Average Error: 15.9 → 0.0
Time: 20.9s
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 r387342 = x;
        double r387343 = y;
        double r387344 = r387342 - r387343;
        double r387345 = 2.0;
        double r387346 = r387342 * r387345;
        double r387347 = r387346 * r387343;
        double r387348 = r387344 / r387347;
        return r387348;
}
↓
double f(double x, double y) {
        double r387349 = 0.5;
        double r387350 = y;
        double r387351 = r387349 / r387350;
        double r387352 = x;
        double r387353 = r387349 / r387352;
        double r387354 = r387351 - r387353;
        return r387354;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

Original15.9
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 15.9

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

  2. Simplified8.4

    \[\leadsto \color{blue}{\frac{\frac{x - y}{x}}{2 \cdot y}}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{0.5 \cdot \frac{1}{y} - 0.5 \cdot \frac{1}{x}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{\frac{0.5}{y} - \frac{0.5}{x}}\]

  5. Final simplification0.0

    \[\leadsto \frac{0.5}{y} - \frac{0.5}{x}\]

Reproduce

herbie shell --seed 2019195 
(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)))