Average Error: 14.7 → 0.0
Time: 1.1s
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 r344640 = x;
        double r344641 = y;
        double r344642 = r344640 + r344641;
        double r344643 = 2.0;
        double r344644 = r344640 * r344643;
        double r344645 = r344644 * r344641;
        double r344646 = r344642 / r344645;
        return r344646;
}
↓
double f(double x, double y) {
        double r344647 = 0.5;
        double r344648 = 1.0;
        double r344649 = y;
        double r344650 = r344648 / r344649;
        double r344651 = x;
        double r344652 = r344648 / r344651;
        double r344653 = r344650 + r344652;
        double r344654 = r344647 * r344653;
        return r344654;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.7
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program 14.7

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

  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 2020003 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, C"
  :precision binary64

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

  (/ (+ x y) (* (* x 2) y)))