Average Error: 0.0 → 0.1
Time: 17.8s
Precision: 64
\[\frac{x - y}{2 - \left(x + y\right)}\]
↓
\[\frac{1}{\frac{2}{x} - \left(1 + \frac{y}{x}\right)} - \frac{y}{2 - \left(x + y\right)}\]
\frac{x - y}{2 - \left(x + y\right)}
↓
\frac{1}{\frac{2}{x} - \left(1 + \frac{y}{x}\right)} - \frac{y}{2 - \left(x + y\right)}
double f(double x, double y) {
        double r634511 = x;
        double r634512 = y;
        double r634513 = r634511 - r634512;
        double r634514 = 2.0;
        double r634515 = r634511 + r634512;
        double r634516 = r634514 - r634515;
        double r634517 = r634513 / r634516;
        return r634517;
}
↓
double f(double x, double y) {
        double r634518 = 1.0;
        double r634519 = 2.0;
        double r634520 = x;
        double r634521 = r634519 / r634520;
        double r634522 = y;
        double r634523 = r634522 / r634520;
        double r634524 = r634518 + r634523;
        double r634525 = r634521 - r634524;
        double r634526 = r634518 / r634525;
        double r634527 = r634520 + r634522;
        double r634528 = r634519 - r634527;
        double r634529 = r634522 / r634528;
        double r634530 = r634526 - r634529;
        return r634530;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.0
Target0.0
Herbie0.1
\[\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)}\]

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{2 - \left(x + y\right)}\]
  2. Using strategy rm

  3. Applied div-sub0.0

    \[\leadsto \color{blue}{\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)}}\]
  4. Using strategy rm

  5. Applied clear-num0.0

    \[\leadsto \color{blue}{\frac{1}{\frac{2 - \left(x + y\right)}{x}}} - \frac{y}{2 - \left(x + y\right)}\]

  6. Taylor expanded around 0 0.1

    \[\leadsto \frac{1}{\color{blue}{2 \cdot \frac{1}{x} - \left(1 + \frac{y}{x}\right)}} - \frac{y}{2 - \left(x + y\right)}\]

  7. Simplified0.1

    \[\leadsto \frac{1}{\color{blue}{\frac{2}{x} - \left(1 + \frac{y}{x}\right)}} - \frac{y}{2 - \left(x + y\right)}\]

  8. Final simplification0.1

    \[\leadsto \frac{1}{\frac{2}{x} - \left(1 + \frac{y}{x}\right)} - \frac{y}{2 - \left(x + y\right)}\]

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :herbie-target
  (- (/ x (- 2 (+ x y))) (/ y (- 2 (+ x y))))

  (/ (- x y) (- 2 (+ x y))))