Average Error: 14.5 → 0.0
Time: 11.1s
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 r23491674 = x;
        double r23491675 = y;
        double r23491676 = r23491674 + r23491675;
        double r23491677 = 2.0;
        double r23491678 = r23491674 * r23491677;
        double r23491679 = r23491678 * r23491675;
        double r23491680 = r23491676 / r23491679;
        return r23491680;
}
↓
double f(double x, double y) {
        double r23491681 = 0.5;
        double r23491682 = x;
        double r23491683 = r23491681 / r23491682;
        double r23491684 = y;
        double r23491685 = r23491681 / r23491684;
        double r23491686 = r23491683 + r23491685;
        return r23491686;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.5
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program 14.5

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

  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 2019162 +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)))