Average Error: 0.0 → 0.0
Time: 2.1s
Precision: binary64
\[\frac{x + y}{x - y}\]
↓
\[\frac{1}{\sqrt[3]{{\left(\frac{x}{x + y}\right)}^{3}} - \frac{y}{x + y}}\]
\frac{x + y}{x - y}
↓
\frac{1}{\sqrt[3]{{\left(\frac{x}{x + y}\right)}^{3}} - \frac{y}{x + y}}
double code(double x, double y) {
	return ((double) (((double) (x + y)) / ((double) (x - y))));
}
↓
double code(double x, double y) {
	return ((double) (1.0 / ((double) (((double) cbrt(((double) pow(((double) (x / ((double) (x + y)))), 3.0)))) - ((double) (y / ((double) (x + y))))))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\frac{1}{\frac{x}{x + y} - \frac{y}{x + y}}\]

Derivation

  1. Initial program 0.0

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

  3. Applied clear-num0.0

    \[\leadsto \color{blue}{\frac{1}{\frac{x - y}{x + y}}}\]
  4. Using strategy rm

  5. Applied div-sub0.0

    \[\leadsto \frac{1}{\color{blue}{\frac{x}{x + y} - \frac{y}{x + y}}}\]
  6. Using strategy rm

  7. Applied add-cbrt-cube23.7

    \[\leadsto \frac{1}{\frac{x}{\color{blue}{\sqrt[3]{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(x + y\right)}}} - \frac{y}{x + y}}\]

  8. Applied add-cbrt-cube27.5

    \[\leadsto \frac{1}{\frac{\color{blue}{\sqrt[3]{\left(x \cdot x\right) \cdot x}}}{\sqrt[3]{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(x + y\right)}} - \frac{y}{x + y}}\]

  9. Applied cbrt-undiv27.5

    \[\leadsto \frac{1}{\color{blue}{\sqrt[3]{\frac{\left(x \cdot x\right) \cdot x}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(x + y\right)}}} - \frac{y}{x + y}}\]

  10. Simplified0.0

    \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{{\left(\frac{x}{x + y}\right)}^{3}}} - \frac{y}{x + y}}\]

  11. Final simplification0.0

    \[\leadsto \frac{1}{\sqrt[3]{{\left(\frac{x}{x + y}\right)}^{3}} - \frac{y}{x + y}}\]

Reproduce

herbie shell --seed 2020184 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (/ 1.0 (- (/ x (+ x y)) (/ y (+ x y))))

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