Average Error: 15.4 → 0.0
Time: 9.4s
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 r30166739 = x;
        double r30166740 = y;
        double r30166741 = r30166739 + r30166740;
        double r30166742 = 2.0;
        double r30166743 = r30166739 * r30166742;
        double r30166744 = r30166743 * r30166740;
        double r30166745 = r30166741 / r30166744;
        return r30166745;
}
↓
double f(double x, double y) {
        double r30166746 = 0.5;
        double r30166747 = y;
        double r30166748 = r30166746 / r30166747;
        double r30166749 = x;
        double r30166750 = r30166746 / r30166749;
        double r30166751 = r30166748 + r30166750;
        return r30166751;
}

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

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

Derivation

  1. Initial program 15.4

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

  2. Taylor expanded around 0 0.0

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

  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 2019169 
(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)))