Average Error: 0.0 → 0.0
Time: 2.0s
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 r343159 = x;
        double r343160 = y;
        double r343161 = 1.0;
        double r343162 = r343159 * r343160;
        double r343163 = 2.0;
        double r343164 = r343162 / r343163;
        double r343165 = r343161 + r343164;
        double r343166 = r343160 / r343165;
        double r343167 = r343159 - r343166;
        return r343167;
}
↓
double f(double x, double y) {
        double r343168 = x;
        double r343169 = y;
        double r343170 = 1.0;
        double r343171 = r343168 * r343169;
        double r343172 = 2.0;
        double r343173 = r343171 / r343172;
        double r343174 = r343170 + r343173;
        double r343175 = r343169 / r343174;
        double r343176 = r343168 - r343175;
        return r343176;
}

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 2019353 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))