Average Error: 61.7 → 0.9
Time: 3.4m
Precision: 64
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(z - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\]
↓
\[\left(\frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}}{e^{z}} \cdot e^{\left(1 - 7\right) - 0.5}\right) \cdot \left(\left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right) + \left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5}\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\]
\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(z - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)
↓
\left(\frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}}{e^{z}} \cdot e^{\left(1 - 7\right) - 0.5}\right) \cdot \left(\left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right) + \left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5}\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)
double f(double z) {
        double r184036 = atan2(1.0, 0.0);
        double r184037 = 2.0;
        double r184038 = r184036 * r184037;
        double r184039 = sqrt(r184038);
        double r184040 = z;
        double r184041 = 1.0;
        double r184042 = r184040 - r184041;
        double r184043 = 7.0;
        double r184044 = r184042 + r184043;
        double r184045 = 0.5;
        double r184046 = r184044 + r184045;
        double r184047 = r184042 + r184045;
        double r184048 = pow(r184046, r184047);
        double r184049 = r184039 * r184048;
        double r184050 = -r184046;
        double r184051 = exp(r184050);
        double r184052 = r184049 * r184051;
        double r184053 = 0.9999999999998099;
        double r184054 = 676.5203681218851;
        double r184055 = r184042 + r184041;
        double r184056 = r184054 / r184055;
        double r184057 = r184053 + r184056;
        double r184058 = -1259.1392167224028;
        double r184059 = r184042 + r184037;
        double r184060 = r184058 / r184059;
        double r184061 = r184057 + r184060;
        double r184062 = 771.3234287776531;
        double r184063 = 3.0;
        double r184064 = r184042 + r184063;
        double r184065 = r184062 / r184064;
        double r184066 = r184061 + r184065;
        double r184067 = -176.6150291621406;
        double r184068 = 4.0;
        double r184069 = r184042 + r184068;
        double r184070 = r184067 / r184069;
        double r184071 = r184066 + r184070;
        double r184072 = 12.507343278686905;
        double r184073 = 5.0;
        double r184074 = r184042 + r184073;
        double r184075 = r184072 / r184074;
        double r184076 = r184071 + r184075;
        double r184077 = -0.13857109526572012;
        double r184078 = 6.0;
        double r184079 = r184042 + r184078;
        double r184080 = r184077 / r184079;
        double r184081 = r184076 + r184080;
        double r184082 = 9.984369578019572e-06;
        double r184083 = r184082 / r184044;
        double r184084 = r184081 + r184083;
        double r184085 = 1.5056327351493116e-07;
        double r184086 = 8.0;
        double r184087 = r184042 + r184086;
        double r184088 = r184085 / r184087;
        double r184089 = r184084 + r184088;
        double r184090 = r184052 * r184089;
        return r184090;
}
↓
double f(double z) {
        double r184091 = z;
        double r184092 = 1.0;
        double r184093 = r184091 - r184092;
        double r184094 = 7.0;
        double r184095 = r184093 + r184094;
        double r184096 = 0.5;
        double r184097 = r184095 + r184096;
        double r184098 = r184093 + r184096;
        double r184099 = pow(r184097, r184098);
        double r184100 = atan2(1.0, 0.0);
        double r184101 = 2.0;
        double r184102 = r184100 * r184101;
        double r184103 = sqrt(r184102);
        double r184104 = r184099 * r184103;
        double r184105 = exp(r184091);
        double r184106 = r184104 / r184105;
        double r184107 = r184092 - r184094;
        double r184108 = r184107 - r184096;
        double r184109 = exp(r184108);
        double r184110 = r184106 * r184109;
        double r184111 = 676.5203681218851;
        double r184112 = r184111 / r184091;
        double r184113 = 0.9999999999998099;
        double r184114 = r184112 + r184113;
        double r184115 = -1259.1392167224028;
        double r184116 = r184093 + r184101;
        double r184117 = r184115 / r184116;
        double r184118 = r184114 + r184117;
        double r184119 = 771.3234287776531;
        double r184120 = 3.0;
        double r184121 = r184093 + r184120;
        double r184122 = r184119 / r184121;
        double r184123 = -176.6150291621406;
        double r184124 = 4.0;
        double r184125 = r184093 + r184124;
        double r184126 = r184123 / r184125;
        double r184127 = r184122 + r184126;
        double r184128 = 12.507343278686905;
        double r184129 = 5.0;
        double r184130 = r184093 + r184129;
        double r184131 = r184128 / r184130;
        double r184132 = r184127 + r184131;
        double r184133 = -0.13857109526572012;
        double r184134 = 6.0;
        double r184135 = r184093 + r184134;
        double r184136 = r184133 / r184135;
        double r184137 = 9.984369578019572e-06;
        double r184138 = r184137 / r184095;
        double r184139 = r184136 + r184138;
        double r184140 = 1.5056327351493116e-07;
        double r184141 = 8.0;
        double r184142 = r184093 + r184141;
        double r184143 = r184140 / r184142;
        double r184144 = r184139 + r184143;
        double r184145 = r184132 + r184144;
        double r184146 = r184118 + r184145;
        double r184147 = r184110 * r184146;
        return r184147;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 61.7

    \[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(z - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\]

  2. Simplified1.1

    \[\leadsto \color{blue}{\frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}} \cdot \left(\left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right) + \left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5}\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)}\]
  3. Using strategy rm

  4. Applied associate-+l-1.1

    \[\leadsto \frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}}{e^{\color{blue}{\left(z - \left(1 - 7\right)\right)} + 0.5}} \cdot \left(\left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right) + \left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5}\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\]

  5. Applied associate-+l-1.1

    \[\leadsto \frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}}{e^{\color{blue}{z - \left(\left(1 - 7\right) - 0.5\right)}}} \cdot \left(\left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right) + \left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5}\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\]

  6. Applied exp-diff1.6

    \[\leadsto \frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}}{\color{blue}{\frac{e^{z}}{e^{\left(1 - 7\right) - 0.5}}}} \cdot \left(\left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right) + \left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5}\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\]

  7. Applied associate-/r/0.9

    \[\leadsto \color{blue}{\left(\frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}}{e^{z}} \cdot e^{\left(1 - 7\right) - 0.5}\right)} \cdot \left(\left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right) + \left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5}\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\]

  8. Final simplification0.9

    \[\leadsto \left(\frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}}{e^{z}} \cdot e^{\left(1 - 7\right) - 0.5}\right) \cdot \left(\left(\left(\frac{676.5203681218850988443591631948947906494}{z} + 0.9999999999998099298181841732002794742584\right) + \frac{-1259.139216722402807135949842631816864014}{\left(z - 1\right) + 2}\right) + \left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(z - 1\right) + 3} + \frac{-176.6150291621405870046146446838974952698}{\left(z - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(z - 1\right) + 5}\right) + \left(\left(\frac{-0.1385710952657201178173096423051902092993}{\left(z - 1\right) + 6} + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\right)\right)\]

Reproduce

herbie shell --seed 2019212 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z greater than 0.5"
  :precision binary64
  (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- z 1) 7) 0.5) (+ (- z 1) 0.5))) (exp (- (+ (+ (- z 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.99999999999980993 (/ 676.520368121885099 (+ (- z 1) 1))) (/ -1259.13921672240281 (+ (- z 1) 2))) (/ 771.32342877765313 (+ (- z 1) 3))) (/ -176.615029162140587 (+ (- z 1) 4))) (/ 12.5073432786869052 (+ (- z 1) 5))) (/ -0.138571095265720118 (+ (- z 1) 6))) (/ 9.98436957801957158e-6 (+ (- z 1) 7))) (/ 1.50563273514931162e-7 (+ (- z 1) 8)))))