Average Error: 14.9 → 0.0
Time: 30.3s
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 r27053354 = x;
        double r27053355 = y;
        double r27053356 = r27053354 - r27053355;
        double r27053357 = 2.0;
        double r27053358 = r27053354 * r27053357;
        double r27053359 = r27053358 * r27053355;
        double r27053360 = r27053356 / r27053359;
        return r27053360;
}
↓
double f(double x, double y) {
        double r27053361 = 0.5;
        double r27053362 = y;
        double r27053363 = r27053361 / r27053362;
        double r27053364 = x;
        double r27053365 = r27053361 / r27053364;
        double r27053366 = r27053363 - r27053365;
        return r27053366;
}

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

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

  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 2019168 +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)))