Average Error: 0.0 → 0.0
Time: 4.4s
Precision: binary64
\[\frac{x + y}{x - y}\]
↓
\[\log \left(\sqrt[3]{{\left(e^{\frac{x + y}{x - y}}\right)}^{3}}\right)\]
\frac{x + y}{x - y}
↓
\log \left(\sqrt[3]{{\left(e^{\frac{x + y}{x - y}}\right)}^{3}}\right)
double code(double x, double y) {
	return ((double) (((double) (x + y)) / ((double) (x - y))));
}
↓
double code(double x, double y) {
	return ((double) log(((double) cbrt(((double) pow(((double) exp(((double) (((double) (x + y)) / ((double) (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-log-exp0.0

    \[\leadsto \color{blue}{\log \left(e^{\frac{x + y}{x - y}}\right)}\]
  4. Using strategy rm

  5. Applied add-cbrt-cube0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020148 
(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)))