Average Error: 0.0 → 0.0
Time: 1.9s
Precision: binary64
\[\frac{x + y}{x - y}\]
↓
\[\sqrt[3]{{\left(\frac{x + y}{x - y}\right)}^{3}}\]
\frac{x + y}{x - y}
↓
\sqrt[3]{{\left(\frac{x + y}{x - y}\right)}^{3}}
(FPCore (x y) :precision binary64 (/ (+ x y) (- x y)))
↓
(FPCore (x y) :precision binary64 (cbrt (pow (/ (+ x y) (- x y)) 3.0)))
double code(double x, double y) {
	return (x + y) / (x - y);
}
↓
double code(double x, double y) {
	return cbrt(pow(((x + y) / (x - y)), 3.0));
}

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 add-cbrt-cube_binary6441.5

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

  4. Applied add-cbrt-cube_binary6442.3

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

  5. Applied cbrt-undiv_binary6442.3

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020219 
(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)))