Average Error: 1.8 → 0.4
Time: 4.2m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\frac{\mathsf{fma}\left(\mathsf{fma}\left(9.984369578019572 \cdot 10^{-06}, 6 - z, -0.13857109526572012 \cdot \left(7 - z\right)\right), \left(\left(\mathsf{fma}\left(\frac{771.3234287776531}{3 - z}, \frac{771.3234287776531}{3 - z}, \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - \frac{771.3234287776531}{3 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621406}{4 - z}, \frac{-176.6150291621406}{4 - z}, \left(0.9999999999998099 - \frac{-176.6150291621406}{4 - z}\right) \cdot 0.9999999999998099\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right), \mathsf{fma}\left(\mathsf{fma}\left(1.5056327351493116 \cdot 10^{-07}, \mathsf{fma}\left(\frac{771.3234287776531}{3 - z}, \frac{771.3234287776531}{3 - z}, \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - \frac{771.3234287776531}{3 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621406}{4 - z}, \frac{-176.6150291621406}{4 - z}, \left(0.9999999999998099 - \frac{-176.6150291621406}{4 - z}\right) \cdot 0.9999999999998099\right), \left(8 - z\right) \cdot \mathsf{fma}\left(\left(0.9999999999998099 \cdot 0.9999999999998099\right) \cdot 0.9999999999998099 + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}, \mathsf{fma}\left(\frac{771.3234287776531}{3 - z}, \frac{771.3234287776531}{3 - z}, \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - \frac{771.3234287776531}{3 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right), \mathsf{fma}\left(\frac{-176.6150291621406}{4 - z}, \frac{-176.6150291621406}{4 - z}, \left(0.9999999999998099 - \frac{-176.6150291621406}{4 - z}\right) \cdot 0.9999999999998099\right) \cdot \left(\left(\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{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z} \cdot \left(\frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right)\right)\right), 5 - z, 12.507343278686905 \cdot \left(\left(\mathsf{fma}\left(\frac{771.3234287776531}{3 - z}, \frac{771.3234287776531}{3 - z}, \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - \frac{771.3234287776531}{3 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621406}{4 - z}, \frac{-176.6150291621406}{4 - z}, \left(0.9999999999998099 - \frac{-176.6150291621406}{4 - z}\right) \cdot 0.9999999999998099\right)\right) \cdot \left(8 - z\right)\right)\right) \cdot \left(\left(6 - z\right) \cdot \left(7 - z\right)\right)\right) \cdot \left(\sqrt{2 \cdot \pi} \cdot \left(\left({\left(\left(7 - z\right) + 0.5\right)}^{\left(1 - z\right)} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(-\left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}\right) \cdot \pi\right)\right)}{\left(\left(\left(6 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\left(\mathsf{fma}\left(\frac{771.3234287776531}{3 - z}, \frac{771.3234287776531}{3 - z}, \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - \frac{771.3234287776531}{3 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621406}{4 - z}, \frac{-176.6150291621406}{4 - z}, \left(0.9999999999998099 - \frac{-176.6150291621406}{4 - z}\right) \cdot 0.9999999999998099\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right)\right)\right) \cdot \sin \left(z \cdot \pi\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)
↓
\frac{\mathsf{fma}\left(\mathsf{fma}\left(9.984369578019572 \cdot 10^{-06}, 6 - z, -0.13857109526572012 \cdot \left(7 - z\right)\right), \left(\left(\mathsf{fma}\left(\frac{771.3234287776531}{3 - z}, \frac{771.3234287776531}{3 - z}, \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - \frac{771.3234287776531}{3 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621406}{4 - z}, \frac{-176.6150291621406}{4 - z}, \left(0.9999999999998099 - \frac{-176.6150291621406}{4 - z}\right) \cdot 0.9999999999998099\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right), \mathsf{fma}\left(\mathsf{fma}\left(1.5056327351493116 \cdot 10^{-07}, \mathsf{fma}\left(\frac{771.3234287776531}{3 - z}, \frac{771.3234287776531}{3 - z}, \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - \frac{771.3234287776531}{3 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621406}{4 - z}, \frac{-176.6150291621406}{4 - z}, \left(0.9999999999998099 - \frac{-176.6150291621406}{4 - z}\right) \cdot 0.9999999999998099\right), \left(8 - z\right) \cdot \mathsf{fma}\left(\left(0.9999999999998099 \cdot 0.9999999999998099\right) \cdot 0.9999999999998099 + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}, \mathsf{fma}\left(\frac{771.3234287776531}{3 - z}, \frac{771.3234287776531}{3 - z}, \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - \frac{771.3234287776531}{3 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right), \mathsf{fma}\left(\frac{-176.6150291621406}{4 - z}, \frac{-176.6150291621406}{4 - z}, \left(0.9999999999998099 - \frac{-176.6150291621406}{4 - z}\right) \cdot 0.9999999999998099\right) \cdot \left(\left(\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{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z} \cdot \left(\frac{771.3234287776531}{3 - z} \cdot \frac{771.3234287776531}{3 - z}\right)\right)\right)\right), 5 - z, 12.507343278686905 \cdot \left(\left(\mathsf{fma}\left(\frac{771.3234287776531}{3 - z}, \frac{771.3234287776531}{3 - z}, \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - \frac{771.3234287776531}{3 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621406}{4 - z}, \frac{-176.6150291621406}{4 - z}, \left(0.9999999999998099 - \frac{-176.6150291621406}{4 - z}\right) \cdot 0.9999999999998099\right)\right) \cdot \left(8 - z\right)\right)\right) \cdot \left(\left(6 - z\right) \cdot \left(7 - z\right)\right)\right) \cdot \left(\sqrt{2 \cdot \pi} \cdot \left(\left({\left(\left(7 - z\right) + 0.5\right)}^{\left(1 - z\right)} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(-\left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}\right) \cdot \pi\right)\right)}{\left(\left(\left(6 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(\left(\mathsf{fma}\left(\frac{771.3234287776531}{3 - z}, \frac{771.3234287776531}{3 - z}, \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - \frac{771.3234287776531}{3 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621406}{4 - z}, \frac{-176.6150291621406}{4 - z}, \left(0.9999999999998099 - \frac{-176.6150291621406}{4 - z}\right) \cdot 0.9999999999998099\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right)\right)\right) \cdot \sin \left(z \cdot \pi\right)}
double f(double z) {
        double r7350271 = atan2(1.0, 0.0);
        double r7350272 = z;
        double r7350273 = r7350271 * r7350272;
        double r7350274 = sin(r7350273);
        double r7350275 = r7350271 / r7350274;
        double r7350276 = 2.0;
        double r7350277 = r7350271 * r7350276;
        double r7350278 = sqrt(r7350277);
        double r7350279 = 1.0;
        double r7350280 = r7350279 - r7350272;
        double r7350281 = r7350280 - r7350279;
        double r7350282 = 7.0;
        double r7350283 = r7350281 + r7350282;
        double r7350284 = 0.5;
        double r7350285 = r7350283 + r7350284;
        double r7350286 = r7350281 + r7350284;
        double r7350287 = pow(r7350285, r7350286);
        double r7350288 = r7350278 * r7350287;
        double r7350289 = -r7350285;
        double r7350290 = exp(r7350289);
        double r7350291 = r7350288 * r7350290;
        double r7350292 = 0.9999999999998099;
        double r7350293 = 676.5203681218851;
        double r7350294 = r7350281 + r7350279;
        double r7350295 = r7350293 / r7350294;
        double r7350296 = r7350292 + r7350295;
        double r7350297 = -1259.1392167224028;
        double r7350298 = r7350281 + r7350276;
        double r7350299 = r7350297 / r7350298;
        double r7350300 = r7350296 + r7350299;
        double r7350301 = 771.3234287776531;
        double r7350302 = 3.0;
        double r7350303 = r7350281 + r7350302;
        double r7350304 = r7350301 / r7350303;
        double r7350305 = r7350300 + r7350304;
        double r7350306 = -176.6150291621406;
        double r7350307 = 4.0;
        double r7350308 = r7350281 + r7350307;
        double r7350309 = r7350306 / r7350308;
        double r7350310 = r7350305 + r7350309;
        double r7350311 = 12.507343278686905;
        double r7350312 = 5.0;
        double r7350313 = r7350281 + r7350312;
        double r7350314 = r7350311 / r7350313;
        double r7350315 = r7350310 + r7350314;
        double r7350316 = -0.13857109526572012;
        double r7350317 = 6.0;
        double r7350318 = r7350281 + r7350317;
        double r7350319 = r7350316 / r7350318;
        double r7350320 = r7350315 + r7350319;
        double r7350321 = 9.984369578019572e-06;
        double r7350322 = r7350321 / r7350283;
        double r7350323 = r7350320 + r7350322;
        double r7350324 = 1.5056327351493116e-07;
        double r7350325 = 8.0;
        double r7350326 = r7350281 + r7350325;
        double r7350327 = r7350324 / r7350326;
        double r7350328 = r7350323 + r7350327;
        double r7350329 = r7350291 * r7350328;
        double r7350330 = r7350275 * r7350329;
        return r7350330;
}
↓
double f(double z) {
        double r7350331 = 9.984369578019572e-06;
        double r7350332 = 6.0;
        double r7350333 = z;
        double r7350334 = r7350332 - r7350333;
        double r7350335 = -0.13857109526572012;
        double r7350336 = 7.0;
        double r7350337 = r7350336 - r7350333;
        double r7350338 = r7350335 * r7350337;
        double r7350339 = fma(r7350331, r7350334, r7350338);
        double r7350340 = 771.3234287776531;
        double r7350341 = 3.0;
        double r7350342 = r7350341 - r7350333;
        double r7350343 = r7350340 / r7350342;
        double r7350344 = 676.5203681218851;
        double r7350345 = 1.0;
        double r7350346 = r7350345 - r7350333;
        double r7350347 = r7350344 / r7350346;
        double r7350348 = -1259.1392167224028;
        double r7350349 = 2.0;
        double r7350350 = r7350349 - r7350333;
        double r7350351 = r7350348 / r7350350;
        double r7350352 = r7350347 + r7350351;
        double r7350353 = r7350352 - r7350343;
        double r7350354 = r7350353 * r7350352;
        double r7350355 = fma(r7350343, r7350343, r7350354);
        double r7350356 = -176.6150291621406;
        double r7350357 = 4.0;
        double r7350358 = r7350357 - r7350333;
        double r7350359 = r7350356 / r7350358;
        double r7350360 = 0.9999999999998099;
        double r7350361 = r7350360 - r7350359;
        double r7350362 = r7350361 * r7350360;
        double r7350363 = fma(r7350359, r7350359, r7350362);
        double r7350364 = r7350355 * r7350363;
        double r7350365 = 8.0;
        double r7350366 = r7350365 - r7350333;
        double r7350367 = r7350364 * r7350366;
        double r7350368 = 5.0;
        double r7350369 = r7350368 - r7350333;
        double r7350370 = r7350367 * r7350369;
        double r7350371 = 1.5056327351493116e-07;
        double r7350372 = r7350360 * r7350360;
        double r7350373 = r7350372 * r7350360;
        double r7350374 = r7350359 * r7350359;
        double r7350375 = r7350374 * r7350359;
        double r7350376 = r7350373 + r7350375;
        double r7350377 = r7350352 * r7350352;
        double r7350378 = r7350377 * r7350352;
        double r7350379 = r7350343 * r7350343;
        double r7350380 = r7350343 * r7350379;
        double r7350381 = r7350378 + r7350380;
        double r7350382 = r7350363 * r7350381;
        double r7350383 = fma(r7350376, r7350355, r7350382);
        double r7350384 = r7350366 * r7350383;
        double r7350385 = fma(r7350371, r7350364, r7350384);
        double r7350386 = 12.507343278686905;
        double r7350387 = r7350386 * r7350367;
        double r7350388 = fma(r7350385, r7350369, r7350387);
        double r7350389 = r7350334 * r7350337;
        double r7350390 = r7350388 * r7350389;
        double r7350391 = fma(r7350339, r7350370, r7350390);
        double r7350392 = atan2(1.0, 0.0);
        double r7350393 = r7350349 * r7350392;
        double r7350394 = sqrt(r7350393);
        double r7350395 = 0.5;
        double r7350396 = r7350337 + r7350395;
        double r7350397 = pow(r7350396, r7350346);
        double r7350398 = r7350345 - r7350395;
        double r7350399 = -r7350398;
        double r7350400 = pow(r7350396, r7350399);
        double r7350401 = exp(r7350396);
        double r7350402 = r7350400 / r7350401;
        double r7350403 = r7350397 * r7350402;
        double r7350404 = r7350403 * r7350392;
        double r7350405 = r7350394 * r7350404;
        double r7350406 = r7350391 * r7350405;
        double r7350407 = r7350389 * r7350370;
        double r7350408 = r7350333 * r7350392;
        double r7350409 = sin(r7350408);
        double r7350410 = r7350407 * r7350409;
        double r7350411 = r7350406 / r7350410;
        return r7350411;
}

Error

Bits error versus z

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. Simplified0.7

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

  4. Applied expm1-log1p-u0.7

    \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}\right)\right)}\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{-0.13857109526572012}{6 - z}\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \frac{12.507343278686905}{5 - z}\right)\right)\]
  5. Using strategy rm

  6. Applied *-un-lft-identity0.7

    \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{\color{blue}{1 \cdot e^{\left(7 - z\right) + 0.5}}}\right)\right)\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{-0.13857109526572012}{6 - z}\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \frac{12.507343278686905}{5 - z}\right)\right)\]

  7. Applied sub-neg0.7

    \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\color{blue}{\left(\left(1 - z\right) + \left(-\left(1 - 0.5\right)\right)\right)}}}{1 \cdot e^{\left(7 - z\right) + 0.5}}\right)\right)\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{-0.13857109526572012}{6 - z}\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \frac{12.507343278686905}{5 - z}\right)\right)\]

  8. Applied unpow-prod-up1.2

    \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\color{blue}{{\left(\left(7 - z\right) + 0.5\right)}^{\left(1 - z\right)} \cdot {\left(\left(7 - z\right) + 0.5\right)}^{\left(-\left(1 - 0.5\right)\right)}}}{1 \cdot e^{\left(7 - z\right) + 0.5}}\right)\right)\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{-0.13857109526572012}{6 - z}\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \frac{12.507343278686905}{5 - z}\right)\right)\]

  9. Applied times-frac0.7

    \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\color{blue}{\frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(1 - z\right)}}{1} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(-\left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}}\right)\right)\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{-0.13857109526572012}{6 - z}\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \frac{12.507343278686905}{5 - z}\right)\right)\]

  10. Simplified0.7

    \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\color{blue}{{\left(\left(7 - z\right) + 0.5\right)}^{\left(1 - z\right)}} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(-\left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}\right)\right)\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{-0.13857109526572012}{6 - z}\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \frac{12.507343278686905}{5 - z}\right)\right)\]
  11. Using strategy rm

  12. Applied flip3-+0.7

    \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \mathsf{expm1}\left(\mathsf{log1p}\left({\left(\left(7 - z\right) + 0.5\right)}^{\left(1 - z\right)} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(-\left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}\right)\right)\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{-0.13857109526572012}{6 - z}\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\frac{-176.6150291621406}{4 - z} + 0.9999999999998099\right) + \color{blue}{\frac{{\left(\frac{771.3234287776531}{2 + \left(1 - z\right)}\right)}^{3} + {\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)}^{3}}{\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)}}\right)\right) + \frac{12.507343278686905}{5 - z}\right)\right)\]

  13. Applied flip3-+0.7

    \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \mathsf{expm1}\left(\mathsf{log1p}\left({\left(\left(7 - z\right) + 0.5\right)}^{\left(1 - z\right)} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(-\left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}\right)\right)\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{-0.13857109526572012}{6 - z}\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\color{blue}{\frac{{\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {0.9999999999998099}^{3}}{\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)}} + \frac{{\left(\frac{771.3234287776531}{2 + \left(1 - z\right)}\right)}^{3} + {\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)}^{3}}{\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)}\right)\right) + \frac{12.507343278686905}{5 - z}\right)\right)\]

  14. Applied frac-add0.7

    \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \mathsf{expm1}\left(\mathsf{log1p}\left({\left(\left(7 - z\right) + 0.5\right)}^{\left(1 - z\right)} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(-\left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}\right)\right)\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{-0.13857109526572012}{6 - z}\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \color{blue}{\frac{\left({\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {0.9999999999998099}^{3}\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left({\left(\frac{771.3234287776531}{2 + \left(1 - z\right)}\right)}^{3} + {\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)}^{3}\right)}{\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)}}\right) + \frac{12.507343278686905}{5 - z}\right)\right)\]

  15. Applied frac-add0.7

    \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \mathsf{expm1}\left(\mathsf{log1p}\left({\left(\left(7 - z\right) + 0.5\right)}^{\left(1 - z\right)} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(-\left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}\right)\right)\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{-0.13857109526572012}{6 - z}\right) + \left(\color{blue}{\frac{1.5056327351493116 \cdot 10^{-07} \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(8 - z\right) \cdot \left(\left({\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {0.9999999999998099}^{3}\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left({\left(\frac{771.3234287776531}{2 + \left(1 - z\right)}\right)}^{3} + {\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)}^{3}\right)\right)}{\left(8 - z\right) \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)}} + \frac{12.507343278686905}{5 - z}\right)\right)\]

  16. Applied frac-add0.9

    \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \mathsf{expm1}\left(\mathsf{log1p}\left({\left(\left(7 - z\right) + 0.5\right)}^{\left(1 - z\right)} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(-\left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}\right)\right)\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{7 - z} + \frac{-0.13857109526572012}{6 - z}\right) + \color{blue}{\frac{\left(1.5056327351493116 \cdot 10^{-07} \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(8 - z\right) \cdot \left(\left({\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {0.9999999999998099}^{3}\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left({\left(\frac{771.3234287776531}{2 + \left(1 - z\right)}\right)}^{3} + {\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)}^{3}\right)\right)\right) \cdot \left(5 - z\right) + \left(\left(8 - z\right) \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \cdot 12.507343278686905}{\left(\left(8 - z\right) \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \cdot \left(5 - z\right)}}\right)\]

  17. Applied frac-add0.9

    \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \mathsf{expm1}\left(\mathsf{log1p}\left({\left(\left(7 - z\right) + 0.5\right)}^{\left(1 - z\right)} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(-\left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}\right)\right)\right) \cdot \left(\color{blue}{\frac{9.984369578019572 \cdot 10^{-06} \cdot \left(6 - z\right) + \left(7 - z\right) \cdot -0.13857109526572012}{\left(7 - z\right) \cdot \left(6 - z\right)}} + \frac{\left(1.5056327351493116 \cdot 10^{-07} \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(8 - z\right) \cdot \left(\left({\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {0.9999999999998099}^{3}\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left({\left(\frac{771.3234287776531}{2 + \left(1 - z\right)}\right)}^{3} + {\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)}^{3}\right)\right)\right) \cdot \left(5 - z\right) + \left(\left(8 - z\right) \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \cdot 12.507343278686905}{\left(\left(8 - z\right) \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \cdot \left(5 - z\right)}\right)\]

  18. Applied frac-add0.7

    \[\leadsto \left(\left(\sqrt{2 \cdot \pi} \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \cdot \mathsf{expm1}\left(\mathsf{log1p}\left({\left(\left(7 - z\right) + 0.5\right)}^{\left(1 - z\right)} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(-\left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}\right)\right)\right) \cdot \color{blue}{\frac{\left(9.984369578019572 \cdot 10^{-06} \cdot \left(6 - z\right) + \left(7 - z\right) \cdot -0.13857109526572012\right) \cdot \left(\left(\left(8 - z\right) \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \cdot \left(5 - z\right)\right) + \left(\left(7 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(1.5056327351493116 \cdot 10^{-07} \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(8 - z\right) \cdot \left(\left({\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {0.9999999999998099}^{3}\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left({\left(\frac{771.3234287776531}{2 + \left(1 - z\right)}\right)}^{3} + {\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)}^{3}\right)\right)\right) \cdot \left(5 - z\right) + \left(\left(8 - z\right) \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \cdot 12.507343278686905\right)}{\left(\left(7 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(\left(8 - z\right) \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \cdot \left(5 - z\right)\right)}}\]

  19. Applied associate-*r/0.7

    \[\leadsto \left(\color{blue}{\frac{\sqrt{2 \cdot \pi} \cdot \pi}{\sin \left(\pi \cdot z\right)}} \cdot \mathsf{expm1}\left(\mathsf{log1p}\left({\left(\left(7 - z\right) + 0.5\right)}^{\left(1 - z\right)} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(-\left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}\right)\right)\right) \cdot \frac{\left(9.984369578019572 \cdot 10^{-06} \cdot \left(6 - z\right) + \left(7 - z\right) \cdot -0.13857109526572012\right) \cdot \left(\left(\left(8 - z\right) \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \cdot \left(5 - z\right)\right) + \left(\left(7 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(1.5056327351493116 \cdot 10^{-07} \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(8 - z\right) \cdot \left(\left({\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {0.9999999999998099}^{3}\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left({\left(\frac{771.3234287776531}{2 + \left(1 - z\right)}\right)}^{3} + {\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)}^{3}\right)\right)\right) \cdot \left(5 - z\right) + \left(\left(8 - z\right) \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \cdot 12.507343278686905\right)}{\left(\left(7 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(\left(8 - z\right) \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \cdot \left(5 - z\right)\right)}\]

  20. Applied associate-*l/0.8

    \[\leadsto \color{blue}{\frac{\left(\sqrt{2 \cdot \pi} \cdot \pi\right) \cdot \mathsf{expm1}\left(\mathsf{log1p}\left({\left(\left(7 - z\right) + 0.5\right)}^{\left(1 - z\right)} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(-\left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}\right)\right)}{\sin \left(\pi \cdot z\right)}} \cdot \frac{\left(9.984369578019572 \cdot 10^{-06} \cdot \left(6 - z\right) + \left(7 - z\right) \cdot -0.13857109526572012\right) \cdot \left(\left(\left(8 - z\right) \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \cdot \left(5 - z\right)\right) + \left(\left(7 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(1.5056327351493116 \cdot 10^{-07} \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(8 - z\right) \cdot \left(\left({\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {0.9999999999998099}^{3}\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left({\left(\frac{771.3234287776531}{2 + \left(1 - z\right)}\right)}^{3} + {\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)}^{3}\right)\right)\right) \cdot \left(5 - z\right) + \left(\left(8 - z\right) \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \cdot 12.507343278686905\right)}{\left(\left(7 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(\left(8 - z\right) \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \cdot \left(5 - z\right)\right)}\]

  21. Applied frac-times0.4

    \[\leadsto \color{blue}{\frac{\left(\left(\sqrt{2 \cdot \pi} \cdot \pi\right) \cdot \mathsf{expm1}\left(\mathsf{log1p}\left({\left(\left(7 - z\right) + 0.5\right)}^{\left(1 - z\right)} \cdot \frac{{\left(\left(7 - z\right) + 0.5\right)}^{\left(-\left(1 - 0.5\right)\right)}}{e^{\left(7 - z\right) + 0.5}}\right)\right)\right) \cdot \left(\left(9.984369578019572 \cdot 10^{-06} \cdot \left(6 - z\right) + \left(7 - z\right) \cdot -0.13857109526572012\right) \cdot \left(\left(\left(8 - z\right) \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \cdot \left(5 - z\right)\right) + \left(\left(7 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(1.5056327351493116 \cdot 10^{-07} \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(8 - z\right) \cdot \left(\left({\left(\frac{-176.6150291621406}{4 - z}\right)}^{3} + {0.9999999999998099}^{3}\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left({\left(\frac{771.3234287776531}{2 + \left(1 - z\right)}\right)}^{3} + {\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)}^{3}\right)\right)\right) \cdot \left(5 - z\right) + \left(\left(8 - z\right) \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \cdot 12.507343278686905\right)\right)}{\sin \left(\pi \cdot z\right) \cdot \left(\left(\left(7 - z\right) \cdot \left(6 - z\right)\right) \cdot \left(\left(\left(8 - z\right) \cdot \left(\left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} + \left(0.9999999999998099 \cdot 0.9999999999998099 - \frac{-176.6150291621406}{4 - z} \cdot 0.9999999999998099\right)\right) \cdot \left(\frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \frac{771.3234287776531}{2 + \left(1 - z\right)} + \left(\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) - \frac{771.3234287776531}{2 + \left(1 - z\right)} \cdot \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \cdot \left(5 - z\right)\right)\right)}}\]

  22. Simplified0.4

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

  23. Simplified0.4

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

  24. Final simplification0.4

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

Reproduce

herbie shell --seed 2019144 +o rules:numerics
(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))))))