Average Error: 0.0 → 0.0
Time: 1.1s
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 r264260 = x;
        double r264261 = y;
        double r264262 = 1.0;
        double r264263 = r264260 * r264261;
        double r264264 = 2.0;
        double r264265 = r264263 / r264264;
        double r264266 = r264262 + r264265;
        double r264267 = r264261 / r264266;
        double r264268 = r264260 - r264267;
        return r264268;
}
↓
double f(double x, double y) {
        double r264269 = x;
        double r264270 = y;
        double r264271 = 1.0;
        double r264272 = r264269 * r264270;
        double r264273 = 2.0;
        double r264274 = r264272 / r264273;
        double r264275 = r264271 + r264274;
        double r264276 = r264270 / r264275;
        double r264277 = r264269 - r264276;
        return r264277;
}

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 2020036 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))