Average Error: 0.0 → 0.0
Time: 13.5s
Precision: 64
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]
↓
\[\left(\frac{162377988252285}{70368744177664} + x \cdot \frac{609359547581365}{2251799813685248}\right) \cdot \sqrt[3]{\frac{1}{{\left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right)}^{3}}} - x\]
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x
↓
\left(\frac{162377988252285}{70368744177664} + x \cdot \frac{609359547581365}{2251799813685248}\right) \cdot \sqrt[3]{\frac{1}{{\left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right)}^{3}}} - x
double f(double x) {
        double r74931 = 2.30753;
        double r74932 = x;
        double r74933 = 0.27061;
        double r74934 = r74932 * r74933;
        double r74935 = r74931 + r74934;
        double r74936 = 1.0;
        double r74937 = 0.99229;
        double r74938 = 0.04481;
        double r74939 = r74932 * r74938;
        double r74940 = r74937 + r74939;
        double r74941 = r74932 * r74940;
        double r74942 = r74936 + r74941;
        double r74943 = r74935 / r74942;
        double r74944 = r74943 - r74932;
        return r74944;
}
↓
double f(double x) {
        double r74945 = 162377988252285.0;
        double r74946 = 70368744177664.0;
        double r74947 = r74945 / r74946;
        double r74948 = x;
        double r74949 = 609359547581365.0;
        double r74950 = 2251799813685248.0;
        double r74951 = r74949 / r74950;
        double r74952 = r74948 * r74951;
        double r74953 = r74947 + r74952;
        double r74954 = 1.0;
        double r74955 = 1.0;
        double r74956 = 8937753748486939.0;
        double r74957 = 9007199254740992.0;
        double r74958 = r74956 / r74957;
        double r74959 = 3228900788839551.0;
        double r74960 = 7.205759403792794e+16;
        double r74961 = r74959 / r74960;
        double r74962 = r74948 * r74961;
        double r74963 = r74958 + r74962;
        double r74964 = r74948 * r74963;
        double r74965 = r74955 + r74964;
        double r74966 = 3.0;
        double r74967 = pow(r74965, r74966);
        double r74968 = r74954 / r74967;
        double r74969 = cbrt(r74968);
        double r74970 = r74953 * r74969;
        double r74971 = r74970 - r74948;
        return r74971;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\frac{\frac{162377988252285}{70368744177664} + x \cdot \frac{609359547581365}{2251799813685248}}{1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)} - x}\]
  3. Using strategy rm

  4. Applied div-inv0.0

    \[\leadsto \color{blue}{\left(\frac{162377988252285}{70368744177664} + x \cdot \frac{609359547581365}{2251799813685248}\right) \cdot \frac{1}{1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)}} - x\]
  5. Using strategy rm

  6. Applied add-cbrt-cube0.0

    \[\leadsto \left(\frac{162377988252285}{70368744177664} + x \cdot \frac{609359547581365}{2251799813685248}\right) \cdot \frac{1}{\color{blue}{\sqrt[3]{\left(\left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right) \cdot \left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right)\right) \cdot \left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right)}}} - x\]

  7. Applied add-cbrt-cube0.0

    \[\leadsto \left(\frac{162377988252285}{70368744177664} + x \cdot \frac{609359547581365}{2251799813685248}\right) \cdot \frac{\color{blue}{\sqrt[3]{\left(1 \cdot 1\right) \cdot 1}}}{\sqrt[3]{\left(\left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right) \cdot \left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right)\right) \cdot \left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right)}} - x\]

  8. Applied cbrt-undiv0.0

    \[\leadsto \left(\frac{162377988252285}{70368744177664} + x \cdot \frac{609359547581365}{2251799813685248}\right) \cdot \color{blue}{\sqrt[3]{\frac{\left(1 \cdot 1\right) \cdot 1}{\left(\left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right) \cdot \left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right)\right) \cdot \left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right)}}} - x\]

  9. Simplified0.0

    \[\leadsto \left(\frac{162377988252285}{70368744177664} + x \cdot \frac{609359547581365}{2251799813685248}\right) \cdot \sqrt[3]{\color{blue}{\frac{1}{{\left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right)}^{3}}}} - x\]

  10. Final simplification0.0

    \[\leadsto \left(\frac{162377988252285}{70368744177664} + x \cdot \frac{609359547581365}{2251799813685248}\right) \cdot \sqrt[3]{\frac{1}{{\left(1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)\right)}^{3}}} - x\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C"
  :precision binary64
  (- (/ (+ 2.30753 (* x 0.27061000000000002)) (+ 1 (* x (+ 0.992290000000000005 (* x 0.044810000000000003))))) x))