Average Error: 60.0 → 0.6
Time: 2.6m
Precision: 64
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]
↓
\[\frac{\left(\left(\left(z \cdot \left(z + 1\right)\right) \cdot \left(\frac{12.507343278686905}{4 + z} - \left(\frac{771.3234287776531}{z + 2} + 0.9999999999998099\right)\right)\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{6 + z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{6 + z} - \frac{9.984369578019572 \cdot 10^{-06}}{6 + z} \cdot \frac{-176.6150291621406}{\left(4 + z\right) + -1}\right) + \frac{-176.6150291621406}{\left(4 + z\right) + -1} \cdot \frac{-176.6150291621406}{\left(4 + z\right) + -1}\right)\right) \cdot \left(1.5056327351493116 \cdot 10^{-07} \cdot \left(z - -5\right) + \left(7 + z\right) \cdot -0.13857109526572012\right) + \left(\left(z - -5\right) \cdot \left(7 + z\right)\right) \cdot \left(\left(\left(z \cdot \left(z + 1\right)\right) \cdot \left(\frac{12.507343278686905}{4 + z} - \left(\frac{771.3234287776531}{z + 2} + 0.9999999999998099\right)\right)\right) \cdot \left({\left(\frac{9.984369578019572 \cdot 10^{-06}}{6 + z}\right)}^{3} + {\left(\frac{-176.6150291621406}{\left(4 + z\right) + -1}\right)}^{3}\right) + \left(\left(z \cdot -1259.1392167224028 + \left(z + 1\right) \cdot 676.5203681218851\right) \cdot \left(\frac{12.507343278686905}{4 + z} - \left(\frac{771.3234287776531}{z + 2} + 0.9999999999998099\right)\right) + \left(z \cdot \left(z + 1\right)\right) \cdot \left(\frac{12.507343278686905}{4 + z} \cdot \frac{12.507343278686905}{4 + z} - \left(\frac{771.3234287776531}{z + 2} + 0.9999999999998099\right) \cdot \left(\frac{771.3234287776531}{z + 2} + 0.9999999999998099\right)\right)\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{6 + z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{6 + z} - \frac{9.984369578019572 \cdot 10^{-06}}{6 + z} \cdot \frac{-176.6150291621406}{\left(4 + z\right) + -1}\right) + \frac{-176.6150291621406}{\left(4 + z\right) + -1} \cdot \frac{-176.6150291621406}{\left(4 + z\right) + -1}\right)\right)}{e^{6 + \left(0.5 + z\right)} \cdot \left(\left(\left(\left(z \cdot \left(z + 1\right)\right) \cdot \left(\frac{12.507343278686905}{4 + z} - \left(\frac{771.3234287776531}{z + 2} + 0.9999999999998099\right)\right)\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{6 + z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{6 + z} - \frac{9.984369578019572 \cdot 10^{-06}}{6 + z} \cdot \frac{-176.6150291621406}{\left(4 + z\right) + -1}\right) + \frac{-176.6150291621406}{\left(4 + z\right) + -1} \cdot \frac{-176.6150291621406}{\left(4 + z\right) + -1}\right)\right) \cdot \left(\left(z - -5\right) \cdot \left(7 + z\right)\right)\right)} \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(6 + \left(0.5 + z\right)\right)}^{\left(0.5 + \left(-1 + z\right)\right)}\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)
↓
\frac{\left(\left(\left(z \cdot \left(z + 1\right)\right) \cdot \left(\frac{12.507343278686905}{4 + z} - \left(\frac{771.3234287776531}{z + 2} + 0.9999999999998099\right)\right)\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{6 + z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{6 + z} - \frac{9.984369578019572 \cdot 10^{-06}}{6 + z} \cdot \frac{-176.6150291621406}{\left(4 + z\right) + -1}\right) + \frac{-176.6150291621406}{\left(4 + z\right) + -1} \cdot \frac{-176.6150291621406}{\left(4 + z\right) + -1}\right)\right) \cdot \left(1.5056327351493116 \cdot 10^{-07} \cdot \left(z - -5\right) + \left(7 + z\right) \cdot -0.13857109526572012\right) + \left(\left(z - -5\right) \cdot \left(7 + z\right)\right) \cdot \left(\left(\left(z \cdot \left(z + 1\right)\right) \cdot \left(\frac{12.507343278686905}{4 + z} - \left(\frac{771.3234287776531}{z + 2} + 0.9999999999998099\right)\right)\right) \cdot \left({\left(\frac{9.984369578019572 \cdot 10^{-06}}{6 + z}\right)}^{3} + {\left(\frac{-176.6150291621406}{\left(4 + z\right) + -1}\right)}^{3}\right) + \left(\left(z \cdot -1259.1392167224028 + \left(z + 1\right) \cdot 676.5203681218851\right) \cdot \left(\frac{12.507343278686905}{4 + z} - \left(\frac{771.3234287776531}{z + 2} + 0.9999999999998099\right)\right) + \left(z \cdot \left(z + 1\right)\right) \cdot \left(\frac{12.507343278686905}{4 + z} \cdot \frac{12.507343278686905}{4 + z} - \left(\frac{771.3234287776531}{z + 2} + 0.9999999999998099\right) \cdot \left(\frac{771.3234287776531}{z + 2} + 0.9999999999998099\right)\right)\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{6 + z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{6 + z} - \frac{9.984369578019572 \cdot 10^{-06}}{6 + z} \cdot \frac{-176.6150291621406}{\left(4 + z\right) + -1}\right) + \frac{-176.6150291621406}{\left(4 + z\right) + -1} \cdot \frac{-176.6150291621406}{\left(4 + z\right) + -1}\right)\right)}{e^{6 + \left(0.5 + z\right)} \cdot \left(\left(\left(\left(z \cdot \left(z + 1\right)\right) \cdot \left(\frac{12.507343278686905}{4 + z} - \left(\frac{771.3234287776531}{z + 2} + 0.9999999999998099\right)\right)\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{6 + z} \cdot \frac{9.984369578019572 \cdot 10^{-06}}{6 + z} - \frac{9.984369578019572 \cdot 10^{-06}}{6 + z} \cdot \frac{-176.6150291621406}{\left(4 + z\right) + -1}\right) + \frac{-176.6150291621406}{\left(4 + z\right) + -1} \cdot \frac{-176.6150291621406}{\left(4 + z\right) + -1}\right)\right) \cdot \left(\left(z - -5\right) \cdot \left(7 + z\right)\right)\right)} \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(6 + \left(0.5 + z\right)\right)}^{\left(0.5 + \left(-1 + z\right)\right)}\right)
double f(double z) {
        double r6269247 = atan2(1.0, 0.0);
        double r6269248 = 2.0;
        double r6269249 = r6269247 * r6269248;
        double r6269250 = sqrt(r6269249);
        double r6269251 = z;
        double r6269252 = 1.0;
        double r6269253 = r6269251 - r6269252;
        double r6269254 = 7.0;
        double r6269255 = r6269253 + r6269254;
        double r6269256 = 0.5;
        double r6269257 = r6269255 + r6269256;
        double r6269258 = r6269253 + r6269256;
        double r6269259 = pow(r6269257, r6269258);
        double r6269260 = r6269250 * r6269259;
        double r6269261 = -r6269257;
        double r6269262 = exp(r6269261);
        double r6269263 = r6269260 * r6269262;
        double r6269264 = 0.9999999999998099;
        double r6269265 = 676.5203681218851;
        double r6269266 = r6269253 + r6269252;
        double r6269267 = r6269265 / r6269266;
        double r6269268 = r6269264 + r6269267;
        double r6269269 = -1259.1392167224028;
        double r6269270 = r6269253 + r6269248;
        double r6269271 = r6269269 / r6269270;
        double r6269272 = r6269268 + r6269271;
        double r6269273 = 771.3234287776531;
        double r6269274 = 3.0;
        double r6269275 = r6269253 + r6269274;
        double r6269276 = r6269273 / r6269275;
        double r6269277 = r6269272 + r6269276;
        double r6269278 = -176.6150291621406;
        double r6269279 = 4.0;
        double r6269280 = r6269253 + r6269279;
        double r6269281 = r6269278 / r6269280;
        double r6269282 = r6269277 + r6269281;
        double r6269283 = 12.507343278686905;
        double r6269284 = 5.0;
        double r6269285 = r6269253 + r6269284;
        double r6269286 = r6269283 / r6269285;
        double r6269287 = r6269282 + r6269286;
        double r6269288 = -0.13857109526572012;
        double r6269289 = 6.0;
        double r6269290 = r6269253 + r6269289;
        double r6269291 = r6269288 / r6269290;
        double r6269292 = r6269287 + r6269291;
        double r6269293 = 9.984369578019572e-06;
        double r6269294 = r6269293 / r6269255;
        double r6269295 = r6269292 + r6269294;
        double r6269296 = 1.5056327351493116e-07;
        double r6269297 = 8.0;
        double r6269298 = r6269253 + r6269297;
        double r6269299 = r6269296 / r6269298;
        double r6269300 = r6269295 + r6269299;
        double r6269301 = r6269263 * r6269300;
        return r6269301;
}
↓
double f(double z) {
        double r6269302 = z;
        double r6269303 = 1.0;
        double r6269304 = r6269302 + r6269303;
        double r6269305 = r6269302 * r6269304;
        double r6269306 = 12.507343278686905;
        double r6269307 = 4.0;
        double r6269308 = r6269307 + r6269302;
        double r6269309 = r6269306 / r6269308;
        double r6269310 = 771.3234287776531;
        double r6269311 = 2.0;
        double r6269312 = r6269302 + r6269311;
        double r6269313 = r6269310 / r6269312;
        double r6269314 = 0.9999999999998099;
        double r6269315 = r6269313 + r6269314;
        double r6269316 = r6269309 - r6269315;
        double r6269317 = r6269305 * r6269316;
        double r6269318 = 9.984369578019572e-06;
        double r6269319 = 6.0;
        double r6269320 = r6269319 + r6269302;
        double r6269321 = r6269318 / r6269320;
        double r6269322 = r6269321 * r6269321;
        double r6269323 = -176.6150291621406;
        double r6269324 = -1.0;
        double r6269325 = r6269308 + r6269324;
        double r6269326 = r6269323 / r6269325;
        double r6269327 = r6269321 * r6269326;
        double r6269328 = r6269322 - r6269327;
        double r6269329 = r6269326 * r6269326;
        double r6269330 = r6269328 + r6269329;
        double r6269331 = r6269317 * r6269330;
        double r6269332 = 1.5056327351493116e-07;
        double r6269333 = -5.0;
        double r6269334 = r6269302 - r6269333;
        double r6269335 = r6269332 * r6269334;
        double r6269336 = 7.0;
        double r6269337 = r6269336 + r6269302;
        double r6269338 = -0.13857109526572012;
        double r6269339 = r6269337 * r6269338;
        double r6269340 = r6269335 + r6269339;
        double r6269341 = r6269331 * r6269340;
        double r6269342 = r6269334 * r6269337;
        double r6269343 = 3.0;
        double r6269344 = pow(r6269321, r6269343);
        double r6269345 = pow(r6269326, r6269343);
        double r6269346 = r6269344 + r6269345;
        double r6269347 = r6269317 * r6269346;
        double r6269348 = -1259.1392167224028;
        double r6269349 = r6269302 * r6269348;
        double r6269350 = 676.5203681218851;
        double r6269351 = r6269304 * r6269350;
        double r6269352 = r6269349 + r6269351;
        double r6269353 = r6269352 * r6269316;
        double r6269354 = r6269309 * r6269309;
        double r6269355 = r6269315 * r6269315;
        double r6269356 = r6269354 - r6269355;
        double r6269357 = r6269305 * r6269356;
        double r6269358 = r6269353 + r6269357;
        double r6269359 = r6269358 * r6269330;
        double r6269360 = r6269347 + r6269359;
        double r6269361 = r6269342 * r6269360;
        double r6269362 = r6269341 + r6269361;
        double r6269363 = 0.5;
        double r6269364 = r6269363 + r6269302;
        double r6269365 = r6269319 + r6269364;
        double r6269366 = exp(r6269365);
        double r6269367 = r6269331 * r6269342;
        double r6269368 = r6269366 * r6269367;
        double r6269369 = r6269362 / r6269368;
        double r6269370 = atan2(1.0, 0.0);
        double r6269371 = r6269370 * r6269311;
        double r6269372 = sqrt(r6269371);
        double r6269373 = r6269324 + r6269302;
        double r6269374 = r6269363 + r6269373;
        double r6269375 = pow(r6269365, r6269374);
        double r6269376 = r6269372 * r6269375;
        double r6269377 = r6269369 * r6269376;
        return r6269377;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 60.0

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

  2. Simplified0.9

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

  4. Applied flip3-+0.9

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

  5. Applied frac-add0.9

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

  6. Applied flip-+0.9

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

  7. Applied frac-add1.0

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

  8. Applied frac-add1.0

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

  9. Applied frac-add1.0

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

  10. Applied frac-add1.0

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

  11. Applied associate-/l/0.6

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

  12. Final simplification0.6

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

Reproduce

herbie shell --seed 2019137 
(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)))))