Average Error: 0.0 → 0.0
Time: 3.6s
Precision: 64
\[x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
↓
\[x - \frac{1}{\sqrt[3]{{\left(\frac{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}{2.30753 + x \cdot 0.27061000000000002}\right)}^{3}}}\]
x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}
↓
x - \frac{1}{\sqrt[3]{{\left(\frac{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}{2.30753 + x \cdot 0.27061000000000002}\right)}^{3}}}
double f(double x) {
        double r94919 = x;
        double r94920 = 2.30753;
        double r94921 = 0.27061;
        double r94922 = r94919 * r94921;
        double r94923 = r94920 + r94922;
        double r94924 = 1.0;
        double r94925 = 0.99229;
        double r94926 = 0.04481;
        double r94927 = r94919 * r94926;
        double r94928 = r94925 + r94927;
        double r94929 = r94928 * r94919;
        double r94930 = r94924 + r94929;
        double r94931 = r94923 / r94930;
        double r94932 = r94919 - r94931;
        return r94932;
}
↓
double f(double x) {
        double r94933 = x;
        double r94934 = 1.0;
        double r94935 = 1.0;
        double r94936 = 0.99229;
        double r94937 = 0.04481;
        double r94938 = r94933 * r94937;
        double r94939 = r94936 + r94938;
        double r94940 = r94939 * r94933;
        double r94941 = r94935 + r94940;
        double r94942 = 2.30753;
        double r94943 = 0.27061;
        double r94944 = r94933 * r94943;
        double r94945 = r94942 + r94944;
        double r94946 = r94941 / r94945;
        double r94947 = 3.0;
        double r94948 = pow(r94946, r94947);
        double r94949 = cbrt(r94948);
        double r94950 = r94934 / r94949;
        double r94951 = r94933 - r94950;
        return r94951;
}

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 clear-num0.0

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

  5. Applied add-cbrt-cube21.8

    \[\leadsto x - \frac{1}{\frac{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}{\color{blue}{\sqrt[3]{\left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)}}}}\]

  6. Applied add-cbrt-cube21.8

    \[\leadsto x - \frac{1}{\frac{\color{blue}{\sqrt[3]{\left(\left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right) \cdot \left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right)\right) \cdot \left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right)}}}{\sqrt[3]{\left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)}}}\]

  7. Applied cbrt-undiv21.8

    \[\leadsto x - \frac{1}{\color{blue}{\sqrt[3]{\frac{\left(\left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right) \cdot \left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right)\right) \cdot \left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right)}{\left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)}}}}\]

  8. Simplified0.0

    \[\leadsto x - \frac{1}{\sqrt[3]{\color{blue}{{\left(\frac{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}{2.30753 + x \cdot 0.27061000000000002}\right)}^{3}}}}\]

  9. Final simplification0.0

    \[\leadsto x - \frac{1}{\sqrt[3]{{\left(\frac{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}{2.30753 + x \cdot 0.27061000000000002}\right)}^{3}}}\]

Reproduce

herbie shell --seed 2020060 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, D"
  :precision binary64
  (- x (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* (+ 0.99229 (* x 0.04481)) x)))))