Average Error: 59.7 → 0.8
Time: 3.0m
Precision: 64
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]
↓
\[\left(\left(\left(\left(\frac{12.507343278686905}{z + 4} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + z} + \left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z + 1}\right)\right)\right) + \frac{-176.6150291621406}{3 + z}\right) + \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-07}}{7 + z}\right) + \frac{-0.13857109526572012}{z + 5}\right)\right) \cdot \left(\frac{\left(\sqrt{2} \cdot {\left(6.5 + z\right)}^{\left(z - 0.5\right)}\right) \cdot \sqrt{\pi}}{e^{0.5 + z}} \cdot e^{-6}\right)\]
\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)
↓
\left(\left(\left(\left(\frac{12.507343278686905}{z + 4} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + z} + \left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z + 1}\right)\right)\right) + \frac{-176.6150291621406}{3 + z}\right) + \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-07}}{7 + z}\right) + \frac{-0.13857109526572012}{z + 5}\right)\right) \cdot \left(\frac{\left(\sqrt{2} \cdot {\left(6.5 + z\right)}^{\left(z - 0.5\right)}\right) \cdot \sqrt{\pi}}{e^{0.5 + z}} \cdot e^{-6}\right)
double f(double z) {
        double r11127384 = atan2(1.0, 0.0);
        double r11127385 = 2.0;
        double r11127386 = r11127384 * r11127385;
        double r11127387 = sqrt(r11127386);
        double r11127388 = z;
        double r11127389 = 1.0;
        double r11127390 = r11127388 - r11127389;
        double r11127391 = 7.0;
        double r11127392 = r11127390 + r11127391;
        double r11127393 = 0.5;
        double r11127394 = r11127392 + r11127393;
        double r11127395 = r11127390 + r11127393;
        double r11127396 = pow(r11127394, r11127395);
        double r11127397 = r11127387 * r11127396;
        double r11127398 = -r11127394;
        double r11127399 = exp(r11127398);
        double r11127400 = r11127397 * r11127399;
        double r11127401 = 0.9999999999998099;
        double r11127402 = 676.5203681218851;
        double r11127403 = r11127390 + r11127389;
        double r11127404 = r11127402 / r11127403;
        double r11127405 = r11127401 + r11127404;
        double r11127406 = -1259.1392167224028;
        double r11127407 = r11127390 + r11127385;
        double r11127408 = r11127406 / r11127407;
        double r11127409 = r11127405 + r11127408;
        double r11127410 = 771.3234287776531;
        double r11127411 = 3.0;
        double r11127412 = r11127390 + r11127411;
        double r11127413 = r11127410 / r11127412;
        double r11127414 = r11127409 + r11127413;
        double r11127415 = -176.6150291621406;
        double r11127416 = 4.0;
        double r11127417 = r11127390 + r11127416;
        double r11127418 = r11127415 / r11127417;
        double r11127419 = r11127414 + r11127418;
        double r11127420 = 12.507343278686905;
        double r11127421 = 5.0;
        double r11127422 = r11127390 + r11127421;
        double r11127423 = r11127420 / r11127422;
        double r11127424 = r11127419 + r11127423;
        double r11127425 = -0.13857109526572012;
        double r11127426 = 6.0;
        double r11127427 = r11127390 + r11127426;
        double r11127428 = r11127425 / r11127427;
        double r11127429 = r11127424 + r11127428;
        double r11127430 = 9.984369578019572e-06;
        double r11127431 = r11127430 / r11127392;
        double r11127432 = r11127429 + r11127431;
        double r11127433 = 1.5056327351493116e-07;
        double r11127434 = 8.0;
        double r11127435 = r11127390 + r11127434;
        double r11127436 = r11127433 / r11127435;
        double r11127437 = r11127432 + r11127436;
        double r11127438 = r11127400 * r11127437;
        return r11127438;
}
↓
double f(double z) {
        double r11127439 = 12.507343278686905;
        double r11127440 = z;
        double r11127441 = 4.0;
        double r11127442 = r11127440 + r11127441;
        double r11127443 = r11127439 / r11127442;
        double r11127444 = 0.9999999999998099;
        double r11127445 = r11127443 + r11127444;
        double r11127446 = 771.3234287776531;
        double r11127447 = 2.0;
        double r11127448 = r11127447 + r11127440;
        double r11127449 = r11127446 / r11127448;
        double r11127450 = 676.5203681218851;
        double r11127451 = r11127450 / r11127440;
        double r11127452 = -1259.1392167224028;
        double r11127453 = 1.0;
        double r11127454 = r11127440 + r11127453;
        double r11127455 = r11127452 / r11127454;
        double r11127456 = r11127451 + r11127455;
        double r11127457 = r11127449 + r11127456;
        double r11127458 = r11127445 + r11127457;
        double r11127459 = -176.6150291621406;
        double r11127460 = 3.0;
        double r11127461 = r11127460 + r11127440;
        double r11127462 = r11127459 / r11127461;
        double r11127463 = r11127458 + r11127462;
        double r11127464 = 9.984369578019572e-06;
        double r11127465 = 6.0;
        double r11127466 = r11127440 + r11127465;
        double r11127467 = r11127464 / r11127466;
        double r11127468 = 1.5056327351493116e-07;
        double r11127469 = 7.0;
        double r11127470 = r11127469 + r11127440;
        double r11127471 = r11127468 / r11127470;
        double r11127472 = r11127467 + r11127471;
        double r11127473 = -0.13857109526572012;
        double r11127474 = 5.0;
        double r11127475 = r11127440 + r11127474;
        double r11127476 = r11127473 / r11127475;
        double r11127477 = r11127472 + r11127476;
        double r11127478 = r11127463 + r11127477;
        double r11127479 = sqrt(r11127447);
        double r11127480 = 6.5;
        double r11127481 = r11127480 + r11127440;
        double r11127482 = 0.5;
        double r11127483 = r11127440 - r11127482;
        double r11127484 = pow(r11127481, r11127483);
        double r11127485 = r11127479 * r11127484;
        double r11127486 = atan2(1.0, 0.0);
        double r11127487 = sqrt(r11127486);
        double r11127488 = r11127485 * r11127487;
        double r11127489 = r11127482 + r11127440;
        double r11127490 = exp(r11127489);
        double r11127491 = r11127488 / r11127490;
        double r11127492 = -6.0;
        double r11127493 = exp(r11127492);
        double r11127494 = r11127491 * r11127493;
        double r11127495 = r11127478 * r11127494;
        return r11127495;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 59.7

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

  2. Simplified1.1

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

  4. Applied associate-+r-1.1

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

  5. Applied exp-diff1.1

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

  6. Applied associate-/r/0.8

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

  7. Taylor expanded around inf 0.8

    \[\leadsto \left(\frac{\color{blue}{\left(\sqrt{2} \cdot {\left(z + 6.5\right)}^{\left(z - 0.5\right)}\right) \cdot \sqrt{\pi}}}{e^{0.5 + z}} \cdot e^{-6}\right) \cdot \left(\left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + 7}\right) + \frac{-0.13857109526572012}{z + 5}\right) + \left(\left(\left(\frac{12.507343278686905}{z + 4} + 0.9999999999998099\right) + \left(\left(\frac{-1259.1392167224028}{1 + z} + \frac{676.5203681218851}{z}\right) + \frac{771.3234287776531}{z + 2}\right)\right) + \frac{-176.6150291621406}{3 + z}\right)\right)\]

  8. Final simplification0.8

    \[\leadsto \left(\left(\left(\left(\frac{12.507343278686905}{z + 4} + 0.9999999999998099\right) + \left(\frac{771.3234287776531}{2 + z} + \left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z + 1}\right)\right)\right) + \frac{-176.6150291621406}{3 + z}\right) + \left(\left(\frac{9.984369578019572 \cdot 10^{-06}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-07}}{7 + z}\right) + \frac{-0.13857109526572012}{z + 5}\right)\right) \cdot \left(\frac{\left(\sqrt{2} \cdot {\left(6.5 + z\right)}^{\left(z - 0.5\right)}\right) \cdot \sqrt{\pi}}{e^{0.5 + z}} \cdot e^{-6}\right)\]

Reproduce

herbie shell --seed 2019162 
(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)))))