Average Error: 15.1 → 0.0
Time: 21.6s
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 r24397363 = x;
        double r24397364 = y;
        double r24397365 = r24397363 - r24397364;
        double r24397366 = 2.0;
        double r24397367 = r24397363 * r24397366;
        double r24397368 = r24397367 * r24397364;
        double r24397369 = r24397365 / r24397368;
        return r24397369;
}
↓
double f(double x, double y) {
        double r24397370 = 0.5;
        double r24397371 = y;
        double r24397372 = r24397370 / r24397371;
        double r24397373 = x;
        double r24397374 = r24397370 / r24397373;
        double r24397375 = r24397372 - r24397374;
        return r24397375;
}

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

Original15.1
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 15.1

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

  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 2019174 
(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)))