Average Error: 15.1 → 0.0
Time: 10.2s
Precision: 64
\[\frac{x - y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[0.5 \cdot \left(\frac{1}{y} - \frac{1}{x}\right)\]
\frac{x - y}{\left(x \cdot 2\right) \cdot y}
↓
0.5 \cdot \left(\frac{1}{y} - \frac{1}{x}\right)
double f(double x, double y) {
        double r464336 = x;
        double r464337 = y;
        double r464338 = r464336 - r464337;
        double r464339 = 2.0;
        double r464340 = r464336 * r464339;
        double r464341 = r464340 * r464337;
        double r464342 = r464338 / r464341;
        return r464342;
}
↓
double f(double x, double y) {
        double r464343 = 0.5;
        double r464344 = 1.0;
        double r464345 = y;
        double r464346 = r464344 / r464345;
        double r464347 = x;
        double r464348 = r464344 / r464347;
        double r464349 = r464346 - r464348;
        double r464350 = r464343 * r464349;
        return r464350;
}

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

    \[\leadsto \color{blue}{0.5 \cdot \left(\frac{1}{y} - \frac{1}{x}\right)}\]

  4. Final simplification0.0

    \[\leadsto 0.5 \cdot \left(\frac{1}{y} - \frac{1}{x}\right)\]

Reproduce

herbie shell --seed 2019294 
(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)))