Average Error: 15.1 → 0.0
Time: 18.8s
Precision: 64
\[\frac{x - y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\frac{0.5}{y} - \frac{0.5}{x}\]
\frac{x - y}{\left(x \cdot 2\right) \cdot y}
↓
\frac{0.5}{y} - \frac{0.5}{x}
double f(double x, double y) {
        double r22464812 = x;
        double r22464813 = y;
        double r22464814 = r22464812 - r22464813;
        double r22464815 = 2.0;
        double r22464816 = r22464812 * r22464815;
        double r22464817 = r22464816 * r22464813;
        double r22464818 = r22464814 / r22464817;
        return r22464818;
}
↓
double f(double x, double y) {
        double r22464819 = 0.5;
        double r22464820 = y;
        double r22464821 = r22464819 / r22464820;
        double r22464822 = x;
        double r22464823 = r22464819 / r22464822;
        double r22464824 = r22464821 - r22464823;
        return r22464824;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

Original15.1
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 15.1

    \[\frac{x - y}{\left(x \cdot 2\right) \cdot y}\]

  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 2019179 +o rules:numerics
(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)))