Average Error: 15.1 → 0.0
Time: 1.6s
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 r495200 = x;
        double r495201 = y;
        double r495202 = r495200 - r495201;
        double r495203 = 2.0;
        double r495204 = r495200 * r495203;
        double r495205 = r495204 * r495201;
        double r495206 = r495202 / r495205;
        return r495206;
}
↓
double f(double x, double y) {
        double r495207 = 0.5;
        double r495208 = 1.0;
        double r495209 = y;
        double r495210 = r495208 / r495209;
        double r495211 = x;
        double r495212 = r495208 / r495211;
        double r495213 = r495210 - r495212;
        double r495214 = r495207 * r495213;
        return r495214;
}

Error

Bits error versus x

Bits error versus y

Try it out

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 2020057 +o rules:numerics
(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)))