Average Error: 0.0 → 0.0
Time: 3.3s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - y \cdot \frac{1}{1 + \frac{1}{\frac{\frac{2}{x}}{y}}}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - y \cdot \frac{1}{1 + \frac{1}{\frac{\frac{2}{x}}{y}}}
double f(double x, double y) {
        double r262158 = x;
        double r262159 = y;
        double r262160 = 1.0;
        double r262161 = r262158 * r262159;
        double r262162 = 2.0;
        double r262163 = r262161 / r262162;
        double r262164 = r262160 + r262163;
        double r262165 = r262159 / r262164;
        double r262166 = r262158 - r262165;
        return r262166;
}
↓
double f(double x, double y) {
        double r262167 = x;
        double r262168 = y;
        double r262169 = 1.0;
        double r262170 = 1.0;
        double r262171 = 2.0;
        double r262172 = r262171 / r262167;
        double r262173 = r262172 / r262168;
        double r262174 = r262169 / r262173;
        double r262175 = r262170 + r262174;
        double r262176 = r262169 / r262175;
        double r262177 = r262168 * r262176;
        double r262178 = r262167 - r262177;
        return r262178;
}

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. Using strategy rm

  3. Applied div-inv0.1

    \[\leadsto x - \color{blue}{y \cdot \frac{1}{1 + \frac{x \cdot y}{2}}}\]
  4. Using strategy rm

  5. Applied clear-num0.1

    \[\leadsto x - y \cdot \frac{1}{1 + \color{blue}{\frac{1}{\frac{2}{x \cdot y}}}}\]

  6. Simplified0.0

    \[\leadsto x - y \cdot \frac{1}{1 + \frac{1}{\color{blue}{\frac{\frac{2}{x}}{y}}}}\]

  7. Final simplification0.0

    \[\leadsto x - y \cdot \frac{1}{1 + \frac{1}{\frac{\frac{2}{x}}{y}}}\]

Reproduce

herbie shell --seed 2019362 +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)))))