Average Error: 59.9 → 0.7
Time: 3.3m
Precision: 64
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]
↓
\[\left(\frac{-0.13857109526572012}{z - -5} + \left(\left(\left(\frac{-1259.1392167224028}{z + 1} + \frac{771.3234287776531}{z + 2}\right) + \left(\frac{676.5203681218851}{z} + \left(\frac{-176.6150291621406}{z - -3} + 0.9999999999998099\right)\right)\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z + 7} + \frac{9.984369578019572 \cdot 10^{-06}}{z + 6}\right) + \frac{12.507343278686905}{4 + z}\right)\right)\right) \cdot \frac{\frac{\sqrt{\sqrt{\pi \cdot 2} \cdot {\left(0.5 + \left(\left(z - 1\right) + 7\right)\right)}^{\left(\left(z - 1\right) + 0.5\right)}} \cdot \sqrt{\sqrt{\pi \cdot 2} \cdot {\left(0.5 + \left(\left(z - 1\right) + 7\right)\right)}^{\left(\left(z - 1\right) + 0.5\right)}}}{e^{\left(z - 1\right) + 7}}}{e^{0.5}}\]
\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{-0.13857109526572012}{z - -5} + \left(\left(\left(\frac{-1259.1392167224028}{z + 1} + \frac{771.3234287776531}{z + 2}\right) + \left(\frac{676.5203681218851}{z} + \left(\frac{-176.6150291621406}{z - -3} + 0.9999999999998099\right)\right)\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z + 7} + \frac{9.984369578019572 \cdot 10^{-06}}{z + 6}\right) + \frac{12.507343278686905}{4 + z}\right)\right)\right) \cdot \frac{\frac{\sqrt{\sqrt{\pi \cdot 2} \cdot {\left(0.5 + \left(\left(z - 1\right) + 7\right)\right)}^{\left(\left(z - 1\right) + 0.5\right)}} \cdot \sqrt{\sqrt{\pi \cdot 2} \cdot {\left(0.5 + \left(\left(z - 1\right) + 7\right)\right)}^{\left(\left(z - 1\right) + 0.5\right)}}}{e^{\left(z - 1\right) + 7}}}{e^{0.5}}
double f(double z) {
        double r14714912 = atan2(1.0, 0.0);
        double r14714913 = 2.0;
        double r14714914 = r14714912 * r14714913;
        double r14714915 = sqrt(r14714914);
        double r14714916 = z;
        double r14714917 = 1.0;
        double r14714918 = r14714916 - r14714917;
        double r14714919 = 7.0;
        double r14714920 = r14714918 + r14714919;
        double r14714921 = 0.5;
        double r14714922 = r14714920 + r14714921;
        double r14714923 = r14714918 + r14714921;
        double r14714924 = pow(r14714922, r14714923);
        double r14714925 = r14714915 * r14714924;
        double r14714926 = -r14714922;
        double r14714927 = exp(r14714926);
        double r14714928 = r14714925 * r14714927;
        double r14714929 = 0.9999999999998099;
        double r14714930 = 676.5203681218851;
        double r14714931 = r14714918 + r14714917;
        double r14714932 = r14714930 / r14714931;
        double r14714933 = r14714929 + r14714932;
        double r14714934 = -1259.1392167224028;
        double r14714935 = r14714918 + r14714913;
        double r14714936 = r14714934 / r14714935;
        double r14714937 = r14714933 + r14714936;
        double r14714938 = 771.3234287776531;
        double r14714939 = 3.0;
        double r14714940 = r14714918 + r14714939;
        double r14714941 = r14714938 / r14714940;
        double r14714942 = r14714937 + r14714941;
        double r14714943 = -176.6150291621406;
        double r14714944 = 4.0;
        double r14714945 = r14714918 + r14714944;
        double r14714946 = r14714943 / r14714945;
        double r14714947 = r14714942 + r14714946;
        double r14714948 = 12.507343278686905;
        double r14714949 = 5.0;
        double r14714950 = r14714918 + r14714949;
        double r14714951 = r14714948 / r14714950;
        double r14714952 = r14714947 + r14714951;
        double r14714953 = -0.13857109526572012;
        double r14714954 = 6.0;
        double r14714955 = r14714918 + r14714954;
        double r14714956 = r14714953 / r14714955;
        double r14714957 = r14714952 + r14714956;
        double r14714958 = 9.984369578019572e-06;
        double r14714959 = r14714958 / r14714920;
        double r14714960 = r14714957 + r14714959;
        double r14714961 = 1.5056327351493116e-07;
        double r14714962 = 8.0;
        double r14714963 = r14714918 + r14714962;
        double r14714964 = r14714961 / r14714963;
        double r14714965 = r14714960 + r14714964;
        double r14714966 = r14714928 * r14714965;
        return r14714966;
}
↓
double f(double z) {
        double r14714967 = -0.13857109526572012;
        double r14714968 = z;
        double r14714969 = -5.0;
        double r14714970 = r14714968 - r14714969;
        double r14714971 = r14714967 / r14714970;
        double r14714972 = -1259.1392167224028;
        double r14714973 = 1.0;
        double r14714974 = r14714968 + r14714973;
        double r14714975 = r14714972 / r14714974;
        double r14714976 = 771.3234287776531;
        double r14714977 = 2.0;
        double r14714978 = r14714968 + r14714977;
        double r14714979 = r14714976 / r14714978;
        double r14714980 = r14714975 + r14714979;
        double r14714981 = 676.5203681218851;
        double r14714982 = r14714981 / r14714968;
        double r14714983 = -176.6150291621406;
        double r14714984 = -3.0;
        double r14714985 = r14714968 - r14714984;
        double r14714986 = r14714983 / r14714985;
        double r14714987 = 0.9999999999998099;
        double r14714988 = r14714986 + r14714987;
        double r14714989 = r14714982 + r14714988;
        double r14714990 = r14714980 + r14714989;
        double r14714991 = 1.5056327351493116e-07;
        double r14714992 = 7.0;
        double r14714993 = r14714968 + r14714992;
        double r14714994 = r14714991 / r14714993;
        double r14714995 = 9.984369578019572e-06;
        double r14714996 = 6.0;
        double r14714997 = r14714968 + r14714996;
        double r14714998 = r14714995 / r14714997;
        double r14714999 = r14714994 + r14714998;
        double r14715000 = 12.507343278686905;
        double r14715001 = 4.0;
        double r14715002 = r14715001 + r14714968;
        double r14715003 = r14715000 / r14715002;
        double r14715004 = r14714999 + r14715003;
        double r14715005 = r14714990 + r14715004;
        double r14715006 = r14714971 + r14715005;
        double r14715007 = atan2(1.0, 0.0);
        double r14715008 = r14715007 * r14714977;
        double r14715009 = sqrt(r14715008);
        double r14715010 = 0.5;
        double r14715011 = r14714968 - r14714973;
        double r14715012 = r14715011 + r14714992;
        double r14715013 = r14715010 + r14715012;
        double r14715014 = r14715011 + r14715010;
        double r14715015 = pow(r14715013, r14715014);
        double r14715016 = r14715009 * r14715015;
        double r14715017 = sqrt(r14715016);
        double r14715018 = r14715017 * r14715017;
        double r14715019 = exp(r14715012);
        double r14715020 = r14715018 / r14715019;
        double r14715021 = exp(r14715010);
        double r14715022 = r14715020 / r14715021;
        double r14715023 = r14715006 * r14715022;
        return r14715023;
}

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. Simplified1.0

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

  4. Applied exp-sum1.0

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

  5. Applied associate-/r*0.7

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

  7. Applied add-sqr-sqrt0.7

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

  8. Final simplification0.7

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

Reproduce

herbie shell --seed 2019132 
(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)))))