Average Error: 0.0 → 0.0
Time: 2.2s
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 r241431 = x;
        double r241432 = y;
        double r241433 = 1.0;
        double r241434 = r241431 * r241432;
        double r241435 = 2.0;
        double r241436 = r241434 / r241435;
        double r241437 = r241433 + r241436;
        double r241438 = r241432 / r241437;
        double r241439 = r241431 - r241438;
        return r241439;
}
↓
double f(double x, double y) {
        double r241440 = x;
        double r241441 = y;
        double r241442 = 1.0;
        double r241443 = r241440 * r241441;
        double r241444 = 2.0;
        double r241445 = r241443 / r241444;
        double r241446 = r241442 + r241445;
        double r241447 = r241441 / r241446;
        double r241448 = r241440 - r241447;
        return r241448;
}

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 2019353 +o rules:numerics
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))