Average Error: 15.4 → 0.0
Time: 13.0s
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 r19954362 = x;
        double r19954363 = y;
        double r19954364 = r19954362 - r19954363;
        double r19954365 = 2.0;
        double r19954366 = r19954362 * r19954365;
        double r19954367 = r19954366 * r19954363;
        double r19954368 = r19954364 / r19954367;
        return r19954368;
}
↓
double f(double x, double y) {
        double r19954369 = 0.5;
        double r19954370 = y;
        double r19954371 = r19954369 / r19954370;
        double r19954372 = x;
        double r19954373 = r19954369 / r19954372;
        double r19954374 = r19954371 - r19954373;
        return r19954374;
}

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

Original15.4
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 15.4

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

  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 2019171 +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)))