Average Error: 0.0 → 0.0
Time: 7.3s
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 r185418 = x;
        double r185419 = y;
        double r185420 = 1.0;
        double r185421 = r185418 * r185419;
        double r185422 = 2.0;
        double r185423 = r185421 / r185422;
        double r185424 = r185420 + r185423;
        double r185425 = r185419 / r185424;
        double r185426 = r185418 - r185425;
        return r185426;
}
↓
double f(double x, double y) {
        double r185427 = x;
        double r185428 = y;
        double r185429 = 1.0;
        double r185430 = r185427 * r185428;
        double r185431 = 2.0;
        double r185432 = r185430 / r185431;
        double r185433 = r185429 + r185432;
        double r185434 = r185428 / r185433;
        double r185435 = r185427 - r185434;
        return r185435;
}

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 2019235 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))