Average Error: 15.5 → 0.0
Time: 11.7s
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 r294793 = x;
        double r294794 = y;
        double r294795 = r294793 - r294794;
        double r294796 = 2.0;
        double r294797 = r294793 * r294796;
        double r294798 = r294797 * r294794;
        double r294799 = r294795 / r294798;
        return r294799;
}
↓
double f(double x, double y) {
        double r294800 = 0.5;
        double r294801 = y;
        double r294802 = r294800 / r294801;
        double r294803 = x;
        double r294804 = r294800 / r294803;
        double r294805 = r294802 - r294804;
        return r294805;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.5
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 15.5

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

  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 2019303 +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)))