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

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

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

  3. Applied clear-num_binary640.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020253 
(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))