Average Error: 14.7 → 0.0
Time: 19.5s
Precision: 64
\[\frac{x - y}{\left(x \cdot 2.0\right) \cdot y}\]
↓
\[\frac{0.5}{y} - \frac{0.5}{x}\]
\frac{x - y}{\left(x \cdot 2.0\right) \cdot y}
↓
\frac{0.5}{y} - \frac{0.5}{x}
double f(double x, double y) {
        double r22678708 = x;
        double r22678709 = y;
        double r22678710 = r22678708 - r22678709;
        double r22678711 = 2.0;
        double r22678712 = r22678708 * r22678711;
        double r22678713 = r22678712 * r22678709;
        double r22678714 = r22678710 / r22678713;
        return r22678714;
}
↓
double f(double x, double y) {
        double r22678715 = 0.5;
        double r22678716 = y;
        double r22678717 = r22678715 / r22678716;
        double r22678718 = x;
        double r22678719 = r22678715 / r22678718;
        double r22678720 = r22678717 - r22678719;
        return r22678720;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

Original14.7
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 14.7

    \[\frac{x - y}{\left(x \cdot 2.0\right) \cdot y}\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{0.5 \cdot \frac{1}{y} - 0.5 \cdot \frac{1}{x}}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{\frac{0.5}{y} - \frac{0.5}{x}}\]

  4. Final simplification0.0

    \[\leadsto \frac{0.5}{y} - \frac{0.5}{x}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, B"

  :herbie-target
  (- (/ 0.5 y) (/ 0.5 x))

  (/ (- x y) (* (* x 2.0) y)))