Average Error: 15.3 → 0.0
Time: 10.9s
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 r24740895 = x;
        double r24740896 = y;
        double r24740897 = r24740895 - r24740896;
        double r24740898 = 2.0;
        double r24740899 = r24740895 * r24740898;
        double r24740900 = r24740899 * r24740896;
        double r24740901 = r24740897 / r24740900;
        return r24740901;
}
↓
double f(double x, double y) {
        double r24740902 = 0.5;
        double r24740903 = y;
        double r24740904 = r24740902 / r24740903;
        double r24740905 = x;
        double r24740906 = r24740902 / r24740905;
        double r24740907 = r24740904 - r24740906;
        return r24740907;
}

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 +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)))