Average Error: 0.0 → 0.0
Time: 10.2s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - \frac{y}{\frac{x \cdot y}{2} + 1}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - \frac{y}{\frac{x \cdot y}{2} + 1}
double f(double x, double y) {
        double r15811431 = x;
        double r15811432 = y;
        double r15811433 = 1.0;
        double r15811434 = r15811431 * r15811432;
        double r15811435 = 2.0;
        double r15811436 = r15811434 / r15811435;
        double r15811437 = r15811433 + r15811436;
        double r15811438 = r15811432 / r15811437;
        double r15811439 = r15811431 - r15811438;
        return r15811439;
}
↓
double f(double x, double y) {
        double r15811440 = x;
        double r15811441 = y;
        double r15811442 = r15811440 * r15811441;
        double r15811443 = 2.0;
        double r15811444 = r15811442 / r15811443;
        double r15811445 = 1.0;
        double r15811446 = r15811444 + r15811445;
        double r15811447 = r15811441 / r15811446;
        double r15811448 = r15811440 - r15811447;
        return r15811448;
}

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

    \[\leadsto x - \frac{y}{\frac{x \cdot y}{2} + 1}\]

Reproduce

herbie shell --seed 2019171 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  (- x (/ y (+ 1.0 (/ (* x y) 2.0)))))