Average Error: 0.0 → 0.0
Time: 743.0ms
Precision: 64
\[\frac{x - y}{x}\]
↓
\[1 - \frac{y}{x}\]
\frac{x - y}{x}
↓
1 - \frac{y}{x}
double f(double x, double y) {
        double r810686 = x;
        double r810687 = y;
        double r810688 = r810686 - r810687;
        double r810689 = r810688 / r810686;
        return r810689;
}
↓
double f(double x, double y) {
        double r810690 = 1.0;
        double r810691 = y;
        double r810692 = x;
        double r810693 = r810691 / r810692;
        double r810694 = r810690 - r810693;
        return r810694;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.0
Target0.0
Herbie0.0
\[1 - \frac{y}{x}\]

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{x}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.0

    \[\leadsto \frac{x - y}{\color{blue}{1 \cdot x}}\]

  4. Applied *-un-lft-identity0.0

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

  5. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{1}{1} \cdot \frac{x - y}{x}}\]

  6. Simplified0.0

    \[\leadsto \color{blue}{1} \cdot \frac{x - y}{x}\]

  7. Simplified0.0

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

  8. Final simplification0.0

    \[\leadsto 1 - \frac{y}{x}\]

Reproduce

herbie shell --seed 2020081 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- 1 (/ y x))

  (/ (- x y) x))