em,mechanics
m·ℓ⁷·σ²·c_n·E_m·e⁻⁴
m = k₀ · ℓ⁻⁷·σ⁻²·c_n⁻¹·E_m⁻¹·e⁴
null
1
4
7
16
15.8
-7.3
false
{"mass": "1", "length": "7", "conductivity": "2", "concentration": "1", "molar_energy": "1", "elem_charge": "-4"}
7
boltzmann,conductivity,elem_charge,gas_constant,length,mass,molar_energy
m·ℓ·σ·E_m·R·k_B·e
chemistry,constants,em,mechanics
m·ℓ⁴·σ²·E_m·R⁻¹·k_B·e⁻⁴
m = k₀ · ℓ⁻⁴·σ⁻²·E_m⁻¹·R·k_B⁻¹·e⁴
null
2
4
4
14
14.2
-7.2
false
{"mass": "1", "length": "4", "conductivity": "2", "molar_energy": "1", "gas_constant": "-1", "boltzmann": "1", "elem_charge": "-4"}
6
cat_activity,conductivity,elem_charge,length,mass,molar_energy
m·ℓ·σ·E_m·z·e
chemistry,constants,em,mechanics
m²·ℓ⁷·σ³·E_m·z·e⁻⁶
E_m = k₀ · m⁻²·ℓ⁻⁷·σ⁻³·z⁻¹·e⁶
null
1
4
7
20
18.6
-10.1
false
{"mass": "2", "length": "7", "conductivity": "3", "molar_energy": "1", "cat_activity": "1", "elem_charge": "-6"}
6
avogadro,conductivity,elem_charge,length,mass,molar_energy
m·ℓ·σ·E_m·e·N_A
chemistry,constants,em,mechanics
m·ℓ⁴·σ²·E_m·e⁻⁴·N_A⁻¹
m = k₀ · ℓ⁻⁴·σ⁻²·E_m⁻¹·e⁴·N_A
null
2
4
4
13
13.2
-6.2
false
{"mass": "1", "length": "4", "conductivity": "2", "molar_energy": "1", "elem_charge": "-4", "avogadro": "-1"}
7
boltzmann,cat_activity,conductivity,elem_charge,gas_constant,length,mass
m·ℓ·σ·R·z·k_B·e
chemistry,constants,em,mechanics
m·ℓ³·σ·R·z·k_B⁻¹·e⁻²
m = k₀ · ℓ⁻³·σ⁻¹·R⁻¹·z⁻¹·k_B·e²
null
2
4
3
10
10.9
-3.9
false
{"mass": "1", "length": "3", "conductivity": "1", "gas_constant": "1", "cat_activity": "1", "boltzmann": "-1", "elem_charge": "-2"}
6
avogadro,cat_activity,conductivity,elem_charge,length,mass
m·ℓ·σ·z·e·N_A
chemistry,constants,em,mechanics
m·ℓ³·σ·z·e⁻²·N_A
m = k₀ · ℓ⁻³·σ⁻¹·z⁻¹·e²·N_A⁻¹
null
2
4
3
9
9.9
-2.9
false
{"mass": "1", "length": "3", "conductivity": "1", "cat_activity": "1", "elem_charge": "-2", "avogadro": "1"}
5
conductivity,elem_charge,length,light_speed,mass
m·ℓ·σ·c₀·e
constants,em,mechanics
m·ℓ²·σ·c₀·e⁻²
m = k₀ · ℓ⁻²·σ⁻¹·c₀⁻¹·e²
null
2
3
2
7
7.1
0.4
false
{"mass": "1", "length": "2", "conductivity": "1", "light_speed": "1", "elem_charge": "-2"}
5
conductivity,elem_charge,grav_const,length,mass
m·ℓ·σ·G·e
constants,em,mechanics
m³·ℓ³·σ²·G·e⁻⁴
G = k₀ · m⁻³·ℓ⁻³·σ⁻²·e⁴
null
2
3
4
13
12.3
-4.8
false
{"mass": "3", "length": "3", "conductivity": "2", "grav_const": "1", "elem_charge": "-4"}
6
amount,elem_charge,length,mass,molar_energy,resistivity
m·ℓ·ρ_e·n·E_m·e
chemistry,constants,em,mechanics
m·ℓ⁴·ρ_e⁻²·n·E_m·e⁻⁴
m = k₀ · ℓ⁻⁴·ρ_e²·n⁻¹·E_m⁻¹·e⁴
null
1
4
4
13
12.2
-3.7
false
{"mass": "1", "length": "4", "resistivity": "-2", "amount": "1", "molar_energy": "1", "elem_charge": "-4"}
6
amount,cat_activity,elem_charge,length,mass,resistivity
m·ℓ·ρ_e·n·z·e
chemistry,constants,em,mechanics
m·ℓ³·ρ_e⁻¹·n⁻¹·z·e⁻²
m = k₀ · ℓ⁻³·ρ_e·n·z⁻¹·e²
null
1
4
3
9
8.9
-0.4
false
{"mass": "1", "length": "3", "resistivity": "-1", "amount": "-1", "cat_activity": "1", "elem_charge": "-2"}
6
elem_charge,length,mass,molar_energy,molar_mass,resistivity
m·ℓ·ρ_e·M_m·E_m·e
chemistry,constants,em,mechanics
m²·ℓ⁴·ρ_e⁻²·M_m⁻¹·E_m·e⁻⁴
M_m = k₀ · m²·ℓ⁴·ρ_e⁻²·E_m·e⁻⁴
null
1
4
4
14
12.9
-4.4
false
{"mass": "2", "length": "4", "resistivity": "-2", "molar_mass": "-1", "molar_energy": "1", "elem_charge": "-4"}
6
concentration,elem_charge,length,mass,molar_energy,resistivity
m·ℓ·ρ_e·c_n·E_m·e
chemistry,constants,em,mechanics
m·ℓ⁷·ρ_e⁻²·c_n·E_m·e⁻⁴
m = k₀ · ℓ⁻⁷·ρ_e²·c_n⁻¹·E_m⁻¹·e⁴
null
1
4
7
16
15.8
-7.3
false
{"mass": "1", "length": "7", "resistivity": "-2", "concentration": "1", "molar_energy": "1", "elem_charge": "-4"}
7
boltzmann,elem_charge,gas_constant,length,mass,molar_energy,resistivity
m·ℓ·ρ_e·E_m·R·k_B·e
chemistry,constants,em,mechanics
m·ℓ⁴·ρ_e⁻²·E_m·R⁻¹·k_B·e⁻⁴
m = k₀ · ℓ⁻⁴·ρ_e²·E_m⁻¹·R·k_B⁻¹·e⁴
null
2
4
4
14
14.2
-7.2
false
{"mass": "1", "length": "4", "resistivity": "-2", "molar_energy": "1", "gas_constant": "-1", "boltzmann": "1", "elem_charge": "-4"}
6
cat_activity,elem_charge,length,mass,molar_energy,resistivity
m·ℓ·ρ_e·E_m·z·e
chemistry,constants,em,mechanics
m²·ℓ⁷·ρ_e⁻³·E_m·z·e⁻⁶
E_m = k₀ · m⁻²·ℓ⁻⁷·ρ_e³·z⁻¹·e⁶
null
1
4
7
20
18.6
-10.1
false
{"mass": "2", "length": "7", "resistivity": "-3", "molar_energy": "1", "cat_activity": "1", "elem_charge": "-6"}
6
avogadro,elem_charge,length,mass,molar_energy,resistivity
m·ℓ·ρ_e·E_m·e·N_A
chemistry,constants,em,mechanics
m·ℓ⁴·ρ_e⁻²·E_m·e⁻⁴·N_A⁻¹
m = k₀ · ℓ⁻⁴·ρ_e²·E_m⁻¹·e⁴·N_A
null
2
4
4
13
13.2
-6.2
false
{"mass": "1", "length": "4", "resistivity": "-2", "molar_energy": "1", "elem_charge": "-4", "avogadro": "-1"}
7
boltzmann,cat_activity,elem_charge,gas_constant,length,mass,resistivity
m·ℓ·ρ_e·R·z·k_B·e
chemistry,constants,em,mechanics
m·ℓ³·ρ_e⁻¹·R·z·k_B⁻¹·e⁻²
m = k₀ · ℓ⁻³·ρ_e·R⁻¹·z⁻¹·k_B·e²
null
2
4
3
10
10.9
-3.9
false
{"mass": "1", "length": "3", "resistivity": "-1", "gas_constant": "1", "cat_activity": "1", "boltzmann": "-1", "elem_charge": "-2"}
6
avogadro,cat_activity,elem_charge,length,mass,resistivity
m·ℓ·ρ_e·z·e·N_A
chemistry,constants,em,mechanics
m·ℓ³·ρ_e⁻¹·z·e⁻²·N_A
m = k₀ · ℓ⁻³·ρ_e·z⁻¹·e²·N_A⁻¹
null
2
4
3
9
9.9
-2.9
false
{"mass": "1", "length": "3", "resistivity": "-1", "cat_activity": "1", "elem_charge": "-2", "avogadro": "1"}
5
elem_charge,length,light_speed,mass,resistivity
m·ℓ·ρ_e·c₀·e
constants,em,mechanics
m·ℓ²·ρ_e⁻¹·c₀·e⁻²
m = k₀ · ℓ⁻²·ρ_e·c₀⁻¹·e²
null
2
3
2
7
7.1
0.4
false
{"mass": "1", "length": "2", "resistivity": "-1", "light_speed": "1", "elem_charge": "-2"}
5
elem_charge,grav_const,length,mass,resistivity
m·ℓ·ρ_e·G·e
constants,em,mechanics
m³·ℓ³·ρ_e⁻²·G·e⁻⁴
G = k₀ · m⁻³·ℓ⁻³·ρ_e²·e⁴
null
2
3
4
13
12.3
-4.8
false
{"mass": "3", "length": "3", "resistivity": "-2", "grav_const": "1", "elem_charge": "-4"}
5
amount,cat_activity,length,mass,molar_energy
m·ℓ·n·E_m·z
chemistry,mechanics
m·ℓ²·n⁻³·E_m⁻¹·z²
m = k₀ · ℓ⁻²·n³·E_m·z⁻²
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "2", "amount": "-3", "molar_energy": "-1", "cat_activity": "2"}
5
amount,grav_const,length,mass,molar_energy
m·ℓ·n·E_m·G
chemistry,constants,mechanics
m²·ℓ⁻¹·n⁻¹·E_m⁻¹·G
ℓ = k₀ · m²·n⁻¹·E_m⁻¹·G
null
1
3
2
6
5.4
3.6
false
{"mass": "2", "length": "-1", "amount": "-1", "molar_energy": "-1", "grav_const": "1"}
5
amount,length,mass,molar_energy,planck
m·ℓ·n·E_m·h
chemistry,constants,mechanics
m·ℓ²·n·E_m·h⁻²
m = k₀ · ℓ⁻²·n⁻¹·E_m⁻¹·h²
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "2", "amount": "1", "molar_energy": "1", "planck": "-2"}
5
amount,cat_activity,grav_const,length,mass
m·ℓ·n·z·G
chemistry,constants,mechanics
m·ℓ⁻³·n²·z⁻²·G
m = k₀ · ℓ³·n⁻²·z²·G⁻¹
null
1
3
3
9
8
1
false
{"mass": "1", "length": "-3", "amount": "2", "cat_activity": "-2", "grav_const": "1"}
5
amount,cat_activity,length,mass,planck
m·ℓ·n·z·h
chemistry,constants,mechanics
m·ℓ²·n⁻¹·z·h⁻¹
m = k₀ · ℓ⁻²·n·z⁻¹·h
null
1
3
2
6
5.4
3.6
false
{"mass": "1", "length": "2", "amount": "-1", "cat_activity": "1", "planck": "-1"}
4
concentration,length,mass,molar_mass
m·ℓ·M_m·c_n
chemistry,mechanics
m·ℓ⁻³·M_m⁻¹·c_n⁻¹
m = k₀ · ℓ³·M_m·c_n
null
0
2
3
6
5
4.5
true
{"mass": "1", "length": "-3", "molar_mass": "-1", "concentration": "-1"}
5
cat_activity,length,mass,molar_energy,molar_mass
m·ℓ·M_m·E_m·z
chemistry,mechanics
m²·ℓ⁻²·M_m⁻³·E_m·z⁻²
E_m = k₀ · m⁻²·ℓ²·M_m³·z²
null
0
2
3
10
8.1
1.4
false
{"mass": "2", "length": "-2", "molar_mass": "-3", "molar_energy": "1", "cat_activity": "-2"}
5
grav_const,length,mass,molar_energy,molar_mass
m·ℓ·M_m·E_m·G
chemistry,constants,mechanics
m·ℓ⁻¹·M_m·E_m⁻¹·G
m = k₀ · ℓ·M_m⁻¹·E_m·G⁻¹
null
1
3
1
5
4.2
4.8
false
{"mass": "1", "length": "-1", "molar_mass": "1", "molar_energy": "-1", "grav_const": "1"}
5
length,mass,molar_energy,molar_mass,planck
m·ℓ·M_m·E_m·h
chemistry,constants,mechanics
m²·ℓ²·M_m⁻¹·E_m·h⁻²
M_m = k₀ · m²·ℓ²·E_m·h⁻²
null
1
3
2
8
6.8
2.2
false
{"mass": "2", "length": "2", "molar_mass": "-1", "molar_energy": "1", "planck": "-2"}
5
cat_activity,length,light_speed,mass,molar_mass
m·ℓ·M_m·z·c₀
chemistry,constants,mechanics
m·ℓ⁻¹·M_m⁻¹·z⁻¹·c₀
m = k₀ · ℓ·M_m·z·c₀⁻¹
null
1
3
1
5
4.2
4.8
false
{"mass": "1", "length": "-1", "molar_mass": "-1", "cat_activity": "-1", "light_speed": "1"}
5
cat_activity,grav_const,length,mass,molar_mass
m·ℓ·M_m·z·G
chemistry,constants,mechanics
m³·ℓ⁻³·M_m⁻²·z⁻²·G
G = k₀ · m⁻³·ℓ³·M_m²·z²
null
1
3
3
11
9.4
-0.4
false
{"mass": "3", "length": "-3", "molar_mass": "-2", "cat_activity": "-2", "grav_const": "1"}
5
cat_activity,concentration,length,mass,molar_energy
m·ℓ·c_n·E_m·z
chemistry,mechanics
m·ℓ⁻⁷·c_n⁻³·E_m⁻¹·z²
m = k₀ · ℓ⁷·c_n³·E_m·z⁻²
null
0
2
7
14
12.9
-3.4
false
{"mass": "1", "length": "-7", "concentration": "-3", "molar_energy": "-1", "cat_activity": "2"}
5
concentration,length,light_speed,mass,molar_energy
m·ℓ·c_n·E_m·c₀
chemistry,constants,mechanics
m·ℓ⁻³·c_n⁻¹·E_m⁻¹·c₀²
m = k₀ · ℓ³·c_n·E_m·c₀⁻²
null
1
3
3
8
7.3
1.7
false
{"mass": "1", "length": "-3", "concentration": "-1", "molar_energy": "-1", "light_speed": "2"}
5
concentration,grav_const,length,mass,molar_energy
m·ℓ·c_n·E_m·G
chemistry,constants,mechanics
m²·ℓ⁻⁴·c_n⁻¹·E_m⁻¹·G
c_n = k₀ · m²·ℓ⁻⁴·E_m⁻¹·G
null
1
3
4
9
8.5
0.5
false
{"mass": "2", "length": "-4", "concentration": "-1", "molar_energy": "-1", "grav_const": "1"}
5
concentration,length,mass,molar_energy,planck
m·ℓ·c_n·E_m·h
chemistry,constants,mechanics
m·ℓ⁵·c_n·E_m·h⁻²
m = k₀ · ℓ⁻⁵·c_n⁻¹·E_m⁻¹·h²
null
1
3
5
10
9.7
-0.7
false
{"mass": "1", "length": "5", "concentration": "1", "molar_energy": "1", "planck": "-2"}
5
cat_activity,concentration,grav_const,length,mass
m·ℓ·c_n·z·G
chemistry,constants,mechanics
m·ℓ³·c_n²·z⁻²·G
m = k₀ · ℓ⁻³·c_n⁻²·z²·G⁻¹
null
1
3
3
9
8
1
false
{"mass": "1", "length": "3", "concentration": "2", "cat_activity": "-2", "grav_const": "1"}
5
cat_activity,concentration,length,mass,planck
m·ℓ·c_n·z·h
chemistry,constants,mechanics
m·ℓ⁻¹·c_n⁻¹·z·h⁻¹
m = k₀ · ℓ·c_n·z⁻¹·h
null
1
3
1
5
4.2
4.8
false
{"mass": "1", "length": "-1", "concentration": "-1", "cat_activity": "1", "planck": "-1"}
6
boltzmann,cat_activity,gas_constant,length,mass,molar_energy
m·ℓ·E_m·R·z·k_B
chemistry,constants,mechanics
m·ℓ²·E_m⁻¹·R³·z²·k_B⁻³
m = k₀ · ℓ⁻²·E_m·R⁻³·z⁻²·k_B³
null
1
3
3
12
10.4
-1.4
false
{"mass": "1", "length": "2", "molar_energy": "-1", "gas_constant": "3", "cat_activity": "2", "boltzmann": "-3"}
6
boltzmann,gas_constant,grav_const,length,mass,molar_energy
m·ℓ·E_m·R·G·k_B
chemistry,constants,mechanics
m²·ℓ⁻¹·E_m⁻¹·R·G·k_B⁻¹
ℓ = k₀ · m²·E_m⁻¹·R·G·k_B⁻¹
null
2
3
2
7
7.4
0.1
false
{"mass": "2", "length": "-1", "molar_energy": "-1", "gas_constant": "1", "grav_const": "1", "boltzmann": "-1"}
6
boltzmann,gas_constant,length,mass,molar_energy,planck
m·ℓ·E_m·R·h·k_B
chemistry,constants,mechanics
m·ℓ²·E_m·R⁻¹·h⁻²·k_B
m = k₀ · ℓ⁻²·E_m⁻¹·R·h²·k_B⁻¹
null
2
3
2
8
8.1
-0.6
false
{"mass": "1", "length": "2", "molar_energy": "1", "gas_constant": "-1", "planck": "-2", "boltzmann": "1"}
5
cat_activity,length,light_speed,mass,molar_energy
m·ℓ·E_m·z·c₀
chemistry,constants,mechanics
m·ℓ⁻¹·E_m⁻¹·z⁻¹·c₀³
m = k₀ · ℓ·E_m·z·c₀⁻³
null
1
3
3
7
6.6
2.4
false
{"mass": "1", "length": "-1", "molar_energy": "-1", "cat_activity": "-1", "light_speed": "3"}
5
cat_activity,grav_const,length,mass,molar_energy
m·ℓ·E_m·z·G
chemistry,constants,mechanics
m⁵·ℓ⁻⁵·E_m⁻²·z⁻²·G³
E_m = k₀ · m⁵ᐟ²·ℓ⁻⁵ᐟ²·z⁻¹·G³ᐟ²
null
1
3
5
17
14.6
-5.6
false
{"mass": "5", "length": "-5", "molar_energy": "-2", "cat_activity": "-2", "grav_const": "3"}
5
cat_activity,length,mass,molar_energy,planck
m·ℓ·E_m·z·h
chemistry,constants,mechanics
m²·ℓ⁴·E_m·z·h⁻³
E_m = k₀ · m⁻²·ℓ⁻⁴·z⁻¹·h³
null
1
3
4
11
9.9
-0.9
false
{"mass": "2", "length": "4", "molar_energy": "1", "cat_activity": "1", "planck": "-3"}
5
avogadro,cat_activity,length,mass,molar_energy
m·ℓ·E_m·z·N_A
chemistry,constants,mechanics
m·ℓ²·E_m⁻¹·z²·N_A³
m = k₀ · ℓ⁻²·E_m·z⁻²·N_A⁻³
null
1
3
3
9
8
1
false
{"mass": "1", "length": "2", "molar_energy": "-1", "cat_activity": "2", "avogadro": "3"}
5
avogadro,grav_const,length,mass,molar_energy
m·ℓ·E_m·G·N_A
chemistry,constants,mechanics
m²·ℓ⁻¹·E_m⁻¹·G·N_A
ℓ = k₀ · m²·E_m⁻¹·G·N_A
null
2
3
2
6
6.4
1.1
false
{"mass": "2", "length": "-1", "molar_energy": "-1", "grav_const": "1", "avogadro": "1"}
5
avogadro,length,mass,molar_energy,planck
m·ℓ·E_m·h·N_A
chemistry,constants,mechanics
m·ℓ²·E_m·h⁻²·N_A⁻¹
m = k₀ · ℓ⁻²·E_m⁻¹·h²·N_A
null
2
3
2
7
7.1
0.4
false
{"mass": "1", "length": "2", "molar_energy": "1", "planck": "-2", "avogadro": "-1"}
6
boltzmann,cat_activity,gas_constant,grav_const,length,mass
m·ℓ·R·z·G·k_B
chemistry,constants,mechanics
m·ℓ⁻³·R⁻²·z⁻²·G·k_B²
m = k₀ · ℓ³·R²·z²·G⁻¹·k_B⁻²
null
2
3
3
11
10.7
-3.2
false
{"mass": "1", "length": "-3", "gas_constant": "-2", "cat_activity": "-2", "grav_const": "1", "boltzmann": "2"}
6
boltzmann,cat_activity,gas_constant,length,mass,planck
m·ℓ·R·z·h·k_B
chemistry,constants,mechanics
m·ℓ²·R·z·h⁻¹·k_B⁻¹
m = k₀ · ℓ⁻²·R⁻¹·z⁻¹·h·k_B
null
2
3
2
7
7.4
0.1
false
{"mass": "1", "length": "2", "gas_constant": "1", "cat_activity": "1", "planck": "-1", "boltzmann": "-1"}
5
avogadro,cat_activity,grav_const,length,mass
m·ℓ·z·G·N_A
chemistry,constants,mechanics
m·ℓ⁻³·z⁻²·G·N_A⁻²
m = k₀ · ℓ³·z²·G⁻¹·N_A²
null
2
3
3
9
9
-1.5
false
{"mass": "1", "length": "-3", "cat_activity": "-2", "grav_const": "1", "avogadro": "-2"}
5
avogadro,cat_activity,length,mass,planck
m·ℓ·z·h·N_A
chemistry,constants,mechanics
m·ℓ²·z·h⁻¹·N_A
m = k₀ · ℓ⁻²·z⁻¹·h·N_A⁻¹
null
2
3
2
6
6.4
1.1
false
{"mass": "1", "length": "2", "cat_activity": "1", "planck": "-1", "avogadro": "1"}
4
grav_const,length,light_speed,mass
m·ℓ·c₀·G
constants,mechanics
m·ℓ⁻¹·c₀⁻²·G
m = k₀ · ℓ·c₀²·G⁻¹
null
2
2
2
5
4.8
3.2
false
{"mass": "1", "length": "-1", "light_speed": "-2", "grav_const": "1"}
4
length,light_speed,mass,planck
m·ℓ·c₀·h
constants,mechanics
m·ℓ·c₀·h⁻¹
m = k₀ · ℓ⁻¹·c₀⁻¹·h
null
2
2
1
4
3.6
4.4
false
{"mass": "1", "length": "1", "light_speed": "1", "planck": "-1"}
4
grav_const,length,mass,planck
m·ℓ·G·h
constants,mechanics
m³·ℓ·G·h⁻²
ℓ = k₀ · m⁻³·G⁻¹·h²
null
2
2
3
7
6.7
1.3
false
{"mass": "3", "length": "1", "grav_const": "1", "planck": "-2"}
4
force,mass,time,velocity
m·t·v·F
mechanics
m·t⁻¹·v·F⁻¹
m = k₀ · t·v⁻¹·F
null
0
1
1
4
2
8
true
{"mass": "1", "time": "-1", "velocity": "1", "force": "-1"}
4
mass,power,time,velocity
m·t·v·P
mechanics
m·t⁻¹·v²·P⁻¹
m = k₀ · t·v⁻²·P
null
0
1
2
5
3.2
6.8
true
{"mass": "1", "time": "-1", "velocity": "2", "power": "-1"}
4
ang_momentum,mass,time,velocity
m·t·v·Lₐ
mechanics
m·t·v²·Lₐ⁻¹
m = k₀ · t⁻¹·v⁻²·Lₐ
null
0
1
2
5
3.2
6.8
true
{"mass": "1", "time": "1", "velocity": "2", "ang_momentum": "-1"}
4
action,mass,time,velocity
m·t·v·S
mechanics
m·t·v²·S⁻¹
m = k₀ · t⁻¹·v⁻²·S
null
0
1
2
5
3.2
6.8
true
{"mass": "1", "time": "1", "velocity": "2", "action": "-1"}