Average Error: 0.0 → 0.0
Time: 1.7s
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 r223172 = x;
        double r223173 = y;
        double r223174 = 1.0;
        double r223175 = r223172 * r223173;
        double r223176 = 2.0;
        double r223177 = r223175 / r223176;
        double r223178 = r223174 + r223177;
        double r223179 = r223173 / r223178;
        double r223180 = r223172 - r223179;
        return r223180;
}
↓
double f(double x, double y) {
        double r223181 = x;
        double r223182 = y;
        double r223183 = 1.0;
        double r223184 = r223181 * r223182;
        double r223185 = 2.0;
        double r223186 = r223184 / r223185;
        double r223187 = r223183 + r223186;
        double r223188 = r223182 / r223187;
        double r223189 = r223181 - r223188;
        return r223189;
}

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 2020003 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))