Average Error: 15.6 → 0.0
Time: 2.0s
Precision: 64
\[\frac{x - y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\frac{1}{2} \cdot \left(\frac{1}{y} - \frac{1}{x}\right)\]
\frac{x - y}{\left(x \cdot 2\right) \cdot y}
↓
\frac{1}{2} \cdot \left(\frac{1}{y} - \frac{1}{x}\right)
double f(double x, double y) {
        double r427447 = x;
        double r427448 = y;
        double r427449 = r427447 - r427448;
        double r427450 = 2.0;
        double r427451 = r427447 * r427450;
        double r427452 = r427451 * r427448;
        double r427453 = r427449 / r427452;
        return r427453;
}
↓
double f(double x, double y) {
        double r427454 = 1.0;
        double r427455 = 2.0;
        double r427456 = r427454 / r427455;
        double r427457 = 1.0;
        double r427458 = y;
        double r427459 = r427457 / r427458;
        double r427460 = x;
        double r427461 = r427457 / r427460;
        double r427462 = r427459 - r427461;
        double r427463 = r427456 * r427462;
        return r427463;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

Original15.6
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 15.6

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

  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

    \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(\frac{1}{y} - \frac{1}{x}\right)}\]

  4. Final simplification0.0

    \[\leadsto \frac{1}{2} \cdot \left(\frac{1}{y} - \frac{1}{x}\right)\]

Reproduce

herbie shell --seed 2019304 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, B"
  :precision binary64

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

  (/ (- x y) (* (* x 2) y)))