Average Error: 0.0 → 0.0
Time: 6.2s
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 r11430169 = x;
        double r11430170 = y;
        double r11430171 = 1.0;
        double r11430172 = r11430169 * r11430170;
        double r11430173 = 2.0;
        double r11430174 = r11430172 / r11430173;
        double r11430175 = r11430171 + r11430174;
        double r11430176 = r11430170 / r11430175;
        double r11430177 = r11430169 - r11430176;
        return r11430177;
}
↓
double f(double x, double y) {
        double r11430178 = x;
        double r11430179 = y;
        double r11430180 = r11430178 * r11430179;
        double r11430181 = 2.0;
        double r11430182 = r11430180 / r11430181;
        double r11430183 = 1.0;
        double r11430184 = r11430182 + r11430183;
        double r11430185 = r11430179 / r11430184;
        double r11430186 = r11430178 - r11430185;
        return r11430186;
}

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 2019192 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  (- x (/ y (+ 1.0 (/ (* x y) 2.0)))))