Average Error: 14.6 → 0.0
Time: 7.6s
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 r20868967 = x;
        double r20868968 = y;
        double r20868969 = r20868967 - r20868968;
        double r20868970 = 2.0;
        double r20868971 = r20868967 * r20868970;
        double r20868972 = r20868971 * r20868968;
        double r20868973 = r20868969 / r20868972;
        return r20868973;
}
↓
double f(double x, double y) {
        double r20868974 = 0.5;
        double r20868975 = y;
        double r20868976 = r20868974 / r20868975;
        double r20868977 = x;
        double r20868978 = r20868974 / r20868977;
        double r20868979 = r20868976 - r20868978;
        return r20868979;
}

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

Original14.6
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 14.6

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

  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 2019163 +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)))