Average Error: 0.0 → 0.0
Time: 15.3s
Precision: 64
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]
↓
\[\left(\frac{x \cdot 0.2706100000000000171951342053944244980812 + 2.307529999999999859028321225196123123169}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} \cdot \left(2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812\right)\right) \cdot \frac{1}{2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812} - x\]
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x
↓
\left(\frac{x \cdot 0.2706100000000000171951342053944244980812 + 2.307529999999999859028321225196123123169}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} \cdot \left(2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812\right)\right) \cdot \frac{1}{2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812} - x
double f(double x) {
        double r66039 = 2.30753;
        double r66040 = x;
        double r66041 = 0.27061;
        double r66042 = r66040 * r66041;
        double r66043 = r66039 + r66042;
        double r66044 = 1.0;
        double r66045 = 0.99229;
        double r66046 = 0.04481;
        double r66047 = r66040 * r66046;
        double r66048 = r66045 + r66047;
        double r66049 = r66040 * r66048;
        double r66050 = r66044 + r66049;
        double r66051 = r66043 / r66050;
        double r66052 = r66051 - r66040;
        return r66052;
}
↓
double f(double x) {
        double r66053 = x;
        double r66054 = 0.27061;
        double r66055 = r66053 * r66054;
        double r66056 = 2.30753;
        double r66057 = r66055 + r66056;
        double r66058 = 1.0;
        double r66059 = 0.99229;
        double r66060 = 0.04481;
        double r66061 = r66053 * r66060;
        double r66062 = r66059 + r66061;
        double r66063 = r66053 * r66062;
        double r66064 = r66058 + r66063;
        double r66065 = r66057 / r66064;
        double r66066 = r66056 - r66055;
        double r66067 = r66065 * r66066;
        double r66068 = 1.0;
        double r66069 = r66068 / r66066;
        double r66070 = r66067 * r66069;
        double r66071 = r66070 - r66053;
        return r66071;
}

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 clear-num0.0

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

  5. Applied flip-+16.1

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

  6. Applied associate-/r/16.1

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

  7. Applied add-cube-cbrt16.1

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}{2.307529999999999859028321225196123123169 \cdot 2.307529999999999859028321225196123123169 - \left(x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \left(x \cdot 0.2706100000000000171951342053944244980812\right)} \cdot \left(2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812\right)} - x\]

  8. Applied times-frac16.1

    \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}{2.307529999999999859028321225196123123169 \cdot 2.307529999999999859028321225196123123169 - \left(x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \left(x \cdot 0.2706100000000000171951342053944244980812\right)}} \cdot \frac{\sqrt[3]{1}}{2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812}} - x\]

  9. Simplified0.0

    \[\leadsto \color{blue}{\left(\frac{x \cdot 0.2706100000000000171951342053944244980812 + 2.307529999999999859028321225196123123169}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} \cdot \left(2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812\right)\right)} \cdot \frac{\sqrt[3]{1}}{2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812} - x\]

  10. Simplified0.0

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

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C"
  :precision binary64
  (- (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* x (+ 0.99229 (* x 0.04481))))) x))