Average Error: 15.4 → 0.0
Time: 9.1s
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 r21712798 = x;
        double r21712799 = y;
        double r21712800 = r21712798 + r21712799;
        double r21712801 = 2.0;
        double r21712802 = r21712798 * r21712801;
        double r21712803 = r21712802 * r21712799;
        double r21712804 = r21712800 / r21712803;
        return r21712804;
}
↓
double f(double x, double y) {
        double r21712805 = 0.5;
        double r21712806 = y;
        double r21712807 = r21712805 / r21712806;
        double r21712808 = x;
        double r21712809 = r21712805 / r21712808;
        double r21712810 = r21712807 + r21712809;
        return r21712810;
}

Error

Bits error versus x

Bits error versus y

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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 +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)))