Average Error: 0.0 → 0.0
Time: 14.6s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\frac{x}{y + x} - \sqrt[3]{\left(y \cdot \frac{1}{y + x}\right) \cdot \left(\frac{y}{y + x} \cdot \frac{y}{y + x}\right)}\]
\frac{x - y}{x + y}
↓
\frac{x}{y + x} - \sqrt[3]{\left(y \cdot \frac{1}{y + x}\right) \cdot \left(\frac{y}{y + x} \cdot \frac{y}{y + x}\right)}
double f(double x, double y) {
        double r37259479 = x;
        double r37259480 = y;
        double r37259481 = r37259479 - r37259480;
        double r37259482 = r37259479 + r37259480;
        double r37259483 = r37259481 / r37259482;
        return r37259483;
}
↓
double f(double x, double y) {
        double r37259484 = x;
        double r37259485 = y;
        double r37259486 = r37259485 + r37259484;
        double r37259487 = r37259484 / r37259486;
        double r37259488 = 1.0;
        double r37259489 = r37259488 / r37259486;
        double r37259490 = r37259485 * r37259489;
        double r37259491 = r37259485 / r37259486;
        double r37259492 = r37259491 * r37259491;
        double r37259493 = r37259490 * r37259492;
        double r37259494 = cbrt(r37259493);
        double r37259495 = r37259487 - r37259494;
        return r37259495;
}

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 div-sub0.0

    \[\leadsto \color{blue}{\frac{x}{x + y} - \frac{y}{x + y}}\]
  4. Using strategy rm

  5. Applied add-cbrt-cube24.4

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

  6. Applied add-cbrt-cube28.1

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

  7. Applied cbrt-undiv28.1

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

  8. Simplified0.0

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

  10. Applied div-inv0.0

    \[\leadsto \frac{x}{x + y} - \sqrt[3]{\left(\frac{y}{x + y} \cdot \frac{y}{x + y}\right) \cdot \color{blue}{\left(y \cdot \frac{1}{x + y}\right)}}\]

  11. Final simplification0.0

    \[\leadsto \frac{x}{y + x} - \sqrt[3]{\left(y \cdot \frac{1}{y + x}\right) \cdot \left(\frac{y}{y + x} \cdot \frac{y}{y + x}\right)}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"

  :herbie-target
  (- (/ x (+ x y)) (/ y (+ x y)))

  (/ (- x y) (+ x y)))