Average Error: 15.6 → 0.0
Time: 13.9s
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 r522817 = x;
        double r522818 = y;
        double r522819 = r522817 - r522818;
        double r522820 = 2.0;
        double r522821 = r522817 * r522820;
        double r522822 = r522821 * r522818;
        double r522823 = r522819 / r522822;
        return r522823;
}
↓
double f(double x, double y) {
        double r522824 = 0.5;
        double r522825 = y;
        double r522826 = r522824 / r522825;
        double r522827 = x;
        double r522828 = r522824 / r522827;
        double r522829 = r522826 - r522828;
        return r522829;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

Original15.6
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 15.6

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

  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 2019323 +o rules:numerics
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, B"
  :precision binary64

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

  (/ (- x y) (* (* x 2) y)))