Average Error: 15.3 → 0.0
Time: 15.8s
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 r25613576 = x;
        double r25613577 = y;
        double r25613578 = r25613576 + r25613577;
        double r25613579 = 2.0;
        double r25613580 = r25613576 * r25613579;
        double r25613581 = r25613580 * r25613577;
        double r25613582 = r25613578 / r25613581;
        return r25613582;
}
↓
double f(double x, double y) {
        double r25613583 = 0.5;
        double r25613584 = x;
        double r25613585 = r25613583 / r25613584;
        double r25613586 = y;
        double r25613587 = r25613583 / r25613586;
        double r25613588 = r25613585 + r25613587;
        return r25613588;
}

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

Original15.3
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program 15.3

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

  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 2019165 
(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)))