Average Error: 15.4 → 0.0
Time: 5.7s
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 r21200103 = x;
        double r21200104 = y;
        double r21200105 = r21200103 + r21200104;
        double r21200106 = 2.0;
        double r21200107 = r21200103 * r21200106;
        double r21200108 = r21200107 * r21200104;
        double r21200109 = r21200105 / r21200108;
        return r21200109;
}
↓
double f(double x, double y) {
        double r21200110 = 0.5;
        double r21200111 = y;
        double r21200112 = r21200110 / r21200111;
        double r21200113 = x;
        double r21200114 = r21200110 / r21200113;
        double r21200115 = r21200112 + r21200114;
        return r21200115;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.4
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program 15.4

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

  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 2019172 +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)))