Average Error: 1.8 → 0.9
Time: 2.0m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\sqrt{2 \cdot \pi} \cdot \frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(-z\right) + 0.5\right)}}{e^{0.5 + \left(7 - z\right)}}\right) \cdot \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{\left(\left(\left(\frac{771.3234287776531}{\left(1 - z\right) + 2} \cdot \frac{771.3234287776531}{\left(1 - z\right) + 2} - \frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right) + \left(0.9999999999998099 \cdot 0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right) \cdot \left(\frac{771.3234287776531}{\left(1 - z\right) + 2} - \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{771.3234287776531}{\left(1 - z\right) + 2} - \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}\right) + \left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{\left(1 - z\right) + 2} - \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right)}{\left(\left(\left(\frac{771.3234287776531}{\left(1 - z\right) + 2} - \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}\right)}\right)\]
\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
↓
\left(\sqrt{2 \cdot \pi} \cdot \frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(\left(-z\right) + 0.5\right)}}{e^{0.5 + \left(7 - z\right)}}\right) \cdot \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{\left(\left(\left(\frac{771.3234287776531}{\left(1 - z\right) + 2} \cdot \frac{771.3234287776531}{\left(1 - z\right) + 2} - \frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right) + \left(0.9999999999998099 \cdot 0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right) \cdot \left(\frac{771.3234287776531}{\left(1 - z\right) + 2} - \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{771.3234287776531}{\left(1 - z\right) + 2} - \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}\right) + \left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}\right) \cdot \left(\left(\left(\frac{771.3234287776531}{\left(1 - z\right) + 2} - \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right)}{\left(\left(\left(\frac{771.3234287776531}{\left(1 - z\right) + 2} - \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}\right)}\right)
double f(double z) {
        double r5560161 = atan2(1.0, 0.0);
        double r5560162 = z;
        double r5560163 = r5560161 * r5560162;
        double r5560164 = sin(r5560163);
        double r5560165 = r5560161 / r5560164;
        double r5560166 = 2.0;
        double r5560167 = r5560161 * r5560166;
        double r5560168 = sqrt(r5560167);
        double r5560169 = 1.0;
        double r5560170 = r5560169 - r5560162;
        double r5560171 = r5560170 - r5560169;
        double r5560172 = 7.0;
        double r5560173 = r5560171 + r5560172;
        double r5560174 = 0.5;
        double r5560175 = r5560173 + r5560174;
        double r5560176 = r5560171 + r5560174;
        double r5560177 = pow(r5560175, r5560176);
        double r5560178 = r5560168 * r5560177;
        double r5560179 = -r5560175;
        double r5560180 = exp(r5560179);
        double r5560181 = r5560178 * r5560180;
        double r5560182 = 0.9999999999998099;
        double r5560183 = 676.5203681218851;
        double r5560184 = r5560171 + r5560169;
        double r5560185 = r5560183 / r5560184;
        double r5560186 = r5560182 + r5560185;
        double r5560187 = -1259.1392167224028;
        double r5560188 = r5560171 + r5560166;
        double r5560189 = r5560187 / r5560188;
        double r5560190 = r5560186 + r5560189;
        double r5560191 = 771.3234287776531;
        double r5560192 = 3.0;
        double r5560193 = r5560171 + r5560192;
        double r5560194 = r5560191 / r5560193;
        double r5560195 = r5560190 + r5560194;
        double r5560196 = -176.6150291621406;
        double r5560197 = 4.0;
        double r5560198 = r5560171 + r5560197;
        double r5560199 = r5560196 / r5560198;
        double r5560200 = r5560195 + r5560199;
        double r5560201 = 12.507343278686905;
        double r5560202 = 5.0;
        double r5560203 = r5560171 + r5560202;
        double r5560204 = r5560201 / r5560203;
        double r5560205 = r5560200 + r5560204;
        double r5560206 = -0.13857109526572012;
        double r5560207 = 6.0;
        double r5560208 = r5560171 + r5560207;
        double r5560209 = r5560206 / r5560208;
        double r5560210 = r5560205 + r5560209;
        double r5560211 = 9.984369578019572e-06;
        double r5560212 = r5560211 / r5560173;
        double r5560213 = r5560210 + r5560212;
        double r5560214 = 1.5056327351493116e-07;
        double r5560215 = 8.0;
        double r5560216 = r5560171 + r5560215;
        double r5560217 = r5560214 / r5560216;
        double r5560218 = r5560213 + r5560217;
        double r5560219 = r5560181 * r5560218;
        double r5560220 = r5560165 * r5560219;
        return r5560220;
}
↓
double f(double z) {
        double r5560221 = 2.0;
        double r5560222 = atan2(1.0, 0.0);
        double r5560223 = r5560221 * r5560222;
        double r5560224 = sqrt(r5560223);
        double r5560225 = 0.5;
        double r5560226 = 7.0;
        double r5560227 = z;
        double r5560228 = r5560226 - r5560227;
        double r5560229 = r5560225 + r5560228;
        double r5560230 = -r5560227;
        double r5560231 = r5560230 + r5560225;
        double r5560232 = pow(r5560229, r5560231);
        double r5560233 = exp(r5560229);
        double r5560234 = r5560232 / r5560233;
        double r5560235 = r5560224 * r5560234;
        double r5560236 = r5560222 * r5560227;
        double r5560237 = sin(r5560236);
        double r5560238 = r5560222 / r5560237;
        double r5560239 = 771.3234287776531;
        double r5560240 = 1.0;
        double r5560241 = r5560240 - r5560227;
        double r5560242 = r5560241 + r5560221;
        double r5560243 = r5560239 / r5560242;
        double r5560244 = r5560243 * r5560243;
        double r5560245 = -176.6150291621406;
        double r5560246 = 4.0;
        double r5560247 = r5560246 - r5560227;
        double r5560248 = r5560245 / r5560247;
        double r5560249 = r5560248 * r5560248;
        double r5560250 = r5560244 - r5560249;
        double r5560251 = 0.9999999999998099;
        double r5560252 = 676.5203681218851;
        double r5560253 = r5560252 / r5560241;
        double r5560254 = -1259.1392167224028;
        double r5560255 = r5560221 - r5560227;
        double r5560256 = r5560254 / r5560255;
        double r5560257 = r5560253 + r5560256;
        double r5560258 = r5560251 - r5560257;
        double r5560259 = r5560250 * r5560258;
        double r5560260 = r5560251 * r5560251;
        double r5560261 = r5560257 * r5560257;
        double r5560262 = r5560260 - r5560261;
        double r5560263 = r5560243 - r5560248;
        double r5560264 = r5560262 * r5560263;
        double r5560265 = r5560259 + r5560264;
        double r5560266 = 1.5056327351493116e-07;
        double r5560267 = 8.0;
        double r5560268 = r5560267 - r5560227;
        double r5560269 = r5560266 / r5560268;
        double r5560270 = 9.984369578019572e-06;
        double r5560271 = r5560270 / r5560228;
        double r5560272 = r5560269 - r5560271;
        double r5560273 = r5560265 * r5560272;
        double r5560274 = r5560269 * r5560269;
        double r5560275 = r5560271 * r5560271;
        double r5560276 = r5560274 - r5560275;
        double r5560277 = r5560263 * r5560258;
        double r5560278 = r5560276 * r5560277;
        double r5560279 = r5560273 + r5560278;
        double r5560280 = -0.13857109526572012;
        double r5560281 = 6.0;
        double r5560282 = r5560281 - r5560227;
        double r5560283 = r5560280 / r5560282;
        double r5560284 = 12.507343278686905;
        double r5560285 = 5.0;
        double r5560286 = r5560285 - r5560227;
        double r5560287 = r5560284 / r5560286;
        double r5560288 = r5560283 - r5560287;
        double r5560289 = r5560279 * r5560288;
        double r5560290 = r5560283 * r5560283;
        double r5560291 = r5560287 * r5560287;
        double r5560292 = r5560290 - r5560291;
        double r5560293 = r5560277 * r5560272;
        double r5560294 = r5560292 * r5560293;
        double r5560295 = r5560289 + r5560294;
        double r5560296 = r5560293 * r5560288;
        double r5560297 = r5560295 / r5560296;
        double r5560298 = r5560238 * r5560297;
        double r5560299 = r5560235 * r5560298;
        return r5560299;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.8

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

  2. Simplified0.9

    \[\leadsto \color{blue}{\left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \frac{-176.6150291621406}{4 - z}\right) + \left(0.9999999999998099 + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} + \frac{12.507343278686905}{5 - z}\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{0.5 + \left(7 - z\right)}} \cdot \sqrt{2 \cdot \pi}\right)}\]
  3. Using strategy rm

  4. Applied flip-+0.9

    \[\leadsto \left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \frac{-176.6150291621406}{4 - z}\right) + \left(0.9999999999998099 + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \color{blue}{\frac{\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}}{\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{0.5 + \left(7 - z\right)}} \cdot \sqrt{2 \cdot \pi}\right)\]

  5. Applied flip-+0.9

    \[\leadsto \left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \frac{-176.6150291621406}{4 - z}\right) + \color{blue}{\frac{0.9999999999998099 \cdot 0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)}{0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)}}\right)\right) + \frac{\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}}{\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{0.5 + \left(7 - z\right)}} \cdot \sqrt{2 \cdot \pi}\right)\]

  6. Applied flip-+0.9

    \[\leadsto \left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \left(\color{blue}{\frac{\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} - \frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z}}{\frac{771.3234287776531}{2 + \left(1 - z\right)} - \frac{-176.6150291621406}{4 - z}}} + \frac{0.9999999999998099 \cdot 0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)}{0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)}\right)\right) + \frac{\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}}{\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{0.5 + \left(7 - z\right)}} \cdot \sqrt{2 \cdot \pi}\right)\]

  7. Applied frac-add0.9

    \[\leadsto \left(\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \color{blue}{\frac{\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} - \frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} - \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)}{\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} - \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)}}\right) + \frac{\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}}{\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{0.5 + \left(7 - z\right)}} \cdot \sqrt{2 \cdot \pi}\right)\]

  8. Applied flip-+0.9

    \[\leadsto \left(\left(\left(\color{blue}{\frac{\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}}{\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}}} + \frac{\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} - \frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} - \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)}{\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} - \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)}\right) + \frac{\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}}{\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{0.5 + \left(7 - z\right)}} \cdot \sqrt{2 \cdot \pi}\right)\]

  9. Applied frac-add0.9

    \[\leadsto \left(\left(\color{blue}{\frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} - \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} - \frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} - \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)}{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} - \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)}} + \frac{\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}}{\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{0.5 + \left(7 - z\right)}} \cdot \sqrt{2 \cdot \pi}\right)\]

  10. Applied frac-add0.9

    \[\leadsto \left(\color{blue}{\frac{\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} \cdot \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} - \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} - \frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} - \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 \cdot 0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} - \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} \cdot \frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z} \cdot \frac{12.507343278686905}{5 - z}\right)}{\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} - \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) \cdot \left(\left(\frac{771.3234287776531}{2 + \left(1 - z\right)} - \frac{-176.6150291621406}{4 - z}\right) \cdot \left(0.9999999999998099 - \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) \cdot \left(\frac{-0.13857109526572012}{6 - z} - \frac{12.507343278686905}{5 - z}\right)}} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \left(\frac{{\left(0.5 + \left(7 - z\right)\right)}^{\left(0.5 + \left(0 - z\right)\right)}}{e^{0.5 + \left(7 - z\right)}} \cdot \sqrt{2 \cdot \pi}\right)\]

  11. Final simplification0.9

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

Reproduce

herbie shell --seed 2019129 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  (* (/ PI (sin (* PI z))) (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- (- 1 z) 1) 7) 0.5) (+ (- (- 1 z) 1) 0.5))) (exp (- (+ (+ (- (- 1 z) 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- (- 1 z) 1) 1))) (/ -1259.1392167224028 (+ (- (- 1 z) 1) 2))) (/ 771.3234287776531 (+ (- (- 1 z) 1) 3))) (/ -176.6150291621406 (+ (- (- 1 z) 1) 4))) (/ 12.507343278686905 (+ (- (- 1 z) 1) 5))) (/ -0.13857109526572012 (+ (- (- 1 z) 1) 6))) (/ 9.984369578019572e-06 (+ (- (- 1 z) 1) 7))) (/ 1.5056327351493116e-07 (+ (- (- 1 z) 1) 8))))))