Average Error: 0.0 → 0.1
Time: 14.0s
Precision: 64
\[x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
↓
\[x - \frac{1}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}} \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}\]
x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}
↓
x - \frac{1}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}} \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}
double f(double x) {
        double r75298 = x;
        double r75299 = 2.30753;
        double r75300 = 0.27061;
        double r75301 = r75298 * r75300;
        double r75302 = r75299 + r75301;
        double r75303 = 1.0;
        double r75304 = 0.99229;
        double r75305 = 0.04481;
        double r75306 = r75298 * r75305;
        double r75307 = r75304 + r75306;
        double r75308 = r75307 * r75298;
        double r75309 = r75303 + r75308;
        double r75310 = r75302 / r75309;
        double r75311 = r75298 - r75310;
        return r75311;
}
↓
double f(double x) {
        double r75312 = x;
        double r75313 = 1.0;
        double r75314 = 1.0;
        double r75315 = 0.99229;
        double r75316 = 0.04481;
        double r75317 = r75312 * r75316;
        double r75318 = r75315 + r75317;
        double r75319 = r75318 * r75312;
        double r75320 = r75314 + r75319;
        double r75321 = sqrt(r75320);
        double r75322 = r75313 / r75321;
        double r75323 = 2.30753;
        double r75324 = 0.27061;
        double r75325 = r75312 * r75324;
        double r75326 = r75323 + r75325;
        double r75327 = r75326 / r75321;
        double r75328 = r75322 * r75327;
        double r75329 = r75312 - r75328;
        return r75329;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.1

    \[\leadsto x - \frac{2.30753 + x \cdot 0.27061000000000002}{\color{blue}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x} \cdot \sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}}\]

  4. Applied *-un-lft-identity0.1

    \[\leadsto x - \frac{\color{blue}{1 \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)}}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x} \cdot \sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}\]

  5. Applied times-frac0.1

    \[\leadsto x - \color{blue}{\frac{1}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}} \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}}\]

  6. Final simplification0.1

    \[\leadsto x - \frac{1}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}} \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}\]

Reproduce

herbie shell --seed 2019198 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, D"
  (- x (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))))