Average Error: 0.0 → 0.0
Time: 2.5s
Precision: binary64
\[x - \frac{2.30753 + x \cdot 0.27061}{1 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}\]
↓
\[x + \frac{2.30753 + x \cdot 0.27061}{\sqrt{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}} \cdot \frac{-1}{\sqrt{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}}\]
x - \frac{2.30753 + x \cdot 0.27061}{1 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}
↓
x + \frac{2.30753 + x \cdot 0.27061}{\sqrt{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}} \cdot \frac{-1}{\sqrt{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}}
double code(double x) {
	return ((double) (x - (((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) (x + ((double) ((((double) (2.30753 + ((double) (x * 0.27061)))) / ((double) sqrt(((double) (1.0 + ((double) (x * ((double) (0.99229 + ((double) (x * 0.04481))))))))))) * (-1.0 / ((double) sqrt(((double) (1.0 + ((double) (x * ((double) (0.99229 + ((double) (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 add-sqr-sqrt0.0

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

  4. Applied *-un-lft-identity0.0

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

  5. Applied times-frac0.0

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

  6. Simplified0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020196 
(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)))))