Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, C

Average Accuracy: 99.6% → 99.5%

Time: 4.1s

Precision: binary64

Cost: 448

Math

\[\frac{x}{y \cdot 3} \]

↓

\[\frac{\frac{1}{y}}{\frac{3}{x}} \]

FPCore

(FPCore (x y) :precision binary64 (/ x (* y 3.0)))

↓

(FPCore (x y) :precision binary64 (/ (/ 1.0 y) (/ 3.0 x)))

C

double code(double x, double y) {
	return x / (y * 3.0);
}

↓

double code(double x, double y) {
	return (1.0 / y) / (3.0 / x);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / (y * 3.0d0)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 / y) / (3.0d0 / x)
end function

Java

public static double code(double x, double y) {
	return x / (y * 3.0);
}

↓

public static double code(double x, double y) {
	return (1.0 / y) / (3.0 / x);
}

Python

def code(x, y):
	return x / (y * 3.0)

↓

def code(x, y):
	return (1.0 / y) / (3.0 / x)

Julia

function code(x, y)
	return Float64(x / Float64(y * 3.0))
end

↓

function code(x, y)
	return Float64(Float64(1.0 / y) / Float64(3.0 / x))
end

MATLAB

function tmp = code(x, y)
	tmp = x / (y * 3.0);
end

↓

function tmp = code(x, y)
	tmp = (1.0 / y) / (3.0 / x);
end

Wolfram

code[x_, y_] := N[(x / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(N[(1.0 / y), $MachinePrecision] / N[(3.0 / x), $MachinePrecision]), $MachinePrecision]

Target

Original	99.6%
Target	99.6%
Herbie	99.5%

\[\frac{\frac{x}{y}}{3} \]

Derivation

1. Initial program 99.6%

   \[\frac{x}{y \cdot 3} \]

2. Applied egg-rr 99.5%

   \[\leadsto \color{blue}{\frac{1}{y} \cdot \frac{x}{3}} \]
   Proof

   [Start] 99.6	\[ \frac{x}{y \cdot 3} \]
   *-un-lft-identity [=>] 99.6	\[ \frac{\color{blue}{1 \cdot x}}{y \cdot 3} \]
   times-frac [=>] 99.5	\[ \color{blue}{\frac{1}{y} \cdot \frac{x}{3}} \]

3. Applied egg-rr 99.5%

   \[\leadsto \color{blue}{\frac{\frac{1}{y}}{\frac{3}{x}}} \]
   Proof

   [Start] 99.5	\[ \frac{1}{y} \cdot \frac{x}{3} \]
   clear-num [=>] 99.4	\[ \frac{1}{y} \cdot \color{blue}{\frac{1}{\frac{3}{x}}} \]
   un-div-inv [=>] 99.5	\[ \color{blue}{\frac{\frac{1}{y}}{\frac{3}{x}}} \]

4. Final simplification 99.5%

   \[\leadsto \frac{\frac{1}{y}}{\frac{3}{x}} \]

Alternatives

Alternative 1
Accuracy	99.5%
Cost	320

\[x \cdot \frac{0.3333333333333333}{y} \]

Alternative 2
Accuracy	99.6%
Cost	320

\[\frac{x}{y \cdot 3} \]

Reproduce

herbie shell --seed 2023130 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"
  :precision binary64

  :herbie-target
  (/ (/ x y) 3.0)

  (/ x (* y 3.0)))