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

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

  2. Simplified0.0

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

  4. Applied add-cbrt-cube0.0

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

  5. Applied add-cbrt-cube21.7

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

  6. Applied cbrt-undiv21.7

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020120 +o rules:numerics
(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)))))