Average Error: 1.8 → 1.0
Time: 4.0m
Precision: 64
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\left(\sqrt{\pi} \cdot \sqrt{2}\right) \cdot \left(\frac{{\left(0.5 + \left(7 + \left(-z\right)\right)\right)}^{\left(\left(-z\right) + 0.5\right)}}{e^{0.5 + \left(7 + \left(-z\right)\right)}} \cdot \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} + \frac{\left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z} \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} - \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot \left(\left(5 - z\right) \cdot \left(9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 - z\right) + 1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(7 - z\right)\right)\right) + \left(\left(\left(5 - z\right) \cdot \left({\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} + {\left(\frac{-1259.139216722402807135949842631816864014}{2 - z}\right)}^{3}\right) + \left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z} \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} - \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot 12.50734327868690520801919774385169148445\right) \cdot \left(8 - z\right)\right) \cdot \left(7 - z\right)}{\left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z} \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} - \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(7 - z\right) \cdot \left(8 - z\right)\right)\right)}\right)\right)\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(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
↓
\left(\sqrt{\pi} \cdot \sqrt{2}\right) \cdot \left(\frac{{\left(0.5 + \left(7 + \left(-z\right)\right)\right)}^{\left(\left(-z\right) + 0.5\right)}}{e^{0.5 + \left(7 + \left(-z\right)\right)}} \cdot \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)} + \frac{\left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z} \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} - \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot \left(\left(5 - z\right) \cdot \left(9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(8 - z\right) + 1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(7 - z\right)\right)\right) + \left(\left(\left(5 - z\right) \cdot \left({\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)}^{3} + {\left(\frac{-1259.139216722402807135949842631816864014}{2 - z}\right)}^{3}\right) + \left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z} \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} - \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot 12.50734327868690520801919774385169148445\right) \cdot \left(8 - z\right)\right) \cdot \left(7 - z\right)}{\left(\left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) \cdot \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right) + \frac{-1259.139216722402807135949842631816864014}{2 - z} \cdot \left(\frac{-1259.139216722402807135949842631816864014}{2 - z} - \left(\left(\frac{771.3234287776531346025876700878143310547}{\left(-z\right) + 3} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right) + \frac{-0.1385710952657201178173096423051902092993}{6 - z}\right)\right)\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(7 - z\right) \cdot \left(8 - z\right)\right)\right)}\right)\right)\right)
double f(double z) {
        double r195084 = atan2(1.0, 0.0);
        double r195085 = z;
        double r195086 = r195084 * r195085;
        double r195087 = sin(r195086);
        double r195088 = r195084 / r195087;
        double r195089 = 2.0;
        double r195090 = r195084 * r195089;
        double r195091 = sqrt(r195090);
        double r195092 = 1.0;
        double r195093 = r195092 - r195085;
        double r195094 = r195093 - r195092;
        double r195095 = 7.0;
        double r195096 = r195094 + r195095;
        double r195097 = 0.5;
        double r195098 = r195096 + r195097;
        double r195099 = r195094 + r195097;
        double r195100 = pow(r195098, r195099);
        double r195101 = r195091 * r195100;
        double r195102 = -r195098;
        double r195103 = exp(r195102);
        double r195104 = r195101 * r195103;
        double r195105 = 0.9999999999998099;
        double r195106 = 676.5203681218851;
        double r195107 = r195094 + r195092;
        double r195108 = r195106 / r195107;
        double r195109 = r195105 + r195108;
        double r195110 = -1259.1392167224028;
        double r195111 = r195094 + r195089;
        double r195112 = r195110 / r195111;
        double r195113 = r195109 + r195112;
        double r195114 = 771.3234287776531;
        double r195115 = 3.0;
        double r195116 = r195094 + r195115;
        double r195117 = r195114 / r195116;
        double r195118 = r195113 + r195117;
        double r195119 = -176.6150291621406;
        double r195120 = 4.0;
        double r195121 = r195094 + r195120;
        double r195122 = r195119 / r195121;
        double r195123 = r195118 + r195122;
        double r195124 = 12.507343278686905;
        double r195125 = 5.0;
        double r195126 = r195094 + r195125;
        double r195127 = r195124 / r195126;
        double r195128 = r195123 + r195127;
        double r195129 = -0.13857109526572012;
        double r195130 = 6.0;
        double r195131 = r195094 + r195130;
        double r195132 = r195129 / r195131;
        double r195133 = r195128 + r195132;
        double r195134 = 9.984369578019572e-06;
        double r195135 = r195134 / r195096;
        double r195136 = r195133 + r195135;
        double r195137 = 1.5056327351493116e-07;
        double r195138 = 8.0;
        double r195139 = r195094 + r195138;
        double r195140 = r195137 / r195139;
        double r195141 = r195136 + r195140;
        double r195142 = r195104 * r195141;
        double r195143 = r195088 * r195142;
        return r195143;
}
↓
double f(double z) {
        double r195144 = atan2(1.0, 0.0);
        double r195145 = sqrt(r195144);
        double r195146 = 2.0;
        double r195147 = sqrt(r195146);
        double r195148 = r195145 * r195147;
        double r195149 = 0.5;
        double r195150 = 7.0;
        double r195151 = z;
        double r195152 = -r195151;
        double r195153 = r195150 + r195152;
        double r195154 = r195149 + r195153;
        double r195155 = r195152 + r195149;
        double r195156 = pow(r195154, r195155);
        double r195157 = exp(r195154);
        double r195158 = r195156 / r195157;
        double r195159 = r195144 * r195151;
        double r195160 = sin(r195159);
        double r195161 = r195144 / r195160;
        double r195162 = -176.6150291621406;
        double r195163 = 4.0;
        double r195164 = r195163 + r195152;
        double r195165 = r195162 / r195164;
        double r195166 = 771.3234287776531;
        double r195167 = 3.0;
        double r195168 = r195152 + r195167;
        double r195169 = r195166 / r195168;
        double r195170 = 0.9999999999998099;
        double r195171 = 676.5203681218851;
        double r195172 = 1.0;
        double r195173 = r195172 - r195151;
        double r195174 = r195171 / r195173;
        double r195175 = r195170 + r195174;
        double r195176 = r195169 + r195175;
        double r195177 = -0.13857109526572012;
        double r195178 = 6.0;
        double r195179 = r195178 - r195151;
        double r195180 = r195177 / r195179;
        double r195181 = r195176 + r195180;
        double r195182 = r195181 * r195181;
        double r195183 = -1259.1392167224028;
        double r195184 = r195146 - r195151;
        double r195185 = r195183 / r195184;
        double r195186 = r195185 - r195181;
        double r195187 = r195185 * r195186;
        double r195188 = r195182 + r195187;
        double r195189 = 5.0;
        double r195190 = r195189 - r195151;
        double r195191 = 9.984369578019572e-06;
        double r195192 = 8.0;
        double r195193 = r195192 - r195151;
        double r195194 = r195191 * r195193;
        double r195195 = 1.5056327351493116e-07;
        double r195196 = r195150 - r195151;
        double r195197 = r195195 * r195196;
        double r195198 = r195194 + r195197;
        double r195199 = r195190 * r195198;
        double r195200 = r195188 * r195199;
        double r195201 = 3.0;
        double r195202 = pow(r195181, r195201);
        double r195203 = pow(r195185, r195201);
        double r195204 = r195202 + r195203;
        double r195205 = r195190 * r195204;
        double r195206 = 12.507343278686905;
        double r195207 = r195188 * r195206;
        double r195208 = r195205 + r195207;
        double r195209 = r195208 * r195193;
        double r195210 = r195209 * r195196;
        double r195211 = r195200 + r195210;
        double r195212 = r195196 * r195193;
        double r195213 = r195190 * r195212;
        double r195214 = r195188 * r195213;
        double r195215 = r195211 / r195214;
        double r195216 = r195165 + r195215;
        double r195217 = r195161 * r195216;
        double r195218 = r195158 * r195217;
        double r195219 = r195148 * r195218;
        return r195219;
}

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

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

  2. Simplified1.3

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

  4. Applied sqrt-prod1.0

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

  6. Applied frac-add1.0

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

  7. Applied flip3-+1.5

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

  8. Applied frac-add1.0

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

  9. Applied frac-add1.5

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

  10. Simplified1.5

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

  11. Simplified1.0

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

  12. Final simplification1.0

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

Reproduce

herbie shell --seed 2019323 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  :precision binary64
  (* (/ 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))))))