Average Error: 59.9 → 0.8
Time: 4.0m
Precision: 64
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]
↓
\[\left(\frac{\sqrt{2 \cdot \pi}}{e^{0.5}} \cdot \left(\left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) + \frac{12.507343278686905}{z + 4}\right) + \frac{-0.13857109526572012}{5 + z}\right) + \frac{\sqrt{2 \cdot \pi}}{e^{0.5}} \cdot \left(\frac{-1259.1392167224028}{z + 1} + \left(\left(\left(\frac{771.3234287776531}{z + 2} + \frac{676.5203681218851}{z}\right) + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right)\right)\right) \cdot \frac{\frac{{\left(0.5 + \left(\left(z - 1\right) + 7\right)\right)}^{\left(\left(z - 1\right) + 0.5\right)}}{e^{7}}}{e^{z - 1}}\]
\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)
↓
\left(\frac{\sqrt{2 \cdot \pi}}{e^{0.5}} \cdot \left(\left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) + \frac{12.507343278686905}{z + 4}\right) + \frac{-0.13857109526572012}{5 + z}\right) + \frac{\sqrt{2 \cdot \pi}}{e^{0.5}} \cdot \left(\frac{-1259.1392167224028}{z + 1} + \left(\left(\left(\frac{771.3234287776531}{z + 2} + \frac{676.5203681218851}{z}\right) + 0.9999999999998099\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right)\right)\right) \cdot \frac{\frac{{\left(0.5 + \left(\left(z - 1\right) + 7\right)\right)}^{\left(\left(z - 1\right) + 0.5\right)}}{e^{7}}}{e^{z - 1}}
double f(double z) {
        double r11838326 = atan2(1.0, 0.0);
        double r11838327 = 2.0;
        double r11838328 = r11838326 * r11838327;
        double r11838329 = sqrt(r11838328);
        double r11838330 = z;
        double r11838331 = 1.0;
        double r11838332 = r11838330 - r11838331;
        double r11838333 = 7.0;
        double r11838334 = r11838332 + r11838333;
        double r11838335 = 0.5;
        double r11838336 = r11838334 + r11838335;
        double r11838337 = r11838332 + r11838335;
        double r11838338 = pow(r11838336, r11838337);
        double r11838339 = r11838329 * r11838338;
        double r11838340 = -r11838336;
        double r11838341 = exp(r11838340);
        double r11838342 = r11838339 * r11838341;
        double r11838343 = 0.9999999999998099;
        double r11838344 = 676.5203681218851;
        double r11838345 = r11838332 + r11838331;
        double r11838346 = r11838344 / r11838345;
        double r11838347 = r11838343 + r11838346;
        double r11838348 = -1259.1392167224028;
        double r11838349 = r11838332 + r11838327;
        double r11838350 = r11838348 / r11838349;
        double r11838351 = r11838347 + r11838350;
        double r11838352 = 771.3234287776531;
        double r11838353 = 3.0;
        double r11838354 = r11838332 + r11838353;
        double r11838355 = r11838352 / r11838354;
        double r11838356 = r11838351 + r11838355;
        double r11838357 = -176.6150291621406;
        double r11838358 = 4.0;
        double r11838359 = r11838332 + r11838358;
        double r11838360 = r11838357 / r11838359;
        double r11838361 = r11838356 + r11838360;
        double r11838362 = 12.507343278686905;
        double r11838363 = 5.0;
        double r11838364 = r11838332 + r11838363;
        double r11838365 = r11838362 / r11838364;
        double r11838366 = r11838361 + r11838365;
        double r11838367 = -0.13857109526572012;
        double r11838368 = 6.0;
        double r11838369 = r11838332 + r11838368;
        double r11838370 = r11838367 / r11838369;
        double r11838371 = r11838366 + r11838370;
        double r11838372 = 9.984369578019572e-06;
        double r11838373 = r11838372 / r11838334;
        double r11838374 = r11838371 + r11838373;
        double r11838375 = 1.5056327351493116e-07;
        double r11838376 = 8.0;
        double r11838377 = r11838332 + r11838376;
        double r11838378 = r11838375 / r11838377;
        double r11838379 = r11838374 + r11838378;
        double r11838380 = r11838342 * r11838379;
        return r11838380;
}
↓
double f(double z) {
        double r11838381 = 2.0;
        double r11838382 = atan2(1.0, 0.0);
        double r11838383 = r11838381 * r11838382;
        double r11838384 = sqrt(r11838383);
        double r11838385 = 0.5;
        double r11838386 = exp(r11838385);
        double r11838387 = r11838384 / r11838386;
        double r11838388 = 9.984369578019572e-06;
        double r11838389 = z;
        double r11838390 = -6.0;
        double r11838391 = r11838389 - r11838390;
        double r11838392 = r11838388 / r11838391;
        double r11838393 = 1.5056327351493116e-07;
        double r11838394 = 7.0;
        double r11838395 = r11838389 + r11838394;
        double r11838396 = r11838393 / r11838395;
        double r11838397 = r11838392 + r11838396;
        double r11838398 = 12.507343278686905;
        double r11838399 = 4.0;
        double r11838400 = r11838389 + r11838399;
        double r11838401 = r11838398 / r11838400;
        double r11838402 = r11838397 + r11838401;
        double r11838403 = -0.13857109526572012;
        double r11838404 = 5.0;
        double r11838405 = r11838404 + r11838389;
        double r11838406 = r11838403 / r11838405;
        double r11838407 = r11838402 + r11838406;
        double r11838408 = r11838387 * r11838407;
        double r11838409 = -1259.1392167224028;
        double r11838410 = 1.0;
        double r11838411 = r11838389 + r11838410;
        double r11838412 = r11838409 / r11838411;
        double r11838413 = 771.3234287776531;
        double r11838414 = r11838389 + r11838381;
        double r11838415 = r11838413 / r11838414;
        double r11838416 = 676.5203681218851;
        double r11838417 = r11838416 / r11838389;
        double r11838418 = r11838415 + r11838417;
        double r11838419 = 0.9999999999998099;
        double r11838420 = r11838418 + r11838419;
        double r11838421 = -176.6150291621406;
        double r11838422 = r11838389 - r11838410;
        double r11838423 = r11838422 + r11838399;
        double r11838424 = r11838421 / r11838423;
        double r11838425 = r11838420 + r11838424;
        double r11838426 = r11838412 + r11838425;
        double r11838427 = r11838387 * r11838426;
        double r11838428 = r11838408 + r11838427;
        double r11838429 = r11838422 + r11838394;
        double r11838430 = r11838385 + r11838429;
        double r11838431 = r11838422 + r11838385;
        double r11838432 = pow(r11838430, r11838431);
        double r11838433 = exp(r11838394);
        double r11838434 = r11838432 / r11838433;
        double r11838435 = exp(r11838422);
        double r11838436 = r11838434 / r11838435;
        double r11838437 = r11838428 * r11838436;
        return r11838437;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 59.9

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

  2. Simplified1.0

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

  4. Applied exp-sum1.0

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

  5. Applied times-frac0.8

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

  6. Applied associate-*l*0.8

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

  8. Applied exp-sum0.8

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

  9. Applied associate-/r*0.8

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

  11. Applied distribute-lft-in0.8

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

  12. Final simplification0.8

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

Reproduce

herbie shell --seed 2019141 
(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)))))