Average Error: 0.0 → 0.0
Time: 13.7s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\frac{\frac{x}{y + x} \cdot \frac{x}{y + x} - \log \left({\left(e^{\frac{y}{y + x}}\right)}^{\left(\frac{y}{y + x}\right)}\right)}{\frac{x}{y + x} + \frac{y}{y + x}}\]
\frac{x - y}{x + y}
↓
\frac{\frac{x}{y + x} \cdot \frac{x}{y + x} - \log \left({\left(e^{\frac{y}{y + x}}\right)}^{\left(\frac{y}{y + x}\right)}\right)}{\frac{x}{y + x} + \frac{y}{y + x}}
double f(double x, double y) {
        double r665695 = x;
        double r665696 = y;
        double r665697 = r665695 - r665696;
        double r665698 = r665695 + r665696;
        double r665699 = r665697 / r665698;
        return r665699;
}
↓
double f(double x, double y) {
        double r665700 = x;
        double r665701 = y;
        double r665702 = r665701 + r665700;
        double r665703 = r665700 / r665702;
        double r665704 = r665703 * r665703;
        double r665705 = r665701 / r665702;
        double r665706 = exp(r665705);
        double r665707 = pow(r665706, r665705);
        double r665708 = log(r665707);
        double r665709 = r665704 - r665708;
        double r665710 = r665703 + r665705;
        double r665711 = r665709 / r665710;
        return r665711;
}

Error

Bits error versus x

Bits error versus y

Try it out

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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. Simplified0.0

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

  4. Applied div-sub0.0

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

  6. Applied flip--0.0

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

  7. Simplified0.0

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

  9. Applied add-log-exp0.0

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

  10. Simplified0.0

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

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 2019195 
(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)))