Average Error: 0.0 → 0.0
Time: 3.3s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
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 r255918 = x;
        double r255919 = y;
        double r255920 = 1.0;
        double r255921 = r255918 * r255919;
        double r255922 = 2.0;
        double r255923 = r255921 / r255922;
        double r255924 = r255920 + r255923;
        double r255925 = r255919 / r255924;
        double r255926 = r255918 - r255925;
        return r255926;
}
↓
double f(double x, double y) {
        double r255927 = x;
        double r255928 = y;
        double r255929 = 1.0;
        double r255930 = r255927 * r255928;
        double r255931 = 2.0;
        double r255932 = r255930 / r255931;
        double r255933 = r255929 + r255932;
        double r255934 = r255928 / r255933;
        double r255935 = r255927 - r255934;
        return r255935;
}

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 2020062 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))