Average Error: 14.6 → 0.0
Time: 4.9s
Precision: 64
\[\frac{x - y}{\left(x \cdot 2.0\right) \cdot y}\]
↓
\[\frac{0.5}{y} - \frac{0.5}{x}\]
\frac{x - y}{\left(x \cdot 2.0\right) \cdot y}
↓
\frac{0.5}{y} - \frac{0.5}{x}
double f(double x, double y) {
        double r27739126 = x;
        double r27739127 = y;
        double r27739128 = r27739126 - r27739127;
        double r27739129 = 2.0;
        double r27739130 = r27739126 * r27739129;
        double r27739131 = r27739130 * r27739127;
        double r27739132 = r27739128 / r27739131;
        return r27739132;
}
↓
double f(double x, double y) {
        double r27739133 = 0.5;
        double r27739134 = y;
        double r27739135 = r27739133 / r27739134;
        double r27739136 = x;
        double r27739137 = r27739133 / r27739136;
        double r27739138 = r27739135 - r27739137;
        return r27739138;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.6
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 14.6

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

  2. Taylor expanded around 0 0.0

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

  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 2019163 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, B"

  :herbie-target
  (- (/ 0.5 y) (/ 0.5 x))

  (/ (- x y) (* (* x 2.0) y)))