Average Error: 0.0 → 0.0
Time: 13.5s
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 r34557189 = x;
        double r34557190 = y;
        double r34557191 = r34557189 - r34557190;
        double r34557192 = r34557189 + r34557190;
        double r34557193 = r34557191 / r34557192;
        return r34557193;
}
↓
double f(double x, double y) {
        double r34557194 = x;
        double r34557195 = y;
        double r34557196 = r34557195 + r34557194;
        double r34557197 = r34557194 / r34557196;
        double r34557198 = 1.0;
        double r34557199 = r34557198 / r34557196;
        double r34557200 = r34557195 * r34557199;
        double r34557201 = r34557195 / r34557196;
        double r34557202 = r34557201 * r34557201;
        double r34557203 = r34557200 * r34557202;
        double r34557204 = cbrt(r34557203);
        double r34557205 = r34557197 - r34557204;
        return r34557205;
}

Error

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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)))