Average Error: 0.0 → 0.3
Time: 2.2s
Precision: binary64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + \log \left({\left(e^{x}\right)}^{\left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)} - x\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + \log \left({\left(e^{x}\right)}^{\left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)} - x
double code(double x) {
	return ((double) ((((double) (2.30753 + ((double) (x * 0.27061)))) / ((double) (1.0 + ((double) (x * ((double) (0.99229 + ((double) (x * 0.04481))))))))) - x));
}
↓
double code(double x) {
	return ((double) ((((double) (2.30753 + ((double) (x * 0.27061)))) / ((double) (1.0 + ((double) log(((double) pow(((double) exp(x)), ((double) (0.99229 + ((double) (x * 0.04481))))))))))) - x));
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
  2. Using strategy rm

  3. Applied add-log-exp0.3

    \[\leadsto \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \color{blue}{\log \left(e^{x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)}} - x\]

  4. Simplified0.3

    \[\leadsto \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \log \color{blue}{\left({\left(e^{x}\right)}^{\left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)}} - x\]

  5. Final simplification0.3

    \[\leadsto \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \log \left({\left(e^{x}\right)}^{\left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)} - x\]

Reproduce

herbie shell --seed 2020182 
(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))