Average Error: 60.0 → 0.9
Time: 3.6m
Precision: 64
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]
↓
\[\left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-07}}{7 + z}\right) \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(0.5 + \left(z - 1\right)\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) + \left(\frac{1}{\frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(1 - 0.5\right)}}{\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{z}}} \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\frac{12.507343278686905}{z + 4} + \left(\frac{-0.13857109526572012}{z - -5} + \left(\left(\left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 + \frac{-1259.1392167224028}{z - -1}\right)\right) + \frac{771.3234287776531}{z + 2}\right) + \frac{-176.6150291621406}{3 + z}\right)\right)\right)\]
\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(0.9999999999998099 + \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{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-07}}{7 + z}\right) \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(0.5 + \left(z - 1\right)\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) + \left(\frac{1}{\frac{{\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(1 - 0.5\right)}}{\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{z}}} \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\frac{12.507343278686905}{z + 4} + \left(\frac{-0.13857109526572012}{z - -5} + \left(\left(\left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 + \frac{-1259.1392167224028}{z - -1}\right)\right) + \frac{771.3234287776531}{z + 2}\right) + \frac{-176.6150291621406}{3 + z}\right)\right)\right)
double f(double z) {
        double r22655098 = atan2(1.0, 0.0);
        double r22655099 = 2.0;
        double r22655100 = r22655098 * r22655099;
        double r22655101 = sqrt(r22655100);
        double r22655102 = z;
        double r22655103 = 1.0;
        double r22655104 = r22655102 - r22655103;
        double r22655105 = 7.0;
        double r22655106 = r22655104 + r22655105;
        double r22655107 = 0.5;
        double r22655108 = r22655106 + r22655107;
        double r22655109 = r22655104 + r22655107;
        double r22655110 = pow(r22655108, r22655109);
        double r22655111 = r22655101 * r22655110;
        double r22655112 = -r22655108;
        double r22655113 = exp(r22655112);
        double r22655114 = r22655111 * r22655113;
        double r22655115 = 0.9999999999998099;
        double r22655116 = 676.5203681218851;
        double r22655117 = r22655104 + r22655103;
        double r22655118 = r22655116 / r22655117;
        double r22655119 = r22655115 + r22655118;
        double r22655120 = -1259.1392167224028;
        double r22655121 = r22655104 + r22655099;
        double r22655122 = r22655120 / r22655121;
        double r22655123 = r22655119 + r22655122;
        double r22655124 = 771.3234287776531;
        double r22655125 = 3.0;
        double r22655126 = r22655104 + r22655125;
        double r22655127 = r22655124 / r22655126;
        double r22655128 = r22655123 + r22655127;
        double r22655129 = -176.6150291621406;
        double r22655130 = 4.0;
        double r22655131 = r22655104 + r22655130;
        double r22655132 = r22655129 / r22655131;
        double r22655133 = r22655128 + r22655132;
        double r22655134 = 12.507343278686905;
        double r22655135 = 5.0;
        double r22655136 = r22655104 + r22655135;
        double r22655137 = r22655134 / r22655136;
        double r22655138 = r22655133 + r22655137;
        double r22655139 = -0.13857109526572012;
        double r22655140 = 6.0;
        double r22655141 = r22655104 + r22655140;
        double r22655142 = r22655139 / r22655141;
        double r22655143 = r22655138 + r22655142;
        double r22655144 = 9.984369578019572e-06;
        double r22655145 = r22655144 / r22655106;
        double r22655146 = r22655143 + r22655145;
        double r22655147 = 1.5056327351493116e-07;
        double r22655148 = 8.0;
        double r22655149 = r22655104 + r22655148;
        double r22655150 = r22655147 / r22655149;
        double r22655151 = r22655146 + r22655150;
        double r22655152 = r22655114 * r22655151;
        return r22655152;
}
↓
double f(double z) {
        double r22655153 = 9.984369578019572e-06;
        double r22655154 = z;
        double r22655155 = 1.0;
        double r22655156 = r22655154 - r22655155;
        double r22655157 = 7.0;
        double r22655158 = r22655156 + r22655157;
        double r22655159 = r22655153 / r22655158;
        double r22655160 = 1.5056327351493116e-07;
        double r22655161 = r22655157 + r22655154;
        double r22655162 = r22655160 / r22655161;
        double r22655163 = r22655159 + r22655162;
        double r22655164 = atan2(1.0, 0.0);
        double r22655165 = 2.0;
        double r22655166 = r22655164 * r22655165;
        double r22655167 = sqrt(r22655166);
        double r22655168 = 0.5;
        double r22655169 = r22655158 + r22655168;
        double r22655170 = r22655168 + r22655156;
        double r22655171 = pow(r22655169, r22655170);
        double r22655172 = r22655167 * r22655171;
        double r22655173 = -r22655169;
        double r22655174 = exp(r22655173);
        double r22655175 = r22655172 * r22655174;
        double r22655176 = r22655163 * r22655175;
        double r22655177 = r22655155 - r22655168;
        double r22655178 = pow(r22655169, r22655177);
        double r22655179 = pow(r22655169, r22655154);
        double r22655180 = r22655167 * r22655179;
        double r22655181 = r22655178 / r22655180;
        double r22655182 = r22655155 / r22655181;
        double r22655183 = r22655182 * r22655174;
        double r22655184 = 12.507343278686905;
        double r22655185 = 4.0;
        double r22655186 = r22655154 + r22655185;
        double r22655187 = r22655184 / r22655186;
        double r22655188 = -0.13857109526572012;
        double r22655189 = -5.0;
        double r22655190 = r22655154 - r22655189;
        double r22655191 = r22655188 / r22655190;
        double r22655192 = 676.5203681218851;
        double r22655193 = r22655192 / r22655154;
        double r22655194 = 0.9999999999998099;
        double r22655195 = -1259.1392167224028;
        double r22655196 = -1.0;
        double r22655197 = r22655154 - r22655196;
        double r22655198 = r22655195 / r22655197;
        double r22655199 = r22655194 + r22655198;
        double r22655200 = r22655193 + r22655199;
        double r22655201 = 771.3234287776531;
        double r22655202 = r22655154 + r22655165;
        double r22655203 = r22655201 / r22655202;
        double r22655204 = r22655200 + r22655203;
        double r22655205 = -176.6150291621406;
        double r22655206 = 3.0;
        double r22655207 = r22655206 + r22655154;
        double r22655208 = r22655205 / r22655207;
        double r22655209 = r22655204 + r22655208;
        double r22655210 = r22655191 + r22655209;
        double r22655211 = r22655187 + r22655210;
        double r22655212 = r22655183 * r22655211;
        double r22655213 = r22655176 + r22655212;
        return r22655213;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 60.0

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

  2. Simplified0.9

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

  4. Applied associate-+l-0.9

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

  5. Applied pow-sub0.9

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

  6. Applied associate-*l/0.9

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

  8. Applied clear-num0.9

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

  9. Final simplification0.9

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

Reproduce

herbie shell --seed 2019104 +o rules:numerics
(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)))))