Average Error: 14.6 → 0.0
Time: 18.6s
Precision: 64
\[\frac{x - y}{\left(x \cdot 2.0\right) \cdot y}\]
↓
\[\frac{0.5}{y} - \frac{0.5}{x}\]
\frac{x - y}{\left(x \cdot 2.0\right) \cdot y}
↓
\frac{0.5}{y} - \frac{0.5}{x}
double f(double x, double y) {
        double r38561573 = x;
        double r38561574 = y;
        double r38561575 = r38561573 - r38561574;
        double r38561576 = 2.0;
        double r38561577 = r38561573 * r38561576;
        double r38561578 = r38561577 * r38561574;
        double r38561579 = r38561575 / r38561578;
        return r38561579;
}
↓
double f(double x, double y) {
        double r38561580 = 0.5;
        double r38561581 = y;
        double r38561582 = r38561580 / r38561581;
        double r38561583 = x;
        double r38561584 = r38561580 / r38561583;
        double r38561585 = r38561582 - r38561584;
        return r38561585;
}

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

Derivation

  1. Initial program 14.6

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

  2. Taylor expanded around 0 0.0

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

  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 2019158 
(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)))