Average Error: 15.0 → 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 r388610 = x;
        double r388611 = y;
        double r388612 = r388610 - r388611;
        double r388613 = 2.0;
        double r388614 = r388610 * r388613;
        double r388615 = r388614 * r388611;
        double r388616 = r388612 / r388615;
        return r388616;
}
↓
double f(double x, double y) {
        double r388617 = 1.0;
        double r388618 = 2.0;
        double r388619 = r388617 / r388618;
        double r388620 = y;
        double r388621 = r388619 / r388620;
        double r388622 = x;
        double r388623 = r388622 * r388618;
        double r388624 = r388617 / r388623;
        double r388625 = r388621 - r388624;
        return r388625;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 15.0

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

  3. Applied div-sub15.0

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

  4. Simplified11.0

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

  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 2019208 
(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)))