Average Error: 0.0 → 0.0
Time: 6.9s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - \frac{y}{\frac{x \cdot y}{2} + 1}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - \frac{y}{\frac{x \cdot y}{2} + 1}
double f(double x, double y) {
        double r168152 = x;
        double r168153 = y;
        double r168154 = 1.0;
        double r168155 = r168152 * r168153;
        double r168156 = 2.0;
        double r168157 = r168155 / r168156;
        double r168158 = r168154 + r168157;
        double r168159 = r168153 / r168158;
        double r168160 = r168152 - r168159;
        return r168160;
}
↓
double f(double x, double y) {
        double r168161 = x;
        double r168162 = y;
        double r168163 = r168161 * r168162;
        double r168164 = 2.0;
        double r168165 = r168163 / r168164;
        double r168166 = 1.0;
        double r168167 = r168165 + r168166;
        double r168168 = r168162 / r168167;
        double r168169 = r168161 - r168168;
        return r168169;
}

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

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

Reproduce

herbie shell --seed 2019195 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  (- x (/ y (+ 1.0 (/ (* x y) 2.0)))))