Average Error: 0.0 → 0.0
Time: 3.0s
Precision: binary64
\[\frac{x - y}{x + y} \]
↓
\[\sqrt[3]{{\left(\frac{x}{x + y} - \frac{y}{x + y}\right)}^{3}} \]
\frac{x - y}{x + y}
↓
\sqrt[3]{{\left(\frac{x}{x + y} - \frac{y}{x + y}\right)}^{3}}

(FPCore (x y) :precision binary64 (/ (- x y) (+ x y)))
↓
(FPCore (x y)
 :precision binary64
 (cbrt (pow (- (/ x (+ x y)) (/ 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 / (x + y)) - (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
\[\frac{x}{x + y} - \frac{y}{x + y} \]

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{x + y} \]

  2. Applied add-cbrt-cube_binary640.0

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

  3. Simplified0.0

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

  4. Applied div-sub_binary640.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2021275 
(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)))