Average Error: 0.0 → 0.0
Time: 2.2s
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 r252133 = x;
        double r252134 = y;
        double r252135 = 1.0;
        double r252136 = r252133 * r252134;
        double r252137 = 2.0;
        double r252138 = r252136 / r252137;
        double r252139 = r252135 + r252138;
        double r252140 = r252134 / r252139;
        double r252141 = r252133 - r252140;
        return r252141;
}
↓
double f(double x, double y) {
        double r252142 = x;
        double r252143 = y;
        double r252144 = 1.0;
        double r252145 = r252142 * r252143;
        double r252146 = 2.0;
        double r252147 = r252145 / r252146;
        double r252148 = r252144 + r252147;
        double r252149 = r252143 / r252148;
        double r252150 = r252142 - r252149;
        return r252150;
}

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 2019353 +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)))))