Average Error: 0.0 → 0.0
Time: 7.5s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\sqrt[3]{{\left(\frac{x - y}{x + y}\right)}^{3}}\]
\frac{x - y}{x + y}
↓
\sqrt[3]{{\left(\frac{x - y}{x + y}\right)}^{3}}
double f(double x, double y) {
        double r928108 = x;
        double r928109 = y;
        double r928110 = r928108 - r928109;
        double r928111 = r928108 + r928109;
        double r928112 = r928110 / r928111;
        return r928112;
}
↓
double f(double x, double y) {
        double r928113 = x;
        double r928114 = y;
        double r928115 = r928113 - r928114;
        double r928116 = r928113 + r928114;
        double r928117 = r928115 / r928116;
        double r928118 = 3.0;
        double r928119 = pow(r928117, r928118);
        double r928120 = cbrt(r928119);
        return r928120;
}

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. Using strategy rm

  3. Applied add-cbrt-cube41.4

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

  4. Applied add-cbrt-cube42.2

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

  5. Applied cbrt-undiv42.2

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

  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 2020042 +o rules:numerics
(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)))