Average Error: 0.0 → 0.0
Time: 2.5s
Precision: binary64
Cost: 13952
\[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\]
↓
\[\sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}\right)}^{3}} - x\]
\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - 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
(FPCore (x)
 :precision binary64
 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
↓
(FPCore (x)
 :precision binary64
 (-
  (cbrt
   (pow
    (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
    3.0))
  x))
double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
}
↓
double code(double x) {
	return cbrt(pow(((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))), 3.0)) - x;
}

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
\[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\]
Alternative 2
Error0.9
Cost832
\[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot 0.99229} - x\]
Alternative 3
Error1.4
Cost192
\[2.30753 - x\]
Alternative 4
Error1.1
Cost456
\[\begin{array}{l} \mathbf{if}\;x \leq -1.0784931178144082 \lor \neg \left(x \leq 1.17885225853273\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;2.30753\\ \end{array}\]
Alternative 5
Error31.7
Cost64
\[2.30753\]
Alternative 6
Error57.1
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.0

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

  3. Applied add-cbrt-cube_binary64_21600.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2021044 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C"
  :precision binary64
  (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))