Average Error: 14.7 → 0.0
Time: 991.0ms
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 r459251 = x;
        double r459252 = y;
        double r459253 = r459251 - r459252;
        double r459254 = 2.0;
        double r459255 = r459251 * r459254;
        double r459256 = r459255 * r459252;
        double r459257 = r459253 / r459256;
        return r459257;
}
↓
double f(double x, double y) {
        double r459258 = 0.5;
        double r459259 = 1.0;
        double r459260 = y;
        double r459261 = r459259 / r459260;
        double r459262 = x;
        double r459263 = r459259 / r459262;
        double r459264 = r459261 - r459263;
        double r459265 = r459258 * r459264;
        return r459265;
}

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

Original14.7
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 14.7

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

  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 2020003 
(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)))