Average Error: 0.0 → 0.0
Time: 15.6s
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 r69188 = 2.30753;
        double r69189 = x;
        double r69190 = 0.27061;
        double r69191 = r69189 * r69190;
        double r69192 = r69188 + r69191;
        double r69193 = 1.0;
        double r69194 = 0.99229;
        double r69195 = 0.04481;
        double r69196 = r69189 * r69195;
        double r69197 = r69194 + r69196;
        double r69198 = r69189 * r69197;
        double r69199 = r69193 + r69198;
        double r69200 = r69192 / r69199;
        double r69201 = r69200 - r69189;
        return r69201;
}
↓
double f(double x) {
        double r69202 = x;
        double r69203 = 0.27061;
        double r69204 = r69202 * r69203;
        double r69205 = 2.30753;
        double r69206 = r69204 + r69205;
        double r69207 = 1.0;
        double r69208 = 0.99229;
        double r69209 = 0.04481;
        double r69210 = r69202 * r69209;
        double r69211 = r69208 + r69210;
        double r69212 = r69202 * r69211;
        double r69213 = r69207 + r69212;
        double r69214 = r69206 / r69213;
        double r69215 = r69205 - r69204;
        double r69216 = r69214 * r69215;
        double r69217 = 1.0;
        double r69218 = r69217 / r69215;
        double r69219 = r69216 * r69218;
        double r69220 = r69219 - r69202;
        return r69220;
}

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))