Average Error: 0.0 → 0.0
Time: 15.5s
Precision: 64
\[x - \frac{2.30753 + x \cdot 0.27061}{1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}\]
↓
\[x - \frac{1}{\frac{x \cdot \left(0.99229 + 0.04481 \cdot x\right) + 1.0}{x \cdot 0.27061 + 2.30753}}\]
x - \frac{2.30753 + x \cdot 0.27061}{1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}
↓
x - \frac{1}{\frac{x \cdot \left(0.99229 + 0.04481 \cdot x\right) + 1.0}{x \cdot 0.27061 + 2.30753}}
double f(double x) {
        double r5410282 = x;
        double r5410283 = 2.30753;
        double r5410284 = 0.27061;
        double r5410285 = r5410282 * r5410284;
        double r5410286 = r5410283 + r5410285;
        double r5410287 = 1.0;
        double r5410288 = 0.99229;
        double r5410289 = 0.04481;
        double r5410290 = r5410282 * r5410289;
        double r5410291 = r5410288 + r5410290;
        double r5410292 = r5410291 * r5410282;
        double r5410293 = r5410287 + r5410292;
        double r5410294 = r5410286 / r5410293;
        double r5410295 = r5410282 - r5410294;
        return r5410295;
}
↓
double f(double x) {
        double r5410296 = x;
        double r5410297 = 1.0;
        double r5410298 = 0.99229;
        double r5410299 = 0.04481;
        double r5410300 = r5410299 * r5410296;
        double r5410301 = r5410298 + r5410300;
        double r5410302 = r5410296 * r5410301;
        double r5410303 = 1.0;
        double r5410304 = r5410302 + r5410303;
        double r5410305 = 0.27061;
        double r5410306 = r5410296 * r5410305;
        double r5410307 = 2.30753;
        double r5410308 = r5410306 + r5410307;
        double r5410309 = r5410304 / r5410308;
        double r5410310 = r5410297 / r5410309;
        double r5410311 = r5410296 - r5410310;
        return r5410311;
}

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

    \[x - \frac{2.30753 + x \cdot 0.27061}{1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}\]
  2. Using strategy rm

  3. Applied clear-num0.0

    \[\leadsto x - \color{blue}{\frac{1}{\frac{1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}{2.30753 + x \cdot 0.27061}}}\]

  4. Final simplification0.0

    \[\leadsto x - \frac{1}{\frac{x \cdot \left(0.99229 + 0.04481 \cdot x\right) + 1.0}{x \cdot 0.27061 + 2.30753}}\]

Reproduce

herbie shell --seed 2019162 
(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)))))