Average Error: 0.0 → 0.0
Time: 3.9s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt[3]{{\left(\frac{x}{x + y}\right)}^{3}} - \frac{y}{x + y}\right)\right)\]
\frac{x - y}{x + y}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt[3]{{\left(\frac{x}{x + y}\right)}^{3}} - \frac{y}{x + y}\right)\right)
double f(double x, double y) {
        double r840259 = x;
        double r840260 = y;
        double r840261 = r840259 - r840260;
        double r840262 = r840259 + r840260;
        double r840263 = r840261 / r840262;
        return r840263;
}
↓
double f(double x, double y) {
        double r840264 = x;
        double r840265 = y;
        double r840266 = r840264 + r840265;
        double r840267 = r840264 / r840266;
        double r840268 = 3.0;
        double r840269 = pow(r840267, r840268);
        double r840270 = cbrt(r840269);
        double r840271 = r840265 / r840266;
        double r840272 = r840270 - r840271;
        double r840273 = expm1(r840272);
        double r840274 = log1p(r840273);
        return r840274;
}

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 div-sub0.0

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

  5. Applied add-cbrt-cube24.4

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

  6. Applied add-cbrt-cube28.2

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

  7. Applied cbrt-undiv28.2

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

  8. Simplified0.0

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

  10. Applied log1p-expm1-u0.0

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt[3]{{\left(\frac{x}{x + y}\right)}^{3}} - \frac{y}{x + y}\right)\right)}\]

  11. Final simplification0.0

    \[\leadsto \mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt[3]{{\left(\frac{x}{x + y}\right)}^{3}} - \frac{y}{x + y}\right)\right)\]

Reproduce

herbie shell --seed 2020064 +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)))