Average Error: 1.8 → 1.8
Time: 57.5s
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\left(\left(\sqrt{2 \cdot \pi} \cdot {\left(\left(7 + \left(\left(1 - z\right) - 1\right)\right) + 0.5\right)}^{\left(0.5 + \left(\left(1 - z\right) - 1\right)\right)}\right) \cdot e^{-\left(\left(7 + \left(\left(1 - z\right) - 1\right)\right) + 0.5\right)}\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 + \left(\left(1 - z\right) - 1\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(\left(1 - z\right) - 1\right)} + \left(\left(\left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \left(\frac{771.3234287776531}{3 + \left(\left(1 - z\right) - 1\right)} + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right)\right)\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{6 + \left(\left(1 - z\right) - 1\right)}\right)\right)\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\]
\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
↓
\left(\left(\left(\sqrt{2 \cdot \pi} \cdot {\left(\left(7 + \left(\left(1 - z\right) - 1\right)\right) + 0.5\right)}^{\left(0.5 + \left(\left(1 - z\right) - 1\right)\right)}\right) \cdot e^{-\left(\left(7 + \left(\left(1 - z\right) - 1\right)\right) + 0.5\right)}\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 + \left(\left(1 - z\right) - 1\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(\left(1 - z\right) - 1\right)} + \left(\left(\left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \left(\frac{771.3234287776531}{3 + \left(\left(1 - z\right) - 1\right)} + \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)\right)\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{6 + \left(\left(1 - z\right) - 1\right)}\right)\right)\right)\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}
double f(double z) {
        double r1507293 = atan2(1.0, 0.0);
        double r1507294 = z;
        double r1507295 = r1507293 * r1507294;
        double r1507296 = sin(r1507295);
        double r1507297 = r1507293 / r1507296;
        double r1507298 = 2.0;
        double r1507299 = r1507293 * r1507298;
        double r1507300 = sqrt(r1507299);
        double r1507301 = 1.0;
        double r1507302 = r1507301 - r1507294;
        double r1507303 = r1507302 - r1507301;
        double r1507304 = 7.0;
        double r1507305 = r1507303 + r1507304;
        double r1507306 = 0.5;
        double r1507307 = r1507305 + r1507306;
        double r1507308 = r1507303 + r1507306;
        double r1507309 = pow(r1507307, r1507308);
        double r1507310 = r1507300 * r1507309;
        double r1507311 = -r1507307;
        double r1507312 = exp(r1507311);
        double r1507313 = r1507310 * r1507312;
        double r1507314 = 0.9999999999998099;
        double r1507315 = 676.5203681218851;
        double r1507316 = r1507303 + r1507301;
        double r1507317 = r1507315 / r1507316;
        double r1507318 = r1507314 + r1507317;
        double r1507319 = -1259.1392167224028;
        double r1507320 = r1507303 + r1507298;
        double r1507321 = r1507319 / r1507320;
        double r1507322 = r1507318 + r1507321;
        double r1507323 = 771.3234287776531;
        double r1507324 = 3.0;
        double r1507325 = r1507303 + r1507324;
        double r1507326 = r1507323 / r1507325;
        double r1507327 = r1507322 + r1507326;
        double r1507328 = -176.6150291621406;
        double r1507329 = 4.0;
        double r1507330 = r1507303 + r1507329;
        double r1507331 = r1507328 / r1507330;
        double r1507332 = r1507327 + r1507331;
        double r1507333 = 12.507343278686905;
        double r1507334 = 5.0;
        double r1507335 = r1507303 + r1507334;
        double r1507336 = r1507333 / r1507335;
        double r1507337 = r1507332 + r1507336;
        double r1507338 = -0.13857109526572012;
        double r1507339 = 6.0;
        double r1507340 = r1507303 + r1507339;
        double r1507341 = r1507338 / r1507340;
        double r1507342 = r1507337 + r1507341;
        double r1507343 = 9.984369578019572e-06;
        double r1507344 = r1507343 / r1507305;
        double r1507345 = r1507342 + r1507344;
        double r1507346 = 1.5056327351493116e-07;
        double r1507347 = 8.0;
        double r1507348 = r1507303 + r1507347;
        double r1507349 = r1507346 / r1507348;
        double r1507350 = r1507345 + r1507349;
        double r1507351 = r1507313 * r1507350;
        double r1507352 = r1507297 * r1507351;
        return r1507352;
}
↓
double f(double z) {
        double r1507353 = 2.0;
        double r1507354 = atan2(1.0, 0.0);
        double r1507355 = r1507353 * r1507354;
        double r1507356 = sqrt(r1507355);
        double r1507357 = 7.0;
        double r1507358 = 1.0;
        double r1507359 = z;
        double r1507360 = r1507358 - r1507359;
        double r1507361 = r1507360 - r1507358;
        double r1507362 = r1507357 + r1507361;
        double r1507363 = 0.5;
        double r1507364 = r1507362 + r1507363;
        double r1507365 = r1507363 + r1507361;
        double r1507366 = pow(r1507364, r1507365);
        double r1507367 = r1507356 * r1507366;
        double r1507368 = -r1507364;
        double r1507369 = exp(r1507368);
        double r1507370 = r1507367 * r1507369;
        double r1507371 = 1.5056327351493116e-07;
        double r1507372 = 8.0;
        double r1507373 = r1507372 + r1507361;
        double r1507374 = r1507371 / r1507373;
        double r1507375 = 9.984369578019572e-06;
        double r1507376 = r1507375 / r1507362;
        double r1507377 = -176.6150291621406;
        double r1507378 = 4.0;
        double r1507379 = r1507361 + r1507378;
        double r1507380 = r1507377 / r1507379;
        double r1507381 = 771.3234287776531;
        double r1507382 = 3.0;
        double r1507383 = r1507382 + r1507361;
        double r1507384 = r1507381 / r1507383;
        double r1507385 = 0.9999999999998099;
        double r1507386 = 676.5203681218851;
        double r1507387 = r1507361 + r1507358;
        double r1507388 = r1507386 / r1507387;
        double r1507389 = r1507385 + r1507388;
        double r1507390 = -1259.1392167224028;
        double r1507391 = r1507361 + r1507353;
        double r1507392 = r1507390 / r1507391;
        double r1507393 = r1507389 + r1507392;
        double r1507394 = r1507384 + r1507393;
        double r1507395 = r1507380 + r1507394;
        double r1507396 = 12.507343278686905;
        double r1507397 = 5.0;
        double r1507398 = r1507361 + r1507397;
        double r1507399 = r1507396 / r1507398;
        double r1507400 = r1507395 + r1507399;
        double r1507401 = -0.13857109526572012;
        double r1507402 = 6.0;
        double r1507403 = r1507402 + r1507361;
        double r1507404 = r1507401 / r1507403;
        double r1507405 = r1507400 + r1507404;
        double r1507406 = r1507376 + r1507405;
        double r1507407 = r1507374 + r1507406;
        double r1507408 = r1507370 * r1507407;
        double r1507409 = r1507354 * r1507359;
        double r1507410 = sin(r1507409);
        double r1507411 = r1507354 / r1507410;
        double r1507412 = r1507408 * r1507411;
        return r1507412;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.8

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

  2. Final simplification1.8

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

Reproduce

herbie shell --seed 2019128 
(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))))))