Average Error: 0.0 → 0.0
Time: 2.4s
Precision: binary64
\[x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
↓
\[x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \sqrt[3]{x} \cdot \left(\left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right)}\]
x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}
↓
x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \sqrt[3]{x} \cdot \left(\left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right)}
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) (((double) (2.30753 + ((double) (x * 0.27061)))) / ((double) (1.0 + ((double) (((double) cbrt(x)) * ((double) (((double) (0.99229 + ((double) (x * 0.04481)))) * ((double) (((double) cbrt(x)) * ((double) cbrt(x))))))))))))));
}

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-cube-cbrt0.0

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

  4. Applied associate-*r*0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020181 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, D"
  :precision binary64
  (- x (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))))