Average Error: 0.0 → 0.0
Time: 7.4s
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 r1089477 = x;
        double r1089478 = y;
        double r1089479 = r1089477 - r1089478;
        double r1089480 = r1089477 + r1089478;
        double r1089481 = r1089479 / r1089480;
        return r1089481;
}
↓
double f(double x, double y) {
        double r1089482 = x;
        double r1089483 = y;
        double r1089484 = r1089482 - r1089483;
        double r1089485 = r1089482 + r1089483;
        double r1089486 = r1089484 / r1089485;
        double r1089487 = 3.0;
        double r1089488 = pow(r1089486, r1089487);
        double r1089489 = cbrt(r1089488);
        return r1089489;
}

Error

Bits error versus x

Bits error versus y

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Results

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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)))