Average Error: 0.0 → 0.0
Time: 10.6s
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 r167441 = x;
        double r167442 = y;
        double r167443 = 1.0;
        double r167444 = r167441 * r167442;
        double r167445 = 2.0;
        double r167446 = r167444 / r167445;
        double r167447 = r167443 + r167446;
        double r167448 = r167442 / r167447;
        double r167449 = r167441 - r167448;
        return r167449;
}
↓
double f(double x, double y) {
        double r167450 = x;
        double r167451 = y;
        double r167452 = 1.0;
        double r167453 = r167450 * r167451;
        double r167454 = 2.0;
        double r167455 = r167453 / r167454;
        double r167456 = r167452 + r167455;
        double r167457 = r167451 / r167456;
        double r167458 = r167450 - r167457;
        return r167458;
}

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 2019323 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))