Average Error: 15.6 → 0.0
Time: 3.9s
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 r376327 = x;
        double r376328 = y;
        double r376329 = r376327 + r376328;
        double r376330 = 2.0;
        double r376331 = r376327 * r376330;
        double r376332 = r376331 * r376328;
        double r376333 = r376329 / r376332;
        return r376333;
}
↓
double f(double x, double y) {
        double r376334 = 1.0;
        double r376335 = 2.0;
        double r376336 = r376334 / r376335;
        double r376337 = 1.0;
        double r376338 = y;
        double r376339 = r376337 / r376338;
        double r376340 = x;
        double r376341 = r376337 / r376340;
        double r376342 = r376339 + r376341;
        double r376343 = r376336 * r376342;
        return r376343;
}

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

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

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, C"
  :precision binary64

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

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