Average Error: 0.0 → 0.0
Time: 8.4s
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 r148057 = x;
        double r148058 = y;
        double r148059 = 1.0;
        double r148060 = r148057 * r148058;
        double r148061 = 2.0;
        double r148062 = r148060 / r148061;
        double r148063 = r148059 + r148062;
        double r148064 = r148058 / r148063;
        double r148065 = r148057 - r148064;
        return r148065;
}
↓
double f(double x, double y) {
        double r148066 = x;
        double r148067 = y;
        double r148068 = 1.0;
        double r148069 = r148066 * r148067;
        double r148070 = 2.0;
        double r148071 = r148069 / r148070;
        double r148072 = r148068 + r148071;
        double r148073 = r148067 / r148072;
        double r148074 = r148066 - r148073;
        return r148074;
}

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 2019291 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))