Average Error: 0.0 → 0.0
Time: 12.7s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - \frac{1}{0.5 \cdot x + \frac{1}{y}}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - \frac{1}{0.5 \cdot x + \frac{1}{y}}
double f(double x, double y) {
        double r173315 = x;
        double r173316 = y;
        double r173317 = 1.0;
        double r173318 = r173315 * r173316;
        double r173319 = 2.0;
        double r173320 = r173318 / r173319;
        double r173321 = r173317 + r173320;
        double r173322 = r173316 / r173321;
        double r173323 = r173315 - r173322;
        return r173323;
}
↓
double f(double x, double y) {
        double r173324 = x;
        double r173325 = 1.0;
        double r173326 = 0.5;
        double r173327 = r173326 * r173324;
        double r173328 = 1.0;
        double r173329 = y;
        double r173330 = r173328 / r173329;
        double r173331 = r173327 + r173330;
        double r173332 = r173325 / r173331;
        double r173333 = r173324 - r173332;
        return r173333;
}

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 clear-num0.1

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

  4. Taylor expanded around 0 0.0

    \[\leadsto x - \frac{1}{\color{blue}{0.5 \cdot x + 1 \cdot \frac{1}{y}}}\]

  5. Simplified0.0

    \[\leadsto x - \frac{1}{\color{blue}{0.5 \cdot x + \frac{1}{y}}}\]

  6. Final simplification0.0

    \[\leadsto x - \frac{1}{0.5 \cdot x + \frac{1}{y}}\]

Reproduce

herbie shell --seed 2019325 
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))