Average Error: 0.0 → 0.0
Time: 2.5s
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 code(double x) {
	return ((double) (x - ((double) (((double) (2.30753 + ((double) (x * 0.27061)))) / ((double) (1.0 + ((double) (((double) (0.99229 + ((double) (x * 0.04481)))) * x))))))));
}
↓
double code(double x) {
	return ((double) (x - ((double) cbrt(((double) pow(((double) (((double) (2.30753 + ((double) (x * 0.27061)))) / ((double) (1.0 + ((double) (((double) (0.99229 + ((double) (x * 0.04481)))) * x)))))), 3.0))))));
}

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-cube21.7

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

  5. Applied cbrt-undiv21.7

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

  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 2020120 
(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)))))