Average Error: 15.0 → 0.0
Time: 8.4s
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 r529272 = x;
        double r529273 = y;
        double r529274 = r529272 + r529273;
        double r529275 = 2.0;
        double r529276 = r529272 * r529275;
        double r529277 = r529276 * r529273;
        double r529278 = r529274 / r529277;
        return r529278;
}
↓
double f(double x, double y) {
        double r529279 = 0.5;
        double r529280 = y;
        double r529281 = r529279 / r529280;
        double r529282 = x;
        double r529283 = r529279 / r529282;
        double r529284 = r529281 + r529283;
        return r529284;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 15.0

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

  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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(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)))