Average Error: 0.0 → 0.0
Time: 2.1s
Precision: binary64
\[x - \frac{2.30753 + x \cdot 0.27061}{1 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}\]
↓
\[x + \left(2.30753 + x \cdot 0.27061\right) \cdot \frac{-1}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}\]
x - \frac{2.30753 + x \cdot 0.27061}{1 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}
↓
x + \left(2.30753 + x \cdot 0.27061\right) \cdot \frac{-1}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}
(FPCore (x)
 :precision binary64
 (- x (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))))
↓
(FPCore (x)
 :precision binary64
 (+
  x
  (*
   (+ 2.30753 (* x 0.27061))
   (/ -1.0 (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))))
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 + ((2.30753 + (x * 0.27061)) * (-1.0 / (1.0 + (x * (0.99229 + (x * 0.04481))))));
}

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

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

  3. Applied div-inv_binary640.0

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

  4. Applied cancel-sign-sub-inv_binary640.0

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

  5. Final simplification0.0

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

Alternatives

Reproduce

herbie shell --seed 2021118 
(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)))))