Average Error: 0.0 → 0.0
Time: 2.7s
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 r176799 = x;
        double r176800 = y;
        double r176801 = 1.0;
        double r176802 = r176799 * r176800;
        double r176803 = 2.0;
        double r176804 = r176802 / r176803;
        double r176805 = r176801 + r176804;
        double r176806 = r176800 / r176805;
        double r176807 = r176799 - r176806;
        return r176807;
}
↓
double f(double x, double y) {
        double r176808 = x;
        double r176809 = y;
        double r176810 = 1.0;
        double r176811 = r176808 * r176809;
        double r176812 = 2.0;
        double r176813 = r176811 / r176812;
        double r176814 = r176810 + r176813;
        double r176815 = r176809 / r176814;
        double r176816 = r176808 - r176815;
        return r176816;
}

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 2020020 +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)))))