Average Error: 0.0 → 0.0
Time: 2.8s
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 r279877 = x;
        double r279878 = y;
        double r279879 = 1.0;
        double r279880 = r279877 * r279878;
        double r279881 = 2.0;
        double r279882 = r279880 / r279881;
        double r279883 = r279879 + r279882;
        double r279884 = r279878 / r279883;
        double r279885 = r279877 - r279884;
        return r279885;
}
↓
double f(double x, double y) {
        double r279886 = x;
        double r279887 = y;
        double r279888 = 1.0;
        double r279889 = r279886 * r279887;
        double r279890 = 2.0;
        double r279891 = r279889 / r279890;
        double r279892 = r279888 + r279891;
        double r279893 = r279887 / r279892;
        double r279894 = r279886 - r279893;
        return r279894;
}

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 2020049 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))