Average Error: 0.0 → 0.0
Time: 8.0s
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 r2481232 = x;
        double r2481233 = 2.30753;
        double r2481234 = 0.27061;
        double r2481235 = r2481232 * r2481234;
        double r2481236 = r2481233 + r2481235;
        double r2481237 = 1.0;
        double r2481238 = 0.99229;
        double r2481239 = 0.04481;
        double r2481240 = r2481232 * r2481239;
        double r2481241 = r2481238 + r2481240;
        double r2481242 = r2481241 * r2481232;
        double r2481243 = r2481237 + r2481242;
        double r2481244 = r2481236 / r2481243;
        double r2481245 = r2481232 - r2481244;
        return r2481245;
}
↓
double f(double x) {
        double r2481246 = x;
        double r2481247 = 1.0;
        double r2481248 = 0.99229;
        double r2481249 = 0.04481;
        double r2481250 = r2481249 * r2481246;
        double r2481251 = r2481248 + r2481250;
        double r2481252 = r2481246 * r2481251;
        double r2481253 = 1.0;
        double r2481254 = r2481252 + r2481253;
        double r2481255 = 0.27061;
        double r2481256 = r2481246 * r2481255;
        double r2481257 = 2.30753;
        double r2481258 = r2481256 + r2481257;
        double r2481259 = r2481254 / r2481258;
        double r2481260 = r2481247 / r2481259;
        double r2481261 = r2481246 - r2481260;
        return r2481261;
}

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 2019156 
(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)))))