Average Error: 0.0 → 0.0
Time: 3.0s
Precision: binary64
\[\frac{x + y}{x - y}\]
↓
\[\sqrt[3]{\sqrt[3]{{\left({\left(\frac{x + y}{x - y}\right)}^{3}\right)}^{3}}}\]
\frac{x + y}{x - y}
↓
\sqrt[3]{\sqrt[3]{{\left({\left(\frac{x + y}{x - y}\right)}^{3}\right)}^{3}}}
(FPCore (x y) :precision binary64 (/ (+ x y) (- x y)))
↓
(FPCore (x y)
 :precision binary64
 (cbrt (cbrt (pow (pow (/ (+ x y) (- x y)) 3.0) 3.0))))
double code(double x, double y) {
	return (x + y) / (x - y);
}
↓
double code(double x, double y) {
	return cbrt(cbrt(pow(pow(((x + y) / (x - y)), 3.0), 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_binary640.0

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

  4. Simplified0.0

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

  6. Applied add-cbrt-cube_binary640.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020260 
(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)))