Average Error: 0.0 → 0.0
Time: 3.3s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - \frac{y}{1 + \frac{x}{\frac{2}{y}}}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - \frac{y}{1 + \frac{x}{\frac{2}{y}}}
double f(double x, double y) {
        double r197361 = x;
        double r197362 = y;
        double r197363 = 1.0;
        double r197364 = r197361 * r197362;
        double r197365 = 2.0;
        double r197366 = r197364 / r197365;
        double r197367 = r197363 + r197366;
        double r197368 = r197362 / r197367;
        double r197369 = r197361 - r197368;
        return r197369;
}
↓
double f(double x, double y) {
        double r197370 = x;
        double r197371 = y;
        double r197372 = 1.0;
        double r197373 = 2.0;
        double r197374 = r197373 / r197371;
        double r197375 = r197370 / r197374;
        double r197376 = r197372 + r197375;
        double r197377 = r197371 / r197376;
        double r197378 = r197370 - r197377;
        return r197378;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
  2. Using strategy rm

  3. Applied associate-/l*0.0

    \[\leadsto x - \frac{y}{1 + \color{blue}{\frac{x}{\frac{2}{y}}}}\]

  4. Final simplification0.0

    \[\leadsto x - \frac{y}{1 + \frac{x}{\frac{2}{y}}}\]

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))