Average Error: 0.0 → 0.0
Time: 6.8s
Precision: 64
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]
↓
\[\left(0.2706100000000000171951342053944244980812 \cdot x + 2.307529999999999859028321225196123123169\right) \cdot \frac{1}{1 + \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right) \cdot x} - x\]
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x
↓
\left(0.2706100000000000171951342053944244980812 \cdot x + 2.307529999999999859028321225196123123169\right) \cdot \frac{1}{1 + \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right) \cdot x} - x
double f(double x) {
        double r2780255 = 2.30753;
        double r2780256 = x;
        double r2780257 = 0.27061;
        double r2780258 = r2780256 * r2780257;
        double r2780259 = r2780255 + r2780258;
        double r2780260 = 1.0;
        double r2780261 = 0.99229;
        double r2780262 = 0.04481;
        double r2780263 = r2780256 * r2780262;
        double r2780264 = r2780261 + r2780263;
        double r2780265 = r2780256 * r2780264;
        double r2780266 = r2780260 + r2780265;
        double r2780267 = r2780259 / r2780266;
        double r2780268 = r2780267 - r2780256;
        return r2780268;
}
↓
double f(double x) {
        double r2780269 = 0.27061;
        double r2780270 = x;
        double r2780271 = r2780269 * r2780270;
        double r2780272 = 2.30753;
        double r2780273 = r2780271 + r2780272;
        double r2780274 = 1.0;
        double r2780275 = 1.0;
        double r2780276 = 0.04481;
        double r2780277 = r2780276 * r2780270;
        double r2780278 = 0.99229;
        double r2780279 = r2780277 + r2780278;
        double r2780280 = r2780279 * r2780270;
        double r2780281 = r2780275 + r2780280;
        double r2780282 = r2780274 / r2780281;
        double r2780283 = r2780273 * r2780282;
        double r2780284 = r2780283 - r2780270;
        return r2780284;
}

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

    \[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]
  2. Using strategy rm

  3. Applied div-inv0.0

    \[\leadsto \color{blue}{\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}} - x\]

  4. Final simplification0.0

    \[\leadsto \left(0.2706100000000000171951342053944244980812 \cdot x + 2.307529999999999859028321225196123123169\right) \cdot \frac{1}{1 + \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right) \cdot x} - x\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C"
  (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))