Average Error: 15.4 → 0.0
Time: 1.7s
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 r574910 = x;
        double r574911 = y;
        double r574912 = r574910 + r574911;
        double r574913 = 2.0;
        double r574914 = r574910 * r574913;
        double r574915 = r574914 * r574911;
        double r574916 = r574912 / r574915;
        return r574916;
}
↓
double f(double x, double y) {
        double r574917 = 0.5;
        double r574918 = 1.0;
        double r574919 = y;
        double r574920 = r574918 / r574919;
        double r574921 = x;
        double r574922 = r574918 / r574921;
        double r574923 = r574920 + r574922;
        double r574924 = r574917 * r574923;
        return r574924;
}

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

Original15.4
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program 15.4

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

  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 2019353 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, C"
  :precision binary64

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

  (/ (+ x y) (* (* x 2) y)))