Average Error: 0.0 → 0.0
Time: 2.4s
Precision: binary64
Cost: 13952
\[x - \frac{2.30753 + x \cdot 0.27061}{1 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}\]
↓
\[x - \sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}\right)}^{3}}\]
x - \frac{2.30753 + x \cdot 0.27061}{1 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}
↓
x - \sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}\right)}^{3}}
(FPCore (x)
 :precision binary64
 (- x (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))))
↓
(FPCore (x)
 :precision binary64
 (-
  x
  (cbrt
   (pow
    (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
    3.0))))
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 - cbrt(pow(((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))), 3.0));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error0.0
Cost1088
\[x - \frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}\]
Alternative 2
Error0.9
Cost832
\[x - \frac{2.30753 + x \cdot 0.27061}{1 + x \cdot 0.99229}\]
Alternative 3
Error1.4
Cost192
\[x + -2.30753\]
Alternative 4
Error1.1
Cost706
\[\begin{array}{l} \mathbf{if}\;x \leq -1.0784931178144082:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.17885225853273:\\ \;\;\;\;-2.30753\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
Alternative 5
Error26.4
Cost706
\[\begin{array}{l} \mathbf{if}\;x \leq -2.8263877807862956:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.17885225853273:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
Alternative 6
Error57.1
Cost64
\[-1\]
Alternative 7
Error62.3
Cost64
\[0\]
Alternative 8
Error62.5
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.0

    \[x - \frac{2.30753 + x \cdot 0.27061}{1 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube_binary64_7960.0

    \[\leadsto x - \color{blue}{\sqrt[3]{\left(\frac{2.30753 + x \cdot 0.27061}{1 + \left(0.99229 + x \cdot 0.04481\right) \cdot x} \cdot \frac{2.30753 + x \cdot 0.27061}{1 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}\right) \cdot \frac{2.30753 + x \cdot 0.27061}{1 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}}}\]

  4. Simplified0.0

    \[\leadsto x - \sqrt[3]{\color{blue}{{\left(\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}\right)}^{3}}}\]

  5. Simplified0.0

    \[\leadsto \color{blue}{x - \sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}\right)}^{3}}}\]

  6. Final simplification0.0

    \[\leadsto x - \sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}\right)}^{3}}\]

Reproduce

herbie shell --seed 2021044 
(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)))))