Average Error: 15.6 → 0.0
Time: 4.2s
Precision: 64
\[\frac{x + y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\frac{0.5}{x} + \frac{0.5}{y}\]
\frac{x + y}{\left(x \cdot 2\right) \cdot y}
↓
\frac{0.5}{x} + \frac{0.5}{y}
double f(double x, double y) {
        double r431515 = x;
        double r431516 = y;
        double r431517 = r431515 + r431516;
        double r431518 = 2.0;
        double r431519 = r431515 * r431518;
        double r431520 = r431519 * r431516;
        double r431521 = r431517 / r431520;
        return r431521;
}
↓
double f(double x, double y) {
        double r431522 = 0.5;
        double r431523 = x;
        double r431524 = r431522 / r431523;
        double r431525 = y;
        double r431526 = r431522 / r431525;
        double r431527 = r431524 + r431526;
        return r431527;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

Original15.6
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program 15.6

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

  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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019198 
(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)))