Average Error: 59.8 → 0.9
Time: 4.8m
Precision: 64
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]
↓
\[\frac{{\left(\left(z + 6\right) + 0.5\right)}^{\left(z - \left(1 - 0.5\right)\right)}}{e^{\left(z + 6\right) + 0.5}} \cdot \left(\sqrt{\pi \cdot 2} \cdot \left(\left(\left(\frac{12.507343278686905}{z + 4} + \left(\left(\frac{771.3234287776531}{2 + z} + \left(\left(\frac{-176.6150291621406}{z + 3} + 0.9999999999998099\right) + \frac{-1259.1392167224028}{z + 1}\right)\right) + \frac{676.5203681218851}{z}\right)\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} + \frac{9.984369578019572 \cdot 10^{-06}}{z + 6}\right)\right) + \frac{-0.13857109526572012}{z - -5}\right)\right)\]
\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)
↓
\frac{{\left(\left(z + 6\right) + 0.5\right)}^{\left(z - \left(1 - 0.5\right)\right)}}{e^{\left(z + 6\right) + 0.5}} \cdot \left(\sqrt{\pi \cdot 2} \cdot \left(\left(\left(\frac{12.507343278686905}{z + 4} + \left(\left(\frac{771.3234287776531}{2 + z} + \left(\left(\frac{-176.6150291621406}{z + 3} + 0.9999999999998099\right) + \frac{-1259.1392167224028}{z + 1}\right)\right) + \frac{676.5203681218851}{z}\right)\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{7 + z} + \frac{9.984369578019572 \cdot 10^{-06}}{z + 6}\right)\right) + \frac{-0.13857109526572012}{z - -5}\right)\right)
double f(double z) {
        double r4980044 = atan2(1.0, 0.0);
        double r4980045 = 2.0;
        double r4980046 = r4980044 * r4980045;
        double r4980047 = sqrt(r4980046);
        double r4980048 = z;
        double r4980049 = 1.0;
        double r4980050 = r4980048 - r4980049;
        double r4980051 = 7.0;
        double r4980052 = r4980050 + r4980051;
        double r4980053 = 0.5;
        double r4980054 = r4980052 + r4980053;
        double r4980055 = r4980050 + r4980053;
        double r4980056 = pow(r4980054, r4980055);
        double r4980057 = r4980047 * r4980056;
        double r4980058 = -r4980054;
        double r4980059 = exp(r4980058);
        double r4980060 = r4980057 * r4980059;
        double r4980061 = 0.9999999999998099;
        double r4980062 = 676.5203681218851;
        double r4980063 = r4980050 + r4980049;
        double r4980064 = r4980062 / r4980063;
        double r4980065 = r4980061 + r4980064;
        double r4980066 = -1259.1392167224028;
        double r4980067 = r4980050 + r4980045;
        double r4980068 = r4980066 / r4980067;
        double r4980069 = r4980065 + r4980068;
        double r4980070 = 771.3234287776531;
        double r4980071 = 3.0;
        double r4980072 = r4980050 + r4980071;
        double r4980073 = r4980070 / r4980072;
        double r4980074 = r4980069 + r4980073;
        double r4980075 = -176.6150291621406;
        double r4980076 = 4.0;
        double r4980077 = r4980050 + r4980076;
        double r4980078 = r4980075 / r4980077;
        double r4980079 = r4980074 + r4980078;
        double r4980080 = 12.507343278686905;
        double r4980081 = 5.0;
        double r4980082 = r4980050 + r4980081;
        double r4980083 = r4980080 / r4980082;
        double r4980084 = r4980079 + r4980083;
        double r4980085 = -0.13857109526572012;
        double r4980086 = 6.0;
        double r4980087 = r4980050 + r4980086;
        double r4980088 = r4980085 / r4980087;
        double r4980089 = r4980084 + r4980088;
        double r4980090 = 9.984369578019572e-06;
        double r4980091 = r4980090 / r4980052;
        double r4980092 = r4980089 + r4980091;
        double r4980093 = 1.5056327351493116e-07;
        double r4980094 = 8.0;
        double r4980095 = r4980050 + r4980094;
        double r4980096 = r4980093 / r4980095;
        double r4980097 = r4980092 + r4980096;
        double r4980098 = r4980060 * r4980097;
        return r4980098;
}
↓
double f(double z) {
        double r4980099 = z;
        double r4980100 = 6.0;
        double r4980101 = r4980099 + r4980100;
        double r4980102 = 0.5;
        double r4980103 = r4980101 + r4980102;
        double r4980104 = 1.0;
        double r4980105 = r4980104 - r4980102;
        double r4980106 = r4980099 - r4980105;
        double r4980107 = pow(r4980103, r4980106);
        double r4980108 = exp(r4980103);
        double r4980109 = r4980107 / r4980108;
        double r4980110 = atan2(1.0, 0.0);
        double r4980111 = 2.0;
        double r4980112 = r4980110 * r4980111;
        double r4980113 = sqrt(r4980112);
        double r4980114 = 12.507343278686905;
        double r4980115 = 4.0;
        double r4980116 = r4980099 + r4980115;
        double r4980117 = r4980114 / r4980116;
        double r4980118 = 771.3234287776531;
        double r4980119 = r4980111 + r4980099;
        double r4980120 = r4980118 / r4980119;
        double r4980121 = -176.6150291621406;
        double r4980122 = 3.0;
        double r4980123 = r4980099 + r4980122;
        double r4980124 = r4980121 / r4980123;
        double r4980125 = 0.9999999999998099;
        double r4980126 = r4980124 + r4980125;
        double r4980127 = -1259.1392167224028;
        double r4980128 = r4980099 + r4980104;
        double r4980129 = r4980127 / r4980128;
        double r4980130 = r4980126 + r4980129;
        double r4980131 = r4980120 + r4980130;
        double r4980132 = 676.5203681218851;
        double r4980133 = r4980132 / r4980099;
        double r4980134 = r4980131 + r4980133;
        double r4980135 = r4980117 + r4980134;
        double r4980136 = 1.5056327351493116e-07;
        double r4980137 = 7.0;
        double r4980138 = r4980137 + r4980099;
        double r4980139 = r4980136 / r4980138;
        double r4980140 = 9.984369578019572e-06;
        double r4980141 = r4980140 / r4980101;
        double r4980142 = r4980139 + r4980141;
        double r4980143 = r4980135 + r4980142;
        double r4980144 = -0.13857109526572012;
        double r4980145 = -5.0;
        double r4980146 = r4980099 - r4980145;
        double r4980147 = r4980144 / r4980146;
        double r4980148 = r4980143 + r4980147;
        double r4980149 = r4980113 * r4980148;
        double r4980150 = r4980109 * r4980149;
        return r4980150;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 59.8

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

  2. Simplified1.1

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

  3. Simplified0.9

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

  4. Final simplification0.9

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

Reproduce

herbie shell --seed 2019151 
(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)))))