Average Error: 15.2 → 0.0
Time: 3.4s
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 r433496 = x;
        double r433497 = y;
        double r433498 = r433496 - r433497;
        double r433499 = 2.0;
        double r433500 = r433496 * r433499;
        double r433501 = r433500 * r433497;
        double r433502 = r433498 / r433501;
        return r433502;
}
↓
double f(double x, double y) {
        double r433503 = 1.0;
        double r433504 = 2.0;
        double r433505 = y;
        double r433506 = r433504 * r433505;
        double r433507 = r433503 / r433506;
        double r433508 = x;
        double r433509 = r433508 * r433504;
        double r433510 = r433503 / r433509;
        double r433511 = r433507 - r433510;
        return r433511;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.2
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 15.2

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

  3. Applied div-sub15.2

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

  4. Simplified11.2

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

  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 2020001 +o rules:numerics
(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)))