Average Error: 15.4 → 0.0
Time: 7.6s
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 r19706938 = x;
        double r19706939 = y;
        double r19706940 = r19706938 - r19706939;
        double r19706941 = 2.0;
        double r19706942 = r19706938 * r19706941;
        double r19706943 = r19706942 * r19706939;
        double r19706944 = r19706940 / r19706943;
        return r19706944;
}
↓
double f(double x, double y) {
        double r19706945 = 0.5;
        double r19706946 = y;
        double r19706947 = r19706945 / r19706946;
        double r19706948 = x;
        double r19706949 = r19706945 / r19706948;
        double r19706950 = r19706947 - r19706949;
        return r19706950;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original15.4
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 15.4

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

  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 2019169 +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)))