Average Error: 15.6 → 0.0
Time: 1.9s
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 r522983 = x;
        double r522984 = y;
        double r522985 = r522983 - r522984;
        double r522986 = 2.0;
        double r522987 = r522983 * r522986;
        double r522988 = r522987 * r522984;
        double r522989 = r522985 / r522988;
        return r522989;
}
↓
double f(double x, double y) {
        double r522990 = 0.5;
        double r522991 = 1.0;
        double r522992 = y;
        double r522993 = r522991 / r522992;
        double r522994 = x;
        double r522995 = r522991 / r522994;
        double r522996 = r522993 - r522995;
        double r522997 = r522990 * r522996;
        return r522997;
}

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. 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 2020056 +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)))