Average Error: 0.0 → 0.0
Time: 2.1s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - \frac{y}{1 + \frac{x \cdot y}{2}}
double f(double x, double y) {
        double r201395 = x;
        double r201396 = y;
        double r201397 = 1.0;
        double r201398 = r201395 * r201396;
        double r201399 = 2.0;
        double r201400 = r201398 / r201399;
        double r201401 = r201397 + r201400;
        double r201402 = r201396 / r201401;
        double r201403 = r201395 - r201402;
        return r201403;
}
↓
double f(double x, double y) {
        double r201404 = x;
        double r201405 = y;
        double r201406 = 1.0;
        double r201407 = r201404 * r201405;
        double r201408 = 2.0;
        double r201409 = r201407 / r201408;
        double r201410 = r201406 + r201409;
        double r201411 = r201405 / r201410;
        double r201412 = r201404 - r201411;
        return r201412;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020060 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))