Average Error: 0.0 → 0.0
Time: 1.8s
Precision: 64
\[x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
↓
\[x - \sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\right)}^{3}}\]
x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}
↓
x - \sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\right)}^{3}}
double f(double x) {
        double r79196 = x;
        double r79197 = 2.30753;
        double r79198 = 0.27061;
        double r79199 = r79196 * r79198;
        double r79200 = r79197 + r79199;
        double r79201 = 1.0;
        double r79202 = 0.99229;
        double r79203 = 0.04481;
        double r79204 = r79196 * r79203;
        double r79205 = r79202 + r79204;
        double r79206 = r79205 * r79196;
        double r79207 = r79201 + r79206;
        double r79208 = r79200 / r79207;
        double r79209 = r79196 - r79208;
        return r79209;
}
↓
double f(double x) {
        double r79210 = x;
        double r79211 = 2.30753;
        double r79212 = 0.27061;
        double r79213 = r79210 * r79212;
        double r79214 = r79211 + r79213;
        double r79215 = 1.0;
        double r79216 = 0.99229;
        double r79217 = 0.04481;
        double r79218 = r79210 * r79217;
        double r79219 = r79216 + r79218;
        double r79220 = r79219 * r79210;
        double r79221 = r79215 + r79220;
        double r79222 = r79214 / r79221;
        double r79223 = 3.0;
        double r79224 = pow(r79222, r79223);
        double r79225 = cbrt(r79224);
        double r79226 = r79210 - r79225;
        return r79226;
}

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-cbrt-cube0.0

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

  4. Applied add-cbrt-cube21.3

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

  5. Applied cbrt-undiv21.3

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020003 
(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)))))