Average Error: 0.0 → 0.0
Time: 3.0s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)}^{3}} - x\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)}^{3}} - x
double code(double x) {
	return (((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x);
}
↓
double code(double x) {
	return (cbrt(pow(((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))), 3.0)) - 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

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

  3. Applied add-cbrt-cube0.0

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

  4. Applied add-cbrt-cube21.2

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

  5. Applied cbrt-undiv21.2

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020106 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C"
  :precision binary64
  (- (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* x (+ 0.99229 (* x 0.04481))))) x))