Average Error: 0.0 → 0.0
Time: 3.5s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\frac{{\left(\frac{x}{x + y}\right)}^{3} - {\left(\frac{y}{x + y}\right)}^{3}}{\frac{y}{x + y} \cdot \left(\frac{y}{x + y} + \frac{x}{x + y}\right) + \frac{x}{x + y} \cdot \frac{x}{x + y}}\]
\frac{x - y}{x + y}
↓
\frac{{\left(\frac{x}{x + y}\right)}^{3} - {\left(\frac{y}{x + y}\right)}^{3}}{\frac{y}{x + y} \cdot \left(\frac{y}{x + y} + \frac{x}{x + y}\right) + \frac{x}{x + y} \cdot \frac{x}{x + y}}
double code(double x, double y) {
	return ((double) (((double) (x - y)) / ((double) (x + y))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (((double) pow(((double) (x / ((double) (x + y)))), 3.0)) - ((double) pow(((double) (y / ((double) (x + y)))), 3.0)))) / ((double) (((double) (((double) (y / ((double) (x + y)))) * ((double) (((double) (y / ((double) (x + y)))) + ((double) (x / ((double) (x + y)))))))) + ((double) (((double) (x / ((double) (x + y)))) * ((double) (x / ((double) (x + y))))))))));
}

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 flip3--0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020130 
(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)))