Average Error: 0.0 → 0.0
Time: 1.4s
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 r274130 = x;
        double r274131 = y;
        double r274132 = 1.0;
        double r274133 = r274130 * r274131;
        double r274134 = 2.0;
        double r274135 = r274133 / r274134;
        double r274136 = r274132 + r274135;
        double r274137 = r274131 / r274136;
        double r274138 = r274130 - r274137;
        return r274138;
}
↓
double f(double x, double y) {
        double r274139 = x;
        double r274140 = y;
        double r274141 = 1.0;
        double r274142 = r274139 * r274140;
        double r274143 = 2.0;
        double r274144 = r274142 / r274143;
        double r274145 = r274141 + r274144;
        double r274146 = r274140 / r274145;
        double r274147 = r274139 - r274146;
        return r274147;
}

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 2020064 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))