Average Error: 0.0 → 0.0
Time: 2.8s
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 r269637 = x;
        double r269638 = y;
        double r269639 = 1.0;
        double r269640 = r269637 * r269638;
        double r269641 = 2.0;
        double r269642 = r269640 / r269641;
        double r269643 = r269639 + r269642;
        double r269644 = r269638 / r269643;
        double r269645 = r269637 - r269644;
        return r269645;
}
↓
double f(double x, double y) {
        double r269646 = x;
        double r269647 = y;
        double r269648 = 1.0;
        double r269649 = r269646 * r269647;
        double r269650 = 2.0;
        double r269651 = r269649 / r269650;
        double r269652 = r269648 + r269651;
        double r269653 = r269647 / r269652;
        double r269654 = r269646 - r269653;
        return r269654;
}

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 2020047 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))