Average Error: 15.4 → 0.0
Time: 2.0s
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 r11052332 = x;
        double r11052333 = y;
        double r11052334 = r11052332 - r11052333;
        double r11052335 = 2.0;
        double r11052336 = r11052332 * r11052335;
        double r11052337 = r11052336 * r11052333;
        double r11052338 = r11052334 / r11052337;
        return r11052338;
}
↓
double f(double x, double y) {
        double r11052339 = 0.5;
        double r11052340 = y;
        double r11052341 = r11052339 / r11052340;
        double r11052342 = x;
        double r11052343 = r11052339 / r11052342;
        double r11052344 = r11052341 - r11052343;
        return r11052344;
}

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
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 15.4

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

  2. Taylor expanded around 0 0.0

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

  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 2019171 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, B"

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

  (/ (- x y) (* (* x 2.0) y)))