Physics.ForceLayout:coulombForce from force-layout-0.4.0.2

Average Error: 10.6 → 0.2

Time: 3.4s

Precision: binary64

Cost: 320

Math

\[\frac{x}{y \cdot y} \]

↓

\[\frac{\frac{x}{y}}{y} \]

FPCore

(FPCore (x y) :precision binary64 (/ x (* y y)))

↓

(FPCore (x y) :precision binary64 (/ (/ x y) y))

C

double code(double x, double y) {
	return x / (y * y);
}

↓

double code(double x, double y) {
	return (x / y) / y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / (y * y)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x / y) / y
end function

Java

public static double code(double x, double y) {
	return x / (y * y);
}

↓

public static double code(double x, double y) {
	return (x / y) / y;
}

Python

def code(x, y):
	return x / (y * y)

↓

def code(x, y):
	return (x / y) / y

Julia

function code(x, y)
	return Float64(x / Float64(y * y))
end

↓

function code(x, y)
	return Float64(Float64(x / y) / y)
end

MATLAB

function tmp = code(x, y)
	tmp = x / (y * y);
end

↓

function tmp = code(x, y)
	tmp = (x / y) / y;
end

Wolfram

code[x_, y_] := N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]

Target

Original	10.6
Target	0.2
Herbie	0.2

\[\frac{\frac{x}{y}}{y} \]

Derivation

1. Initial program 10.6

   \[\frac{x}{y \cdot y} \]

2. Applied egg-rr 0.2

   \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{y}} \]

3. Taylor expanded in x around 0 10.6

   \[\leadsto \color{blue}{\frac{x}{{y}^{2}}} \]

4. Simplified 0.2

   \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}} \]
   Proof

   [Start] 10.6	\[ \frac{x}{{y}^{2}} \]
   unpow2 [=>] 10.6	\[ \frac{x}{\color{blue}{y \cdot y}} \]
   associate-/r* [=>] 0.2	\[ \color{blue}{\frac{\frac{x}{y}}{y}} \]

5. Final simplification 0.2

   \[\leadsto \frac{\frac{x}{y}}{y} \]

Alternatives

Alternative 1
Error	10.6
Cost	320

\[\frac{x}{y \cdot y} \]

Reproduce

herbie shell --seed 2023040 
(FPCore (x y)
  :name "Physics.ForceLayout:coulombForce from force-layout-0.4.0.2"
  :precision binary64

  :herbie-target
  (/ (/ x y) y)

  (/ x (* y y)))