Average Error: 14.6 → 0.0
Time: 7.0s
Precision: 64
\[\frac{x + y}{\left(x \cdot 2.0\right) \cdot y}\]
↓
\[\frac{0.5}{x} + \frac{0.5}{y}\]
\frac{x + y}{\left(x \cdot 2.0\right) \cdot y}
↓
\frac{0.5}{x} + \frac{0.5}{y}
double f(double x, double y) {
        double r24314418 = x;
        double r24314419 = y;
        double r24314420 = r24314418 + r24314419;
        double r24314421 = 2.0;
        double r24314422 = r24314418 * r24314421;
        double r24314423 = r24314422 * r24314419;
        double r24314424 = r24314420 / r24314423;
        return r24314424;
}
↓
double f(double x, double y) {
        double r24314425 = 0.5;
        double r24314426 = x;
        double r24314427 = r24314425 / r24314426;
        double r24314428 = y;
        double r24314429 = r24314425 / r24314428;
        double r24314430 = r24314427 + r24314429;
        return r24314430;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.6
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program 14.6

    \[\frac{x + y}{\left(x \cdot 2.0\right) \cdot y}\]

  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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019158 +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)))