Average Error: 15.3 → 0.0
Time: 5.9s
Precision: 64
\[\frac{x + y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\frac{0.5}{y} + \frac{0.5}{x}\]
\frac{x + y}{\left(x \cdot 2\right) \cdot y}
↓
\frac{0.5}{y} + \frac{0.5}{x}
double f(double x, double y) {
        double r27542640 = x;
        double r27542641 = y;
        double r27542642 = r27542640 + r27542641;
        double r27542643 = 2.0;
        double r27542644 = r27542640 * r27542643;
        double r27542645 = r27542644 * r27542641;
        double r27542646 = r27542642 / r27542645;
        return r27542646;
}
↓
double f(double x, double y) {
        double r27542647 = 0.5;
        double r27542648 = y;
        double r27542649 = r27542647 / r27542648;
        double r27542650 = x;
        double r27542651 = r27542647 / r27542650;
        double r27542652 = r27542649 + r27542651;
        return r27542652;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.3
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program 15.3

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

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

    \[\leadsto \color{blue}{\frac{0.5}{y} + \frac{0.5}{x}}\]

  4. Final simplification0.0

    \[\leadsto \frac{0.5}{y} + \frac{0.5}{x}\]

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, C"

  :herbie-target
  (+ (/ 0.5 x) (/ 0.5 y))

  (/ (+ x y) (* (* x 2.0) y)))