Jmat.Real.gamma, branch z greater than 0.5

Average Error: 61.6 → 1.1

Time: 3.2m

Precision: 64

• could not determine a ground truth for program body

  1. z = 1.957382309183684e+68

Math

\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(z - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\]

↓

\[\left(338.2601840609425494221795815974473953247 \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \left(\frac{{\left(\log 6.5\right)}^{2} \cdot \left(z \cdot \sqrt{2}\right)}{e^{6.5}} \cdot \sqrt{\pi}\right)\right) + \left(2581.191799681222164508653804659843444824 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right) + \left(676.5203681218850988443591631948947906494 \cdot \left(\frac{\sqrt{2}}{z \cdot e^{6.5}} \cdot e^{\log \left(\sqrt{\pi}\right) - \left(\log 6.5 \cdot 1\right) \cdot 0.5}\right) + \left(676.5203681218850988443591631948947906494 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\log 6.5 \cdot \sqrt{2}}{e^{6.5}} \cdot {\left(\frac{1}{{6.5}^{1}}\right)}^{0.5}\right)\right) + 169.1300920304712747110897907987236976624 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{5}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right)\right)\right)\right)\right) - 1656.810451873720467119710519909858703613 \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \left(\frac{\log 6.5 \cdot \left(z \cdot \sqrt{2}\right)}{e^{6.5}} \cdot \sqrt{\pi}\right) + \sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{6.5}} \cdot {\left(\frac{1}{{6.5}^{1}}\right)}^{0.5}\right)\right)\]

C

double f(double z) {
        double r134128 = atan2(1.0, 0.0);
        double r134129 = 2.0;
        double r134130 = r134128 * r134129;
        double r134131 = sqrt(r134130);
        double r134132 = z;
        double r134133 = 1.0;
        double r134134 = r134132 - r134133;
        double r134135 = 7.0;
        double r134136 = r134134 + r134135;
        double r134137 = 0.5;
        double r134138 = r134136 + r134137;
        double r134139 = r134134 + r134137;
        double r134140 = pow(r134138, r134139);
        double r134141 = r134131 * r134140;
        double r134142 = -r134138;
        double r134143 = exp(r134142);
        double r134144 = r134141 * r134143;
        double r134145 = 0.9999999999998099;
        double r134146 = 676.5203681218851;
        double r134147 = r134134 + r134133;
        double r134148 = r134146 / r134147;
        double r134149 = r134145 + r134148;
        double r134150 = -1259.1392167224028;
        double r134151 = r134134 + r134129;
        double r134152 = r134150 / r134151;
        double r134153 = r134149 + r134152;
        double r134154 = 771.3234287776531;
        double r134155 = 3.0;
        double r134156 = r134134 + r134155;
        double r134157 = r134154 / r134156;
        double r134158 = r134153 + r134157;
        double r134159 = -176.6150291621406;
        double r134160 = 4.0;
        double r134161 = r134134 + r134160;
        double r134162 = r134159 / r134161;
        double r134163 = r134158 + r134162;
        double r134164 = 12.507343278686905;
        double r134165 = 5.0;
        double r134166 = r134134 + r134165;
        double r134167 = r134164 / r134166;
        double r134168 = r134163 + r134167;
        double r134169 = -0.13857109526572012;
        double r134170 = 6.0;
        double r134171 = r134134 + r134170;
        double r134172 = r134169 / r134171;
        double r134173 = r134168 + r134172;
        double r134174 = 9.984369578019572e-06;
        double r134175 = r134174 / r134136;
        double r134176 = r134173 + r134175;
        double r134177 = 1.5056327351493116e-07;
        double r134178 = 8.0;
        double r134179 = r134134 + r134178;
        double r134180 = r134177 / r134179;
        double r134181 = r134176 + r134180;
        double r134182 = r134144 * r134181;
        return r134182;
}

↓

double f(double z) {
        double r134183 = 338.26018406094255;
        double r134184 = 1.0;
        double r134185 = 6.5;
        double r134186 = 1.0;
        double r134187 = pow(r134185, r134186);
        double r134188 = r134184 / r134187;
        double r134189 = 0.5;
        double r134190 = pow(r134188, r134189);
        double r134191 = log(r134185);
        double r134192 = 2.0;
        double r134193 = pow(r134191, r134192);
        double r134194 = z;
        double r134195 = 2.0;
        double r134196 = sqrt(r134195);
        double r134197 = r134194 * r134196;
        double r134198 = r134193 * r134197;
        double r134199 = exp(r134185);
        double r134200 = r134198 / r134199;
        double r134201 = atan2(1.0, 0.0);
        double r134202 = sqrt(r134201);
        double r134203 = r134200 * r134202;
        double r134204 = r134190 * r134203;
        double r134205 = r134183 * r134204;
        double r134206 = 2581.191799681222;
        double r134207 = r134196 * r134194;
        double r134208 = r134207 / r134199;
        double r134209 = r134190 * r134202;
        double r134210 = r134208 * r134209;
        double r134211 = r134206 * r134210;
        double r134212 = 676.5203681218851;
        double r134213 = r134194 * r134199;
        double r134214 = r134196 / r134213;
        double r134215 = log(r134202);
        double r134216 = r134191 * r134186;
        double r134217 = r134216 * r134189;
        double r134218 = r134215 - r134217;
        double r134219 = exp(r134218);
        double r134220 = r134214 * r134219;
        double r134221 = r134212 * r134220;
        double r134222 = r134191 * r134196;
        double r134223 = r134222 / r134199;
        double r134224 = r134223 * r134190;
        double r134225 = r134202 * r134224;
        double r134226 = r134212 * r134225;
        double r134227 = 169.13009203047127;
        double r134228 = 5.0;
        double r134229 = pow(r134185, r134228);
        double r134230 = r134184 / r134229;
        double r134231 = pow(r134230, r134189);
        double r134232 = r134231 * r134202;
        double r134233 = r134208 * r134232;
        double r134234 = r134227 * r134233;
        double r134235 = r134226 + r134234;
        double r134236 = r134221 + r134235;
        double r134237 = r134211 + r134236;
        double r134238 = r134205 + r134237;
        double r134239 = 1656.8104518737205;
        double r134240 = r134191 * r134197;
        double r134241 = r134240 / r134199;
        double r134242 = r134241 * r134202;
        double r134243 = r134190 * r134242;
        double r134244 = r134196 / r134199;
        double r134245 = r134244 * r134190;
        double r134246 = r134202 * r134245;
        double r134247 = r134243 + r134246;
        double r134248 = r134239 * r134247;
        double r134249 = r134238 - r134248;
        return r134249;
}

Error

Bits error versus z

Derivation

1. Initial program 61.6

   \[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(z - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\]

2. Simplified 1.2

   \[\leadsto \color{blue}{\frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}} \cdot \left(\left(\frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4} + \left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right)\right) + \left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \left(\left(\frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5} + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7} + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\right)}\]

3. Taylor expanded around 0 1.5

   \[\leadsto \color{blue}{\left(338.2601840609425494221795815974473953247 \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \left(\frac{{\left(\log 6.5\right)}^{2} \cdot \left(z \cdot \sqrt{2}\right)}{e^{6.5}} \cdot \sqrt{\pi}\right)\right) + \left(2581.191799681222164508653804659843444824 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right) + \left(676.5203681218850988443591631948947906494 \cdot \left(\frac{\sqrt{2}}{z \cdot e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right) + \left(676.5203681218850988443591631948947906494 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\log 6.5 \cdot \sqrt{2}}{e^{6.5}} \cdot {\left(\frac{1}{{6.5}^{1}}\right)}^{0.5}\right)\right) + 169.1300920304712747110897907987236976624 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{5}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right)\right)\right)\right)\right) - \left(1656.810451873720467119710519909858703613 \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \left(\frac{\log 6.5 \cdot \left(z \cdot \sqrt{2}\right)}{e^{6.5}} \cdot \sqrt{\pi}\right)\right) + 1656.810451873720467119710519909858703613 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{6.5}} \cdot {\left(\frac{1}{{6.5}^{1}}\right)}^{0.5}\right)\right)\right)}\]

4. Simplified 1.5

   \[\leadsto \color{blue}{\left(338.2601840609425494221795815974473953247 \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \left(\frac{{\left(\log 6.5\right)}^{2} \cdot \left(z \cdot \sqrt{2}\right)}{e^{6.5}} \cdot \sqrt{\pi}\right)\right) + \left(2581.191799681222164508653804659843444824 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right) + \left(676.5203681218850988443591631948947906494 \cdot \left(\frac{\sqrt{2}}{z \cdot e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right) + \left(676.5203681218850988443591631948947906494 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\log 6.5 \cdot \sqrt{2}}{e^{6.5}} \cdot {\left(\frac{1}{{6.5}^{1}}\right)}^{0.5}\right)\right) + 169.1300920304712747110897907987236976624 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{5}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right)\right)\right)\right)\right) - 1656.810451873720467119710519909858703613 \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \left(\frac{\log 6.5 \cdot \left(z \cdot \sqrt{2}\right)}{e^{6.5}} \cdot \sqrt{\pi}\right) + \sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{6.5}} \cdot {\left(\frac{1}{{6.5}^{1}}\right)}^{0.5}\right)\right)}\]
5. Using strategy rm

6. Applied add-exp-log 1.5

   \[\leadsto \left(338.2601840609425494221795815974473953247 \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \left(\frac{{\left(\log 6.5\right)}^{2} \cdot \left(z \cdot \sqrt{2}\right)}{e^{6.5}} \cdot \sqrt{\pi}\right)\right) + \left(2581.191799681222164508653804659843444824 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right) + \left(676.5203681218850988443591631948947906494 \cdot \left(\frac{\sqrt{2}}{z \cdot e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \color{blue}{e^{\log \left(\sqrt{\pi}\right)}}\right)\right) + \left(676.5203681218850988443591631948947906494 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\log 6.5 \cdot \sqrt{2}}{e^{6.5}} \cdot {\left(\frac{1}{{6.5}^{1}}\right)}^{0.5}\right)\right) + 169.1300920304712747110897907987236976624 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{5}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right)\right)\right)\right)\right) - 1656.810451873720467119710519909858703613 \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \left(\frac{\log 6.5 \cdot \left(z \cdot \sqrt{2}\right)}{e^{6.5}} \cdot \sqrt{\pi}\right) + \sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{6.5}} \cdot {\left(\frac{1}{{6.5}^{1}}\right)}^{0.5}\right)\right)\]

7. Applied add-exp-log 1.5

   \[\leadsto \left(338.2601840609425494221795815974473953247 \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \left(\frac{{\left(\log 6.5\right)}^{2} \cdot \left(z \cdot \sqrt{2}\right)}{e^{6.5}} \cdot \sqrt{\pi}\right)\right) + \left(2581.191799681222164508653804659843444824 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right) + \left(676.5203681218850988443591631948947906494 \cdot \left(\frac{\sqrt{2}}{z \cdot e^{6.5}} \cdot \left({\left(\frac{1}{{\color{blue}{\left(e^{\log 6.5}\right)}}^{1}}\right)}^{0.5} \cdot e^{\log \left(\sqrt{\pi}\right)}\right)\right) + \left(676.5203681218850988443591631948947906494 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\log 6.5 \cdot \sqrt{2}}{e^{6.5}} \cdot {\left(\frac{1}{{6.5}^{1}}\right)}^{0.5}\right)\right) + 169.1300920304712747110897907987236976624 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{5}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right)\right)\right)\right)\right) - 1656.810451873720467119710519909858703613 \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \left(\frac{\log 6.5 \cdot \left(z \cdot \sqrt{2}\right)}{e^{6.5}} \cdot \sqrt{\pi}\right) + \sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{6.5}} \cdot {\left(\frac{1}{{6.5}^{1}}\right)}^{0.5}\right)\right)\]

8. Applied pow-exp 1.5

   \[\leadsto \left(338.2601840609425494221795815974473953247 \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \left(\frac{{\left(\log 6.5\right)}^{2} \cdot \left(z \cdot \sqrt{2}\right)}{e^{6.5}} \cdot \sqrt{\pi}\right)\right) + \left(2581.191799681222164508653804659843444824 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right) + \left(676.5203681218850988443591631948947906494 \cdot \left(\frac{\sqrt{2}}{z \cdot e^{6.5}} \cdot \left({\left(\frac{1}{\color{blue}{e^{\log 6.5 \cdot 1}}}\right)}^{0.5} \cdot e^{\log \left(\sqrt{\pi}\right)}\right)\right) + \left(676.5203681218850988443591631948947906494 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\log 6.5 \cdot \sqrt{2}}{e^{6.5}} \cdot {\left(\frac{1}{{6.5}^{1}}\right)}^{0.5}\right)\right) + 169.1300920304712747110897907987236976624 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{5}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right)\right)\right)\right)\right) - 1656.810451873720467119710519909858703613 \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \left(\frac{\log 6.5 \cdot \left(z \cdot \sqrt{2}\right)}{e^{6.5}} \cdot \sqrt{\pi}\right) + \sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{6.5}} \cdot {\left(\frac{1}{{6.5}^{1}}\right)}^{0.5}\right)\right)\]

9. Applied rec-exp 1.5

   \[\leadsto \left(338.2601840609425494221795815974473953247 \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \left(\frac{{\left(\log 6.5\right)}^{2} \cdot \left(z \cdot \sqrt{2}\right)}{e^{6.5}} \cdot \sqrt{\pi}\right)\right) + \left(2581.191799681222164508653804659843444824 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right) + \left(676.5203681218850988443591631948947906494 \cdot \left(\frac{\sqrt{2}}{z \cdot e^{6.5}} \cdot \left({\color{blue}{\left(e^{-\log 6.5 \cdot 1}\right)}}^{0.5} \cdot e^{\log \left(\sqrt{\pi}\right)}\right)\right) + \left(676.5203681218850988443591631948947906494 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\log 6.5 \cdot \sqrt{2}}{e^{6.5}} \cdot {\left(\frac{1}{{6.5}^{1}}\right)}^{0.5}\right)\right) + 169.1300920304712747110897907987236976624 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{5}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right)\right)\right)\right)\right) - 1656.810451873720467119710519909858703613 \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \left(\frac{\log 6.5 \cdot \left(z \cdot \sqrt{2}\right)}{e^{6.5}} \cdot \sqrt{\pi}\right) + \sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{6.5}} \cdot {\left(\frac{1}{{6.5}^{1}}\right)}^{0.5}\right)\right)\]

10. Applied pow-exp 1.5

    \[\leadsto \left(338.2601840609425494221795815974473953247 \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \left(\frac{{\left(\log 6.5\right)}^{2} \cdot \left(z \cdot \sqrt{2}\right)}{e^{6.5}} \cdot \sqrt{\pi}\right)\right) + \left(2581.191799681222164508653804659843444824 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right) + \left(676.5203681218850988443591631948947906494 \cdot \left(\frac{\sqrt{2}}{z \cdot e^{6.5}} \cdot \left(\color{blue}{e^{\left(-\log 6.5 \cdot 1\right) \cdot 0.5}} \cdot e^{\log \left(\sqrt{\pi}\right)}\right)\right) + \left(676.5203681218850988443591631948947906494 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\log 6.5 \cdot \sqrt{2}}{e^{6.5}} \cdot {\left(\frac{1}{{6.5}^{1}}\right)}^{0.5}\right)\right) + 169.1300920304712747110897907987236976624 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{5}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right)\right)\right)\right)\right) - 1656.810451873720467119710519909858703613 \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \left(\frac{\log 6.5 \cdot \left(z \cdot \sqrt{2}\right)}{e^{6.5}} \cdot \sqrt{\pi}\right) + \sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{6.5}} \cdot {\left(\frac{1}{{6.5}^{1}}\right)}^{0.5}\right)\right)\]

11. Applied prod-exp 1.1

    \[\leadsto \left(338.2601840609425494221795815974473953247 \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \left(\frac{{\left(\log 6.5\right)}^{2} \cdot \left(z \cdot \sqrt{2}\right)}{e^{6.5}} \cdot \sqrt{\pi}\right)\right) + \left(2581.191799681222164508653804659843444824 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right) + \left(676.5203681218850988443591631948947906494 \cdot \left(\frac{\sqrt{2}}{z \cdot e^{6.5}} \cdot \color{blue}{e^{\left(-\log 6.5 \cdot 1\right) \cdot 0.5 + \log \left(\sqrt{\pi}\right)}}\right) + \left(676.5203681218850988443591631948947906494 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\log 6.5 \cdot \sqrt{2}}{e^{6.5}} \cdot {\left(\frac{1}{{6.5}^{1}}\right)}^{0.5}\right)\right) + 169.1300920304712747110897907987236976624 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{5}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right)\right)\right)\right)\right) - 1656.810451873720467119710519909858703613 \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \left(\frac{\log 6.5 \cdot \left(z \cdot \sqrt{2}\right)}{e^{6.5}} \cdot \sqrt{\pi}\right) + \sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{6.5}} \cdot {\left(\frac{1}{{6.5}^{1}}\right)}^{0.5}\right)\right)\]

12. Simplified 1.1

    \[\leadsto \left(338.2601840609425494221795815974473953247 \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \left(\frac{{\left(\log 6.5\right)}^{2} \cdot \left(z \cdot \sqrt{2}\right)}{e^{6.5}} \cdot \sqrt{\pi}\right)\right) + \left(2581.191799681222164508653804659843444824 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right) + \left(676.5203681218850988443591631948947906494 \cdot \left(\frac{\sqrt{2}}{z \cdot e^{6.5}} \cdot e^{\color{blue}{\log \left(\sqrt{\pi}\right) - \left(\log 6.5 \cdot 1\right) \cdot 0.5}}\right) + \left(676.5203681218850988443591631948947906494 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\log 6.5 \cdot \sqrt{2}}{e^{6.5}} \cdot {\left(\frac{1}{{6.5}^{1}}\right)}^{0.5}\right)\right) + 169.1300920304712747110897907987236976624 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{5}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right)\right)\right)\right)\right) - 1656.810451873720467119710519909858703613 \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \left(\frac{\log 6.5 \cdot \left(z \cdot \sqrt{2}\right)}{e^{6.5}} \cdot \sqrt{\pi}\right) + \sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{6.5}} \cdot {\left(\frac{1}{{6.5}^{1}}\right)}^{0.5}\right)\right)\]

13. Final simplification 1.1

    \[\leadsto \left(338.2601840609425494221795815974473953247 \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \left(\frac{{\left(\log 6.5\right)}^{2} \cdot \left(z \cdot \sqrt{2}\right)}{e^{6.5}} \cdot \sqrt{\pi}\right)\right) + \left(2581.191799681222164508653804659843444824 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right) + \left(676.5203681218850988443591631948947906494 \cdot \left(\frac{\sqrt{2}}{z \cdot e^{6.5}} \cdot e^{\log \left(\sqrt{\pi}\right) - \left(\log 6.5 \cdot 1\right) \cdot 0.5}\right) + \left(676.5203681218850988443591631948947906494 \cdot \left(\sqrt{\pi} \cdot \left(\frac{\log 6.5 \cdot \sqrt{2}}{e^{6.5}} \cdot {\left(\frac{1}{{6.5}^{1}}\right)}^{0.5}\right)\right) + 169.1300920304712747110897907987236976624 \cdot \left(\frac{\sqrt{2} \cdot z}{e^{6.5}} \cdot \left({\left(\frac{1}{{6.5}^{5}}\right)}^{0.5} \cdot \sqrt{\pi}\right)\right)\right)\right)\right)\right) - 1656.810451873720467119710519909858703613 \cdot \left({\left(\frac{1}{{6.5}^{1}}\right)}^{0.5} \cdot \left(\frac{\log 6.5 \cdot \left(z \cdot \sqrt{2}\right)}{e^{6.5}} \cdot \sqrt{\pi}\right) + \sqrt{\pi} \cdot \left(\frac{\sqrt{2}}{e^{6.5}} \cdot {\left(\frac{1}{{6.5}^{1}}\right)}^{0.5}\right)\right)\]

Reproduce

herbie shell --seed 2019325 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z greater than 0.5"
  :precision binary64
  (* (* (* (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)))))