Average Error: 14.9 → 0.0
Time: 2.2s
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 r7871300 = x;
        double r7871301 = y;
        double r7871302 = r7871300 - r7871301;
        double r7871303 = 2.0;
        double r7871304 = r7871300 * r7871303;
        double r7871305 = r7871304 * r7871301;
        double r7871306 = r7871302 / r7871305;
        return r7871306;
}
↓
double f(double x, double y) {
        double r7871307 = 0.5;
        double r7871308 = y;
        double r7871309 = r7871307 / r7871308;
        double r7871310 = x;
        double r7871311 = r7871307 / r7871310;
        double r7871312 = r7871309 - r7871311;
        return r7871312;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.9
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 14.9

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

  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 2019156 +o rules:numerics
(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)))