Average Error: 15.6 → 0.0
Time: 1.5s
Precision: 64
\[\frac{x - y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\frac{1}{2 \cdot y} - \frac{1}{x \cdot 2}\]
\frac{x - y}{\left(x \cdot 2\right) \cdot y}
↓
\frac{1}{2 \cdot y} - \frac{1}{x \cdot 2}
double f(double x, double y) {
        double r501382 = x;
        double r501383 = y;
        double r501384 = r501382 - r501383;
        double r501385 = 2.0;
        double r501386 = r501382 * r501385;
        double r501387 = r501386 * r501383;
        double r501388 = r501384 / r501387;
        return r501388;
}
↓
double f(double x, double y) {
        double r501389 = 1.0;
        double r501390 = 2.0;
        double r501391 = y;
        double r501392 = r501390 * r501391;
        double r501393 = r501389 / r501392;
        double r501394 = x;
        double r501395 = r501394 * r501390;
        double r501396 = r501389 / r501395;
        double r501397 = r501393 - r501396;
        return r501397;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.6
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 15.6

    \[\frac{x - y}{\left(x \cdot 2\right) \cdot y}\]
  2. Using strategy rm

  3. Applied div-sub15.6

    \[\leadsto \color{blue}{\frac{x}{\left(x \cdot 2\right) \cdot y} - \frac{y}{\left(x \cdot 2\right) \cdot y}}\]

  4. Simplified11.7

    \[\leadsto \color{blue}{\frac{1}{2 \cdot y}} - \frac{y}{\left(x \cdot 2\right) \cdot y}\]

  5. Simplified0.0

    \[\leadsto \frac{1}{2 \cdot y} - \color{blue}{\frac{1}{x \cdot 2}}\]

  6. Final simplification0.0

    \[\leadsto \frac{1}{2 \cdot y} - \frac{1}{x \cdot 2}\]

Reproduce

herbie shell --seed 2020100 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, B"
  :precision binary64

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

  (/ (- x y) (* (* x 2) y)))