Average Error: 0.0 → 0.0
Time: 1.9s
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 r289925 = x;
        double r289926 = y;
        double r289927 = 1.0;
        double r289928 = r289925 * r289926;
        double r289929 = 2.0;
        double r289930 = r289928 / r289929;
        double r289931 = r289927 + r289930;
        double r289932 = r289926 / r289931;
        double r289933 = r289925 - r289932;
        return r289933;
}
↓
double f(double x, double y) {
        double r289934 = x;
        double r289935 = y;
        double r289936 = 1.0;
        double r289937 = r289934 * r289935;
        double r289938 = 2.0;
        double r289939 = r289937 / r289938;
        double r289940 = r289936 + r289939;
        double r289941 = r289935 / r289940;
        double r289942 = r289934 - r289941;
        return r289942;
}

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 2020034 +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)))))