Average Error: 15.6 → 0.0
Time: 14.4s
Precision: 64
\[\frac{x - y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\frac{\frac{1}{2}}{y} - \frac{1}{x \cdot 2}\]
\frac{x - y}{\left(x \cdot 2\right) \cdot y}
↓
\frac{\frac{1}{2}}{y} - \frac{1}{x \cdot 2}
double f(double x, double y) {
        double r415345 = x;
        double r415346 = y;
        double r415347 = r415345 - r415346;
        double r415348 = 2.0;
        double r415349 = r415345 * r415348;
        double r415350 = r415349 * r415346;
        double r415351 = r415347 / r415350;
        return r415351;
}
↓
double f(double x, double y) {
        double r415352 = 1.0;
        double r415353 = 2.0;
        double r415354 = r415352 / r415353;
        double r415355 = y;
        double r415356 = r415354 / r415355;
        double r415357 = x;
        double r415358 = r415357 * r415353;
        double r415359 = r415352 / r415358;
        double r415360 = r415356 - r415359;
        return r415360;
}

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

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(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)))