Average Error: 0.0 → 0.0
Time: 23.8s
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 r12304640 = x;
        double r12304641 = y;
        double r12304642 = 1.0;
        double r12304643 = r12304640 * r12304641;
        double r12304644 = 2.0;
        double r12304645 = r12304643 / r12304644;
        double r12304646 = r12304642 + r12304645;
        double r12304647 = r12304641 / r12304646;
        double r12304648 = r12304640 - r12304647;
        return r12304648;
}
↓
double f(double x, double y) {
        double r12304649 = x;
        double r12304650 = y;
        double r12304651 = r12304649 * r12304650;
        double r12304652 = 2.0;
        double r12304653 = r12304651 / r12304652;
        double r12304654 = 1.0;
        double r12304655 = r12304653 + r12304654;
        double r12304656 = r12304650 / r12304655;
        double r12304657 = r12304649 - r12304656;
        return r12304657;
}

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 2019168 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  (- x (/ y (+ 1.0 (/ (* x y) 2.0)))))