Average Error: 59.9 → 0.9
Time: 2.1m
Precision: 64
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]
↓
\[\left(\frac{\left(\frac{9.984369578019572 \cdot 10^{-06}}{z - -6} + \left(\left(\frac{-0.13857109526572012}{z - -5} + \frac{-176.6150291621406}{z + 3}\right) + \frac{12.507343278686905}{4 + z}\right)\right) + \left(\left(\left(\left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) + \frac{771.3234287776531}{2 + z}\right) + \frac{-1259.1392167224028}{z + 1}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{z - -7}\right)}{e^{0.5}} \cdot \frac{1}{e^{z - -6}}\right) \cdot e^{\log \left(\sqrt{\pi \cdot 2}\right) + \left(z - \left(1 - 0.5\right)\right) \cdot \log \left(\left(z - -6\right) + 0.5\right)}\]
\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)
↓
\left(\frac{\left(\frac{9.984369578019572 \cdot 10^{-06}}{z - -6} + \left(\left(\frac{-0.13857109526572012}{z - -5} + \frac{-176.6150291621406}{z + 3}\right) + \frac{12.507343278686905}{4 + z}\right)\right) + \left(\left(\left(\left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) + \frac{771.3234287776531}{2 + z}\right) + \frac{-1259.1392167224028}{z + 1}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{z - -7}\right)}{e^{0.5}} \cdot \frac{1}{e^{z - -6}}\right) \cdot e^{\log \left(\sqrt{\pi \cdot 2}\right) + \left(z - \left(1 - 0.5\right)\right) \cdot \log \left(\left(z - -6\right) + 0.5\right)}
double f(double z) {
        double r3685909 = atan2(1.0, 0.0);
        double r3685910 = 2.0;
        double r3685911 = r3685909 * r3685910;
        double r3685912 = sqrt(r3685911);
        double r3685913 = z;
        double r3685914 = 1.0;
        double r3685915 = r3685913 - r3685914;
        double r3685916 = 7.0;
        double r3685917 = r3685915 + r3685916;
        double r3685918 = 0.5;
        double r3685919 = r3685917 + r3685918;
        double r3685920 = r3685915 + r3685918;
        double r3685921 = pow(r3685919, r3685920);
        double r3685922 = r3685912 * r3685921;
        double r3685923 = -r3685919;
        double r3685924 = exp(r3685923);
        double r3685925 = r3685922 * r3685924;
        double r3685926 = 0.9999999999998099;
        double r3685927 = 676.5203681218851;
        double r3685928 = r3685915 + r3685914;
        double r3685929 = r3685927 / r3685928;
        double r3685930 = r3685926 + r3685929;
        double r3685931 = -1259.1392167224028;
        double r3685932 = r3685915 + r3685910;
        double r3685933 = r3685931 / r3685932;
        double r3685934 = r3685930 + r3685933;
        double r3685935 = 771.3234287776531;
        double r3685936 = 3.0;
        double r3685937 = r3685915 + r3685936;
        double r3685938 = r3685935 / r3685937;
        double r3685939 = r3685934 + r3685938;
        double r3685940 = -176.6150291621406;
        double r3685941 = 4.0;
        double r3685942 = r3685915 + r3685941;
        double r3685943 = r3685940 / r3685942;
        double r3685944 = r3685939 + r3685943;
        double r3685945 = 12.507343278686905;
        double r3685946 = 5.0;
        double r3685947 = r3685915 + r3685946;
        double r3685948 = r3685945 / r3685947;
        double r3685949 = r3685944 + r3685948;
        double r3685950 = -0.13857109526572012;
        double r3685951 = 6.0;
        double r3685952 = r3685915 + r3685951;
        double r3685953 = r3685950 / r3685952;
        double r3685954 = r3685949 + r3685953;
        double r3685955 = 9.984369578019572e-06;
        double r3685956 = r3685955 / r3685917;
        double r3685957 = r3685954 + r3685956;
        double r3685958 = 1.5056327351493116e-07;
        double r3685959 = 8.0;
        double r3685960 = r3685915 + r3685959;
        double r3685961 = r3685958 / r3685960;
        double r3685962 = r3685957 + r3685961;
        double r3685963 = r3685925 * r3685962;
        return r3685963;
}
↓
double f(double z) {
        double r3685964 = 9.984369578019572e-06;
        double r3685965 = z;
        double r3685966 = -6.0;
        double r3685967 = r3685965 - r3685966;
        double r3685968 = r3685964 / r3685967;
        double r3685969 = -0.13857109526572012;
        double r3685970 = -5.0;
        double r3685971 = r3685965 - r3685970;
        double r3685972 = r3685969 / r3685971;
        double r3685973 = -176.6150291621406;
        double r3685974 = 3.0;
        double r3685975 = r3685965 + r3685974;
        double r3685976 = r3685973 / r3685975;
        double r3685977 = r3685972 + r3685976;
        double r3685978 = 12.507343278686905;
        double r3685979 = 4.0;
        double r3685980 = r3685979 + r3685965;
        double r3685981 = r3685978 / r3685980;
        double r3685982 = r3685977 + r3685981;
        double r3685983 = r3685968 + r3685982;
        double r3685984 = 676.5203681218851;
        double r3685985 = r3685984 / r3685965;
        double r3685986 = 0.9999999999998099;
        double r3685987 = r3685985 + r3685986;
        double r3685988 = 771.3234287776531;
        double r3685989 = 2.0;
        double r3685990 = r3685989 + r3685965;
        double r3685991 = r3685988 / r3685990;
        double r3685992 = r3685987 + r3685991;
        double r3685993 = -1259.1392167224028;
        double r3685994 = 1.0;
        double r3685995 = r3685965 + r3685994;
        double r3685996 = r3685993 / r3685995;
        double r3685997 = r3685992 + r3685996;
        double r3685998 = 1.5056327351493116e-07;
        double r3685999 = -7.0;
        double r3686000 = r3685965 - r3685999;
        double r3686001 = r3685998 / r3686000;
        double r3686002 = r3685997 + r3686001;
        double r3686003 = r3685983 + r3686002;
        double r3686004 = 0.5;
        double r3686005 = exp(r3686004);
        double r3686006 = r3686003 / r3686005;
        double r3686007 = exp(r3685967);
        double r3686008 = r3685994 / r3686007;
        double r3686009 = r3686006 * r3686008;
        double r3686010 = atan2(1.0, 0.0);
        double r3686011 = r3686010 * r3685989;
        double r3686012 = sqrt(r3686011);
        double r3686013 = log(r3686012);
        double r3686014 = r3685994 - r3686004;
        double r3686015 = r3685965 - r3686014;
        double r3686016 = r3685967 + r3686004;
        double r3686017 = log(r3686016);
        double r3686018 = r3686015 * r3686017;
        double r3686019 = r3686013 + r3686018;
        double r3686020 = exp(r3686019);
        double r3686021 = r3686009 * r3686020;
        return r3686021;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 59.9

    \[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]

  2. Simplified0.9

    \[\leadsto \color{blue}{\left({\left(\left(z - -6\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \left(\left(\frac{771.3234287776531}{z + 2} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right)}{e^{\left(z - -6\right) + 0.5}}}\]
  3. Using strategy rm

  4. Applied add-exp-log0.9

    \[\leadsto \color{blue}{e^{\log \left({\left(\left(z - -6\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right)}} \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \left(\left(\frac{771.3234287776531}{z + 2} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right)}{e^{\left(z - -6\right) + 0.5}}\]

  5. Simplified0.9

    \[\leadsto e^{\color{blue}{\log \left(\sqrt{\pi \cdot 2}\right) + \left(z - \left(1 - 0.5\right)\right) \cdot \log \left(0.5 + \left(z - -6\right)\right)}} \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \left(\left(\frac{771.3234287776531}{z + 2} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right)}{e^{\left(z - -6\right) + 0.5}}\]
  6. Using strategy rm

  7. Applied exp-sum0.9

    \[\leadsto e^{\log \left(\sqrt{\pi \cdot 2}\right) + \left(z - \left(1 - 0.5\right)\right) \cdot \log \left(0.5 + \left(z - -6\right)\right)} \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \left(\left(\frac{771.3234287776531}{z + 2} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right)}{\color{blue}{e^{z - -6} \cdot e^{0.5}}}\]

  8. Applied *-un-lft-identity0.9

    \[\leadsto e^{\log \left(\sqrt{\pi \cdot 2}\right) + \left(z - \left(1 - 0.5\right)\right) \cdot \log \left(0.5 + \left(z - -6\right)\right)} \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \left(\left(\frac{771.3234287776531}{z + 2} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \color{blue}{1 \cdot \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}}\right)}{e^{z - -6} \cdot e^{0.5}}\]

  9. Applied *-un-lft-identity0.9

    \[\leadsto e^{\log \left(\sqrt{\pi \cdot 2}\right) + \left(z - \left(1 - 0.5\right)\right) \cdot \log \left(0.5 + \left(z - -6\right)\right)} \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \left(\left(\frac{771.3234287776531}{z + 2} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right) + \left(\color{blue}{1 \cdot \left(\frac{12.507343278686905}{z + 4} + \left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right)\right)} + 1 \cdot \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right)}{e^{z - -6} \cdot e^{0.5}}\]

  10. Applied distribute-lft-out0.9

    \[\leadsto e^{\log \left(\sqrt{\pi \cdot 2}\right) + \left(z - \left(1 - 0.5\right)\right) \cdot \log \left(0.5 + \left(z - -6\right)\right)} \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \left(\left(\frac{771.3234287776531}{z + 2} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right) + \color{blue}{1 \cdot \left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right)}}{e^{z - -6} \cdot e^{0.5}}\]

  11. Applied *-un-lft-identity0.9

    \[\leadsto e^{\log \left(\sqrt{\pi \cdot 2}\right) + \left(z - \left(1 - 0.5\right)\right) \cdot \log \left(0.5 + \left(z - -6\right)\right)} \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \color{blue}{1 \cdot \left(\left(\frac{771.3234287776531}{z + 2} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)}\right) + 1 \cdot \left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right)}{e^{z - -6} \cdot e^{0.5}}\]

  12. Applied *-un-lft-identity0.9

    \[\leadsto e^{\log \left(\sqrt{\pi \cdot 2}\right) + \left(z - \left(1 - 0.5\right)\right) \cdot \log \left(0.5 + \left(z - -6\right)\right)} \cdot \frac{\left(\color{blue}{1 \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{z - -7}} + 1 \cdot \left(\left(\frac{771.3234287776531}{z + 2} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right) + 1 \cdot \left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right)}{e^{z - -6} \cdot e^{0.5}}\]

  13. Applied distribute-lft-out0.9

    \[\leadsto e^{\log \left(\sqrt{\pi \cdot 2}\right) + \left(z - \left(1 - 0.5\right)\right) \cdot \log \left(0.5 + \left(z - -6\right)\right)} \cdot \frac{\color{blue}{1 \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \left(\left(\frac{771.3234287776531}{z + 2} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right)} + 1 \cdot \left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right)}{e^{z - -6} \cdot e^{0.5}}\]

  14. Applied distribute-lft-out0.9

    \[\leadsto e^{\log \left(\sqrt{\pi \cdot 2}\right) + \left(z - \left(1 - 0.5\right)\right) \cdot \log \left(0.5 + \left(z - -6\right)\right)} \cdot \frac{\color{blue}{1 \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \left(\left(\frac{771.3234287776531}{z + 2} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right)\right)}}{e^{z - -6} \cdot e^{0.5}}\]

  15. Applied times-frac0.9

    \[\leadsto e^{\log \left(\sqrt{\pi \cdot 2}\right) + \left(z - \left(1 - 0.5\right)\right) \cdot \log \left(0.5 + \left(z - -6\right)\right)} \cdot \color{blue}{\left(\frac{1}{e^{z - -6}} \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \left(\left(\frac{771.3234287776531}{z + 2} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right)}{e^{0.5}}\right)}\]

  16. Final simplification0.9

    \[\leadsto \left(\frac{\left(\frac{9.984369578019572 \cdot 10^{-06}}{z - -6} + \left(\left(\frac{-0.13857109526572012}{z - -5} + \frac{-176.6150291621406}{z + 3}\right) + \frac{12.507343278686905}{4 + z}\right)\right) + \left(\left(\left(\left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) + \frac{771.3234287776531}{2 + z}\right) + \frac{-1259.1392167224028}{z + 1}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{z - -7}\right)}{e^{0.5}} \cdot \frac{1}{e^{z - -6}}\right) \cdot e^{\log \left(\sqrt{\pi \cdot 2}\right) + \left(z - \left(1 - 0.5\right)\right) \cdot \log \left(\left(z - -6\right) + 0.5\right)}\]

Reproduce

herbie shell --seed 2019153 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z greater than 0.5"
  (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- z 1) 7) 0.5) (+ (- z 1) 0.5))) (exp (- (+ (+ (- z 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- z 1) 1))) (/ -1259.1392167224028 (+ (- z 1) 2))) (/ 771.3234287776531 (+ (- z 1) 3))) (/ -176.6150291621406 (+ (- z 1) 4))) (/ 12.507343278686905 (+ (- z 1) 5))) (/ -0.13857109526572012 (+ (- z 1) 6))) (/ 9.984369578019572e-06 (+ (- z 1) 7))) (/ 1.5056327351493116e-07 (+ (- z 1) 8)))))