Average Error: 0.0 → 0.1
Time: 10.1s
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 r224412 = x;
        double r224413 = y;
        double r224414 = 1.0;
        double r224415 = r224412 * r224413;
        double r224416 = 2.0;
        double r224417 = r224415 / r224416;
        double r224418 = r224414 + r224417;
        double r224419 = r224413 / r224418;
        double r224420 = r224412 - r224419;
        return r224420;
}
↓
double f(double x, double y) {
        double r224421 = x;
        double r224422 = y;
        double r224423 = 1.0;
        double r224424 = 2.0;
        double r224425 = r224424 / r224422;
        double r224426 = r224421 / r224425;
        double r224427 = r224423 + r224426;
        double r224428 = r224422 / r224427;
        double r224429 = r224421 - r224428;
        return r224429;
}

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*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019212 +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)))))