Average Error: 15.6 → 0.0
Time: 1.7s
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 r2055564 = x;
        double r2055565 = y;
        double r2055566 = r2055564 - r2055565;
        double r2055567 = 2.0;
        double r2055568 = r2055564 * r2055567;
        double r2055569 = r2055568 * r2055565;
        double r2055570 = r2055566 / r2055569;
        return r2055570;
}
↓
double f(double x, double y) {
        double r2055571 = 1.0;
        double r2055572 = 2.0;
        double r2055573 = y;
        double r2055574 = r2055572 * r2055573;
        double r2055575 = r2055571 / r2055574;
        double r2055576 = x;
        double r2055577 = r2055576 * r2055572;
        double r2055578 = r2055571 / r2055577;
        double r2055579 = r2055575 - r2055578;
        return r2055579;
}

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. Simplified11.9

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

  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 2020047 +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)))