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 r741302 = x;
        double r741303 = y;
        double r741304 = r741302 - r741303;
        double r741305 = r741302 + r741303;
        double r741306 = r741304 / r741305;
        return r741306;
}
↓
double f(double x, double y) {
        double r741307 = x;
        double r741308 = y;
        double r741309 = r741308 + r741307;
        double r741310 = r741307 / r741309;
        double r741311 = 3.0;
        double r741312 = pow(r741310, r741311);
        double r741313 = r741308 / r741309;
        double r741314 = pow(r741313, r741311);
        double r741315 = r741312 - r741314;
        double r741316 = r741310 + r741313;
        double r741317 = r741316 * r741313;
        double r741318 = r741310 * r741310;
        double r741319 = r741317 + r741318;
        double r741320 = r741315 / r741319;
        return r741320;
}

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)))