Average Error: 0.0 → 0.0
Time: 5.4s
Precision: 64
\[x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
↓
\[x - \log \left({\left(e^{\frac{1}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right) \cdot 1}}\right)}^{\left(0.27061000000000002 \cdot x\right)} \cdot {\left(e^{\frac{1}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right) \cdot 1}}\right)}^{2.30753}\right)\]
x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}
↓
x - \log \left({\left(e^{\frac{1}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right) \cdot 1}}\right)}^{\left(0.27061000000000002 \cdot x\right)} \cdot {\left(e^{\frac{1}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right) \cdot 1}}\right)}^{2.30753}\right)
double code(double x) {
	return (x - ((2.30753 + (x * 0.27061)) / (1.0 + ((0.99229 + (x * 0.04481)) * x))));
}
↓
double code(double x) {
	return (x - log((pow(exp((1.0 / (fma(x, fma(0.04481, x, 0.99229), 1.0) * 1.0))), (0.27061 * x)) * pow(exp((1.0 / (fma(x, fma(0.04481, x, 0.99229), 1.0) * 1.0))), 2.30753))));
}

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-log-exp0.0

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

  4. Simplified0.0

    \[\leadsto x - \log \color{blue}{\left({\left(e^{\frac{1}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right) \cdot 1}}\right)}^{\left(\mathsf{fma}\left(0.27061000000000002, x, 2.30753\right)\right)}\right)}\]
  5. Using strategy rm

  6. Applied fma-udef0.0

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

  7. Applied unpow-prod-up0.0

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

  8. Final simplification0.0

    \[\leadsto x - \log \left({\left(e^{\frac{1}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right) \cdot 1}}\right)}^{\left(0.27061000000000002 \cdot x\right)} \cdot {\left(e^{\frac{1}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right) \cdot 1}}\right)}^{2.30753}\right)\]

Reproduce

herbie shell --seed 2020057 +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)))))