Average Error: 15.7 → 0.0
Time: 1.4s
Precision: 64
\[\frac{x - y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[0.5 \cdot \left(\frac{1}{y} - \frac{1}{x}\right)\]
\frac{x - y}{\left(x \cdot 2\right) \cdot y}
↓
0.5 \cdot \left(\frac{1}{y} - \frac{1}{x}\right)
double f(double x, double y) {
        double r562866 = x;
        double r562867 = y;
        double r562868 = r562866 - r562867;
        double r562869 = 2.0;
        double r562870 = r562866 * r562869;
        double r562871 = r562870 * r562867;
        double r562872 = r562868 / r562871;
        return r562872;
}
↓
double f(double x, double y) {
        double r562873 = 0.5;
        double r562874 = 1.0;
        double r562875 = y;
        double r562876 = r562874 / r562875;
        double r562877 = x;
        double r562878 = r562874 / r562877;
        double r562879 = r562876 - r562878;
        double r562880 = r562873 * r562879;
        return r562880;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.7
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 15.7

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

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{0.5 \cdot \frac{1}{y} - 0.5 \cdot \frac{1}{x}}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{0.5 \cdot \left(\frac{1}{y} - \frac{1}{x}\right)}\]

  4. Final simplification0.0

    \[\leadsto 0.5 \cdot \left(\frac{1}{y} - \frac{1}{x}\right)\]

Reproduce

herbie shell --seed 2020036 
(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)))