Average Error: 15.2 → 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 r96528673 = x;
        double r96528674 = y;
        double r96528675 = r96528673 + r96528674;
        double r96528676 = 2.0;
        double r96528677 = r96528673 * r96528676;
        double r96528678 = r96528677 * r96528674;
        double r96528679 = r96528675 / r96528678;
        return r96528679;
}
↓
double f(double x, double y) {
        double r96528680 = 0.5;
        double r96528681 = y;
        double r96528682 = r96528680 / r96528681;
        double r96528683 = x;
        double r96528684 = r96528680 / r96528683;
        double r96528685 = r96528682 + r96528684;
        return r96528685;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

Original15.2
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program 15.2

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

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{0.5 \cdot \frac{1}{x} + 0.5 \cdot \frac{1}{y}}\]

  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 2019173 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, C"

  :herbie-target
  (+ (/ 0.5 x) (/ 0.5 y))

  (/ (+ x y) (* (* x 2.0) y)))