Average Error: 0.0 → 0.0
Time: 2.0s
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 r223242 = x;
        double r223243 = y;
        double r223244 = 1.0;
        double r223245 = r223242 * r223243;
        double r223246 = 2.0;
        double r223247 = r223245 / r223246;
        double r223248 = r223244 + r223247;
        double r223249 = r223243 / r223248;
        double r223250 = r223242 - r223249;
        return r223250;
}
↓
double f(double x, double y) {
        double r223251 = x;
        double r223252 = y;
        double r223253 = 1.0;
        double r223254 = r223251 * r223252;
        double r223255 = 2.0;
        double r223256 = r223254 / r223255;
        double r223257 = r223253 + r223256;
        double r223258 = r223252 / r223257;
        double r223259 = r223251 - r223258;
        return r223259;
}

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 2020060 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))