Full-simplify improvements

[sharkdp]

input, current result, desired result

input	current result	desired result
gal/in	6.135792 gal^(2/3) ➞	231 in²
Pa m²	1 Pa m²	1 N (qalculate: 1 J/m)
J/s	1 J/s	1 W
sqrt(ℏ gravitational_constant / speed_of_light^3)	1.61626e-35 J^(1/2)·s/kg^(1/2)	1.61626e-35 m
m * g / cm	1 g·m/cm ➞	100 g
mph * s/m	1 mph·s/m ➞	0.44704
J/atm*mpg/mi	9.52979e-7 J·mpg^(3/2)/atm ➞	0.00260718
3% * 1kg	3 %·kg ➞	0.03 kg

They seem to fall into different categories:

• can be simplified to scalar (seems easy to fix?)
  • mph * s/m, 1 mph·s/m, 0.44704
  • J/atm*mpg/mi, 9.52979e-7 J·mpg^(3/2)/atm, 0.00260718
• just give us the base unit for this dimension (see also: Introduce unit systems #116)
  • sqrt(ℏ gravitational_constant / speed_of_light^3), 1.61626e-35 J^(1/2)·s/kg^(1/2), 1.61626e-35 m
  • J/s, 1 J/s, 1 W
  • Pa m², 1 Pa m², 1 N
  • m * g / cm, 1 g·m/cm, 100 g
  • 3% * 1kg, 3 %·kg, 0.03 kg
• more complex cases
  • gal/in, 6.135792 gal^(2/3), 231 in²

Additional references:

• Advanced simplification purescript-quantities#27
• Canonical unit for dimension #3
• Automatic simplification insect#257

[sharkdp]

The trivial case is fixed, e.g. we now have mph · s/m = 0.44704.

[sharkdp]

Another case closed: m * g / cm is now simplified to 100 g.

[sharkdp]

And another one: 3% · kg is now simplified to 0.03 kg

[sharkdp]

This is quite ridiculous:

The bohr radius definition in the current prelude

4 pi ε0 ℏ^2 / (electron_charge^2 electron_mass)

leads to

5.29177e-11 F·J²/(C²·kg·m·Hz²)

instead of the simplified

5.29177e-11 m

[sharkdp]

Both the bohr_radius case as well as the gal/in case have been resolved with #142

[sharkdp]

Just a few more examples that need to "just work":

• 50 Ω * 2 A -> 100 V
• 10 N / 5 Pa -> 2 m²