Average Error: 0.0 → 0.0
Time: 8.6s
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 r108205 = x;
        double r108206 = y;
        double r108207 = 1.0;
        double r108208 = r108205 * r108206;
        double r108209 = 2.0;
        double r108210 = r108208 / r108209;
        double r108211 = r108207 + r108210;
        double r108212 = r108206 / r108211;
        double r108213 = r108205 - r108212;
        return r108213;
}
↓
double f(double x, double y) {
        double r108214 = x;
        double r108215 = y;
        double r108216 = 1.0;
        double r108217 = r108214 * r108215;
        double r108218 = 2.0;
        double r108219 = r108217 / r108218;
        double r108220 = r108216 + r108219;
        double r108221 = r108215 / r108220;
        double r108222 = r108214 - r108221;
        return r108222;
}

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 2019326 +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)))))