Average Error: 0.0 → 0.0
Time: 23.3s
Precision: 64
\[x - \frac{2.30753 + x \cdot 0.27061}{1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}\]
↓
\[x - \frac{\frac{\frac{2.30753 + x \cdot 0.27061}{\sqrt[3]{\left(0.04481 \cdot x + 0.99229\right) \cdot x + 1.0}}}{\sqrt[3]{\left(0.04481 \cdot x + 0.99229\right) \cdot x + 1.0}}}{\sqrt[3]{\left(0.04481 \cdot x + 0.99229\right) \cdot x + 1.0}}\]
x - \frac{2.30753 + x \cdot 0.27061}{1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}
↓
x - \frac{\frac{\frac{2.30753 + x \cdot 0.27061}{\sqrt[3]{\left(0.04481 \cdot x + 0.99229\right) \cdot x + 1.0}}}{\sqrt[3]{\left(0.04481 \cdot x + 0.99229\right) \cdot x + 1.0}}}{\sqrt[3]{\left(0.04481 \cdot x + 0.99229\right) \cdot x + 1.0}}
double f(double x) {
        double r5803159 = x;
        double r5803160 = 2.30753;
        double r5803161 = 0.27061;
        double r5803162 = r5803159 * r5803161;
        double r5803163 = r5803160 + r5803162;
        double r5803164 = 1.0;
        double r5803165 = 0.99229;
        double r5803166 = 0.04481;
        double r5803167 = r5803159 * r5803166;
        double r5803168 = r5803165 + r5803167;
        double r5803169 = r5803168 * r5803159;
        double r5803170 = r5803164 + r5803169;
        double r5803171 = r5803163 / r5803170;
        double r5803172 = r5803159 - r5803171;
        return r5803172;
}
↓
double f(double x) {
        double r5803173 = x;
        double r5803174 = 2.30753;
        double r5803175 = 0.27061;
        double r5803176 = r5803173 * r5803175;
        double r5803177 = r5803174 + r5803176;
        double r5803178 = 0.04481;
        double r5803179 = r5803178 * r5803173;
        double r5803180 = 0.99229;
        double r5803181 = r5803179 + r5803180;
        double r5803182 = r5803181 * r5803173;
        double r5803183 = 1.0;
        double r5803184 = r5803182 + r5803183;
        double r5803185 = cbrt(r5803184);
        double r5803186 = r5803177 / r5803185;
        double r5803187 = r5803186 / r5803185;
        double r5803188 = r5803187 / r5803185;
        double r5803189 = r5803173 - r5803188;
        return r5803189;
}

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 add-cube-cbrt0.0

    \[\leadsto x - \frac{2.30753 + x \cdot 0.27061}{\color{blue}{\left(\sqrt[3]{1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x} \cdot \sqrt[3]{1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}\right) \cdot \sqrt[3]{1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}}}\]

  4. Applied associate-/r*0.0

    \[\leadsto x - \color{blue}{\frac{\frac{2.30753 + x \cdot 0.27061}{\sqrt[3]{1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x} \cdot \sqrt[3]{1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}}}{\sqrt[3]{1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}}}\]
  5. Using strategy rm

  6. Applied associate-/r*0.0

    \[\leadsto x - \frac{\color{blue}{\frac{\frac{2.30753 + x \cdot 0.27061}{\sqrt[3]{1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}}}{\sqrt[3]{1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}}}}{\sqrt[3]{1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}}\]

  7. Final simplification0.0

    \[\leadsto x - \frac{\frac{\frac{2.30753 + x \cdot 0.27061}{\sqrt[3]{\left(0.04481 \cdot x + 0.99229\right) \cdot x + 1.0}}}{\sqrt[3]{\left(0.04481 \cdot x + 0.99229\right) \cdot x + 1.0}}}{\sqrt[3]{\left(0.04481 \cdot x + 0.99229\right) \cdot x + 1.0}}\]

Reproduce

herbie shell --seed 2019163 
(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)))))