Average Error: 0.0 → 0.0
Time: 8.2s
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 r174156 = x;
        double r174157 = y;
        double r174158 = 1.0;
        double r174159 = r174156 * r174157;
        double r174160 = 2.0;
        double r174161 = r174159 / r174160;
        double r174162 = r174158 + r174161;
        double r174163 = r174157 / r174162;
        double r174164 = r174156 - r174163;
        return r174164;
}
↓
double f(double x, double y) {
        double r174165 = x;
        double r174166 = y;
        double r174167 = 1.0;
        double r174168 = r174165 * r174166;
        double r174169 = 2.0;
        double r174170 = r174168 / r174169;
        double r174171 = r174167 + r174170;
        double r174172 = r174166 / r174171;
        double r174173 = r174165 - r174172;
        return r174173;
}

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 2020045 +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)))))