Average Error: 14.9 → 0.0
Time: 4.8s
Precision: 64
\[\frac{x + y}{\left(x \cdot 2.0\right) \cdot y}\]
↓
\[\frac{0.5}{x} + \frac{0.5}{y}\]
\frac{x + y}{\left(x \cdot 2.0\right) \cdot y}
↓
\frac{0.5}{x} + \frac{0.5}{y}
double f(double x, double y) {
        double r8765477 = x;
        double r8765478 = y;
        double r8765479 = r8765477 + r8765478;
        double r8765480 = 2.0;
        double r8765481 = r8765477 * r8765480;
        double r8765482 = r8765481 * r8765478;
        double r8765483 = r8765479 / r8765482;
        return r8765483;
}
↓
double f(double x, double y) {
        double r8765484 = 0.5;
        double r8765485 = x;
        double r8765486 = r8765484 / r8765485;
        double r8765487 = y;
        double r8765488 = r8765484 / r8765487;
        double r8765489 = r8765486 + r8765488;
        return r8765489;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.9
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program 14.9

    \[\frac{x + y}{\left(x \cdot 2.0\right) \cdot y}\]

  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

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

  4. Final simplification0.0

    \[\leadsto \frac{0.5}{x} + \frac{0.5}{y}\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(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)))