Average Error: 14.9 → 0.0
Time: 2.1s
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 r529239 = x;
        double r529240 = y;
        double r529241 = r529239 + r529240;
        double r529242 = 2.0;
        double r529243 = r529239 * r529242;
        double r529244 = r529243 * r529240;
        double r529245 = r529241 / r529244;
        return r529245;
}
↓
double f(double x, double y) {
        double r529246 = 0.5;
        double r529247 = 1.0;
        double r529248 = y;
        double r529249 = r529247 / r529248;
        double r529250 = x;
        double r529251 = r529247 / r529250;
        double r529252 = r529249 + r529251;
        double r529253 = r529246 * r529252;
        return r529253;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.9
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program 14.9

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

  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 2019322 
(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)))