Average Error: 15.3 → 0.0
Time: 9.0s
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 r24912102 = x;
        double r24912103 = y;
        double r24912104 = r24912102 - r24912103;
        double r24912105 = 2.0;
        double r24912106 = r24912102 * r24912105;
        double r24912107 = r24912106 * r24912103;
        double r24912108 = r24912104 / r24912107;
        return r24912108;
}
↓
double f(double x, double y) {
        double r24912109 = 0.5;
        double r24912110 = y;
        double r24912111 = r24912109 / r24912110;
        double r24912112 = x;
        double r24912113 = r24912109 / r24912112;
        double r24912114 = r24912111 - r24912113;
        return r24912114;
}

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. 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 2019170 
(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)))