Average Error: 0.0 → 0.0
Time: 1.3s
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 r192162 = x;
        double r192163 = y;
        double r192164 = 1.0;
        double r192165 = r192162 * r192163;
        double r192166 = 2.0;
        double r192167 = r192165 / r192166;
        double r192168 = r192164 + r192167;
        double r192169 = r192163 / r192168;
        double r192170 = r192162 - r192169;
        return r192170;
}
↓
double f(double x, double y) {
        double r192171 = x;
        double r192172 = y;
        double r192173 = 1.0;
        double r192174 = r192171 * r192172;
        double r192175 = 2.0;
        double r192176 = r192174 / r192175;
        double r192177 = r192173 + r192176;
        double r192178 = r192172 / r192177;
        double r192179 = r192171 - r192178;
        return r192179;
}

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 2020036 +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)))))