Average Error: 0.0 → 0.0
Time: 2.1s
Precision: binary64
\[\frac{x - y}{x + y}\]
↓
\[\frac{x}{x + y} - \sqrt[3]{{\left(\frac{y}{x + y}\right)}^{3}}\]
\frac{x - y}{x + y}
↓
\frac{x}{x + y} - \sqrt[3]{{\left(\frac{y}{x + y}\right)}^{3}}
double code(double x, double y) {
	return ((double) (((double) (x - y)) / ((double) (x + y))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (x / ((double) (x + y)))) - ((double) cbrt(((double) pow(((double) (y / ((double) (x + y)))), 3.0))))));
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.0
Target0.0
Herbie0.0
\[\frac{x}{x + y} - \frac{y}{x + y}\]

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{x + y}\]
  2. Using strategy rm

  3. Applied div-sub0.0

    \[\leadsto \color{blue}{\frac{x}{x + y} - \frac{y}{x + y}}\]
  4. Using strategy rm

  5. Applied add-cbrt-cube23.6

    \[\leadsto \frac{x}{x + y} - \frac{y}{\color{blue}{\sqrt[3]{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(x + y\right)}}}\]

  6. Applied add-cbrt-cube27.5

    \[\leadsto \frac{x}{x + y} - \frac{\color{blue}{\sqrt[3]{\left(y \cdot y\right) \cdot y}}}{\sqrt[3]{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(x + y\right)}}\]

  7. Applied cbrt-undiv27.5

    \[\leadsto \frac{x}{x + y} - \color{blue}{\sqrt[3]{\frac{\left(y \cdot y\right) \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(x + y\right)}}}\]

  8. Simplified0.0

    \[\leadsto \frac{x}{x + y} - \sqrt[3]{\color{blue}{{\left(\frac{y}{x + y}\right)}^{3}}}\]

  9. Final simplification0.0

    \[\leadsto \frac{x}{x + y} - \sqrt[3]{{\left(\frac{y}{x + y}\right)}^{3}}\]

Reproduce

herbie shell --seed 2020162 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

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

  (/ (- x y) (+ x y)))