Average Error: 0.0 → 0.0
Time: 2.3s
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 r230934 = x;
        double r230935 = y;
        double r230936 = 1.0;
        double r230937 = r230934 * r230935;
        double r230938 = 2.0;
        double r230939 = r230937 / r230938;
        double r230940 = r230936 + r230939;
        double r230941 = r230935 / r230940;
        double r230942 = r230934 - r230941;
        return r230942;
}
↓
double f(double x, double y) {
        double r230943 = x;
        double r230944 = y;
        double r230945 = 1.0;
        double r230946 = r230943 * r230944;
        double r230947 = 2.0;
        double r230948 = r230946 / r230947;
        double r230949 = r230945 + r230948;
        double r230950 = r230944 / r230949;
        double r230951 = r230943 - r230950;
        return r230951;
}

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 2020060 +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)))))