Average Error: 15.3 → 0.0
Time: 20.3s
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 r416515 = x;
        double r416516 = y;
        double r416517 = r416515 - r416516;
        double r416518 = 2.0;
        double r416519 = r416515 * r416518;
        double r416520 = r416519 * r416516;
        double r416521 = r416517 / r416520;
        return r416521;
}
↓
double f(double x, double y) {
        double r416522 = 0.5;
        double r416523 = y;
        double r416524 = r416522 / r416523;
        double r416525 = x;
        double r416526 = r416522 / r416525;
        double r416527 = r416524 - r416526;
        return r416527;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original15.3
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 15.3

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

  2. Simplified7.4

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

  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 2019194 
(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)))