Average Error: 15.6 → 0.0
Time: 16.5s
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 r433665 = x;
        double r433666 = y;
        double r433667 = r433665 - r433666;
        double r433668 = 2.0;
        double r433669 = r433665 * r433668;
        double r433670 = r433669 * r433666;
        double r433671 = r433667 / r433670;
        return r433671;
}
↓
double f(double x, double y) {
        double r433672 = 0.5;
        double r433673 = y;
        double r433674 = r433672 / r433673;
        double r433675 = x;
        double r433676 = r433672 / r433675;
        double r433677 = r433674 - r433676;
        return r433677;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original15.6
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 15.6

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

  2. Simplified7.8

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

  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 2019196 +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)))