Average Error: 0.0 → 0.0
Time: 13.2s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\frac{{\left(\frac{x}{y + x}\right)}^{3} - {\left(\frac{y}{y + x}\right)}^{3}}{\left(\frac{x}{y + x} + \frac{y}{y + x}\right) \cdot \frac{y}{y + x} + \frac{x}{y + x} \cdot \frac{x}{y + x}}\]
\frac{x - y}{x + y}
↓
\frac{{\left(\frac{x}{y + x}\right)}^{3} - {\left(\frac{y}{y + x}\right)}^{3}}{\left(\frac{x}{y + x} + \frac{y}{y + x}\right) \cdot \frac{y}{y + x} + \frac{x}{y + x} \cdot \frac{x}{y + x}}
double f(double x, double y) {
        double r629685 = x;
        double r629686 = y;
        double r629687 = r629685 - r629686;
        double r629688 = r629685 + r629686;
        double r629689 = r629687 / r629688;
        return r629689;
}
↓
double f(double x, double y) {
        double r629690 = x;
        double r629691 = y;
        double r629692 = r629691 + r629690;
        double r629693 = r629690 / r629692;
        double r629694 = 3.0;
        double r629695 = pow(r629693, r629694);
        double r629696 = r629691 / r629692;
        double r629697 = pow(r629696, r629694);
        double r629698 = r629695 - r629697;
        double r629699 = r629693 + r629696;
        double r629700 = r629699 * r629696;
        double r629701 = r629693 * r629693;
        double r629702 = r629700 + r629701;
        double r629703 = r629698 / r629702;
        return r629703;
}

Error

Bits error versus x

Bits error versus y

Try it out

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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. Simplified0.0

    \[\leadsto \color{blue}{\frac{x}{y + x}} - \frac{y}{x + y}\]

  5. Simplified0.0

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

  7. Applied flip3--0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 
(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)))