Average Error: 14.9 → 0.0
Time: 1.9s
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 r10597383 = x;
        double r10597384 = y;
        double r10597385 = r10597383 - r10597384;
        double r10597386 = 2.0;
        double r10597387 = r10597383 * r10597386;
        double r10597388 = r10597387 * r10597384;
        double r10597389 = r10597385 / r10597388;
        return r10597389;
}
↓
double f(double x, double y) {
        double r10597390 = 0.5;
        double r10597391 = y;
        double r10597392 = r10597390 / r10597391;
        double r10597393 = x;
        double r10597394 = r10597390 / r10597393;
        double r10597395 = r10597392 - r10597394;
        return r10597395;
}

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

Original14.9
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 14.9

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

  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 2019156 
(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)))