Average Error: 1.8 → 0.4
Time: 1.1min
Precision: binary64
\[z \leq 0.5\]
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{\pi \cdot 2} \cdot \left({\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)} \cdot \frac{\frac{\left(7 - z\right) \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left({\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)}^{3} + {\left(\frac{-176.6150291621406}{4 - z}\right)}^{3}\right) + 12.507343278686905 \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) + -0.13857109526572012 \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right) + 9.984369578019572 \cdot 10^{-06} \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right)}{\left(7 - z\right) \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}}{e^{\left(7 - z\right) + 0.5}}\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(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
↓
\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{\pi \cdot 2} \cdot \left({\left(\left(7 - z\right) + 0.5\right)}^{\left(0.5 - z\right)} \cdot \frac{\frac{\left(7 - z\right) \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left({\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)}^{3} + {\left(\frac{-176.6150291621406}{4 - z}\right)}^{3}\right) + 12.507343278686905 \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) + -0.13857109526572012 \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right) + 9.984369578019572 \cdot 10^{-06} \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right)}{\left(7 - z\right) \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}}{e^{\left(7 - z\right) + 0.5}}\right)\right)
(FPCore (z)
 :precision binary64
 (*
  (/ PI (sin (* PI z)))
  (*
   (*
    (*
     (sqrt (* PI 2.0))
     (pow (+ (+ (- (- 1.0 z) 1.0) 7.0) 0.5) (+ (- (- 1.0 z) 1.0) 0.5)))
    (exp (- (+ (+ (- (- 1.0 z) 1.0) 7.0) 0.5))))
   (+
    (+
     (+
      (+
       (+
        (+
         (+
          (+
           0.9999999999998099
           (/ 676.5203681218851 (+ (- (- 1.0 z) 1.0) 1.0)))
          (/ -1259.1392167224028 (+ (- (- 1.0 z) 1.0) 2.0)))
         (/ 771.3234287776531 (+ (- (- 1.0 z) 1.0) 3.0)))
        (/ -176.6150291621406 (+ (- (- 1.0 z) 1.0) 4.0)))
       (/ 12.507343278686905 (+ (- (- 1.0 z) 1.0) 5.0)))
      (/ -0.13857109526572012 (+ (- (- 1.0 z) 1.0) 6.0)))
     (/ 9.984369578019572e-06 (+ (- (- 1.0 z) 1.0) 7.0)))
    (/ 1.5056327351493116e-07 (+ (- (- 1.0 z) 1.0) 8.0))))))
↓
(FPCore (z)
 :precision binary64
 (*
  (/ PI (sin (* PI z)))
  (*
   (sqrt (* PI 2.0))
   (*
    (pow (+ (- 7.0 z) 0.5) (- 0.5 z))
    (/
     (+
      (/
       (+
        (*
         (- 7.0 z)
         (+
          (*
           (- 6.0 z)
           (+
            (*
             (- 5.0 z)
             (+
              (pow
               (+
                (+
                 (/ -1259.1392167224028 (- 2.0 z))
                 (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
                (/ 771.3234287776531 (- 3.0 z)))
               3.0)
              (pow (/ -176.6150291621406 (- 4.0 z)) 3.0)))
            (*
             12.507343278686905
             (+
              (*
               (+
                (+
                 (/ -1259.1392167224028 (- 2.0 z))
                 (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
                (/ 771.3234287776531 (- 3.0 z)))
               (+
                (+
                 (/ -1259.1392167224028 (- 2.0 z))
                 (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
                (/ 771.3234287776531 (- 3.0 z))))
              (*
               (/ -176.6150291621406 (- 4.0 z))
               (-
                (/ -176.6150291621406 (- 4.0 z))
                (+
                 (+
                  (/ -1259.1392167224028 (- 2.0 z))
                  (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
                 (/ 771.3234287776531 (- 3.0 z)))))))))
          (*
           -0.13857109526572012
           (*
            (- 5.0 z)
            (+
             (*
              (+
               (+
                (/ -1259.1392167224028 (- 2.0 z))
                (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
               (/ 771.3234287776531 (- 3.0 z)))
              (+
               (+
                (/ -1259.1392167224028 (- 2.0 z))
                (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
               (/ 771.3234287776531 (- 3.0 z))))
             (*
              (/ -176.6150291621406 (- 4.0 z))
              (-
               (/ -176.6150291621406 (- 4.0 z))
               (+
                (+
                 (/ -1259.1392167224028 (- 2.0 z))
                 (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
                (/ 771.3234287776531 (- 3.0 z))))))))))
        (*
         9.984369578019572e-06
         (*
          (- 6.0 z)
          (*
           (- 5.0 z)
           (+
            (*
             (+
              (+
               (/ -1259.1392167224028 (- 2.0 z))
               (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
              (/ 771.3234287776531 (- 3.0 z)))
             (+
              (+
               (/ -1259.1392167224028 (- 2.0 z))
               (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
              (/ 771.3234287776531 (- 3.0 z))))
            (*
             (/ -176.6150291621406 (- 4.0 z))
             (-
              (/ -176.6150291621406 (- 4.0 z))
              (+
               (+
                (/ -1259.1392167224028 (- 2.0 z))
                (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
               (/ 771.3234287776531 (- 3.0 z))))))))))
       (*
        (- 7.0 z)
        (*
         (- 6.0 z)
         (*
          (- 5.0 z)
          (+
           (*
            (+
             (+
              (/ -1259.1392167224028 (- 2.0 z))
              (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
             (/ 771.3234287776531 (- 3.0 z)))
            (+
             (+
              (/ -1259.1392167224028 (- 2.0 z))
              (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
             (/ 771.3234287776531 (- 3.0 z))))
           (*
            (/ -176.6150291621406 (- 4.0 z))
            (-
             (/ -176.6150291621406 (- 4.0 z))
             (+
              (+
               (/ -1259.1392167224028 (- 2.0 z))
               (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
              (/ 771.3234287776531 (- 3.0 z))))))))))
      (/ 1.5056327351493116e-07 (- 8.0 z)))
     (exp (+ (- 7.0 z) 0.5)))))))
double code(double z) {
	return ((double) ((((double) M_PI) / ((double) sin(((double) (((double) M_PI) * z))))) * ((double) (((double) (((double) (((double) sqrt(((double) (((double) M_PI) * 2.0)))) * ((double) pow(((double) (((double) (((double) (((double) (1.0 - z)) - 1.0)) + 7.0)) + 0.5)), ((double) (((double) (((double) (1.0 - z)) - 1.0)) + 0.5)))))) * ((double) exp(((double) -(((double) (((double) (((double) (((double) (1.0 - z)) - 1.0)) + 7.0)) + 0.5)))))))) * ((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (0.9999999999998099 + (676.5203681218851 / ((double) (((double) (((double) (1.0 - z)) - 1.0)) + 1.0))))) + (-1259.1392167224028 / ((double) (((double) (((double) (1.0 - z)) - 1.0)) + 2.0))))) + (771.3234287776531 / ((double) (((double) (((double) (1.0 - z)) - 1.0)) + 3.0))))) + (-176.6150291621406 / ((double) (((double) (((double) (1.0 - z)) - 1.0)) + 4.0))))) + (12.507343278686905 / ((double) (((double) (((double) (1.0 - z)) - 1.0)) + 5.0))))) + (-0.13857109526572012 / ((double) (((double) (((double) (1.0 - z)) - 1.0)) + 6.0))))) + (9.984369578019572e-06 / ((double) (((double) (((double) (1.0 - z)) - 1.0)) + 7.0))))) + (1.5056327351493116e-07 / ((double) (((double) (((double) (1.0 - z)) - 1.0)) + 8.0)))))))));
}
↓
double code(double z) {
	return ((double) ((((double) M_PI) / ((double) sin(((double) (((double) M_PI) * z))))) * ((double) (((double) sqrt(((double) (((double) M_PI) * 2.0)))) * ((double) (((double) pow(((double) (((double) (7.0 - z)) + 0.5)), ((double) (0.5 - z)))) * (((double) ((((double) (((double) (((double) (7.0 - z)) * ((double) (((double) (((double) (6.0 - z)) * ((double) (((double) (((double) (5.0 - z)) * ((double) (((double) pow(((double) (((double) ((-1259.1392167224028 / ((double) (2.0 - z))) + ((double) (0.9999999999998099 + (676.5203681218851 / ((double) (1.0 - z))))))) + (771.3234287776531 / ((double) (3.0 - z))))), 3.0)) + ((double) pow((-176.6150291621406 / ((double) (4.0 - z))), 3.0)))))) + ((double) (12.507343278686905 * ((double) (((double) (((double) (((double) ((-1259.1392167224028 / ((double) (2.0 - z))) + ((double) (0.9999999999998099 + (676.5203681218851 / ((double) (1.0 - z))))))) + (771.3234287776531 / ((double) (3.0 - z))))) * ((double) (((double) ((-1259.1392167224028 / ((double) (2.0 - z))) + ((double) (0.9999999999998099 + (676.5203681218851 / ((double) (1.0 - z))))))) + (771.3234287776531 / ((double) (3.0 - z))))))) + ((double) ((-176.6150291621406 / ((double) (4.0 - z))) * ((double) ((-176.6150291621406 / ((double) (4.0 - z))) - ((double) (((double) ((-1259.1392167224028 / ((double) (2.0 - z))) + ((double) (0.9999999999998099 + (676.5203681218851 / ((double) (1.0 - z))))))) + (771.3234287776531 / ((double) (3.0 - z))))))))))))))))) + ((double) (-0.13857109526572012 * ((double) (((double) (5.0 - z)) * ((double) (((double) (((double) (((double) ((-1259.1392167224028 / ((double) (2.0 - z))) + ((double) (0.9999999999998099 + (676.5203681218851 / ((double) (1.0 - z))))))) + (771.3234287776531 / ((double) (3.0 - z))))) * ((double) (((double) ((-1259.1392167224028 / ((double) (2.0 - z))) + ((double) (0.9999999999998099 + (676.5203681218851 / ((double) (1.0 - z))))))) + (771.3234287776531 / ((double) (3.0 - z))))))) + ((double) ((-176.6150291621406 / ((double) (4.0 - z))) * ((double) ((-176.6150291621406 / ((double) (4.0 - z))) - ((double) (((double) ((-1259.1392167224028 / ((double) (2.0 - z))) + ((double) (0.9999999999998099 + (676.5203681218851 / ((double) (1.0 - z))))))) + (771.3234287776531 / ((double) (3.0 - z))))))))))))))))))) + ((double) (9.984369578019572e-06 * ((double) (((double) (6.0 - z)) * ((double) (((double) (5.0 - z)) * ((double) (((double) (((double) (((double) ((-1259.1392167224028 / ((double) (2.0 - z))) + ((double) (0.9999999999998099 + (676.5203681218851 / ((double) (1.0 - z))))))) + (771.3234287776531 / ((double) (3.0 - z))))) * ((double) (((double) ((-1259.1392167224028 / ((double) (2.0 - z))) + ((double) (0.9999999999998099 + (676.5203681218851 / ((double) (1.0 - z))))))) + (771.3234287776531 / ((double) (3.0 - z))))))) + ((double) ((-176.6150291621406 / ((double) (4.0 - z))) * ((double) ((-176.6150291621406 / ((double) (4.0 - z))) - ((double) (((double) ((-1259.1392167224028 / ((double) (2.0 - z))) + ((double) (0.9999999999998099 + (676.5203681218851 / ((double) (1.0 - z))))))) + (771.3234287776531 / ((double) (3.0 - z))))))))))))))))))) / ((double) (((double) (7.0 - z)) * ((double) (((double) (6.0 - z)) * ((double) (((double) (5.0 - z)) * ((double) (((double) (((double) (((double) ((-1259.1392167224028 / ((double) (2.0 - z))) + ((double) (0.9999999999998099 + (676.5203681218851 / ((double) (1.0 - z))))))) + (771.3234287776531 / ((double) (3.0 - z))))) * ((double) (((double) ((-1259.1392167224028 / ((double) (2.0 - z))) + ((double) (0.9999999999998099 + (676.5203681218851 / ((double) (1.0 - z))))))) + (771.3234287776531 / ((double) (3.0 - z))))))) + ((double) ((-176.6150291621406 / ((double) (4.0 - z))) * ((double) ((-176.6150291621406 / ((double) (4.0 - z))) - ((double) (((double) ((-1259.1392167224028 / ((double) (2.0 - z))) + ((double) (0.9999999999998099 + (676.5203681218851 / ((double) (1.0 - z))))))) + (771.3234287776531 / ((double) (3.0 - z)))))))))))))))))) + (1.5056327351493116e-07 / ((double) (8.0 - z))))) / ((double) exp(((double) (((double) (7.0 - z)) + 0.5)))))))))));
}

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

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

  2. Simplified1.8

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

  4. Applied flip3-+_binary641.2

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

  5. Applied frac-add_binary641.2

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

  6. Applied frac-add_binary641.2

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

  7. Applied frac-add_binary640.4

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

  8. Simplified0.4

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

  9. Simplified0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2020210 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  :precision binary64
  :pre (<= z 0.5)
  (* (/ PI (sin (* PI z))) (* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- (- 1.0 z) 1.0) 7.0) 0.5) (+ (- (- 1.0 z) 1.0) 0.5))) (exp (- (+ (+ (- (- 1.0 z) 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- (- 1.0 z) 1.0) 1.0))) (/ -1259.1392167224028 (+ (- (- 1.0 z) 1.0) 2.0))) (/ 771.3234287776531 (+ (- (- 1.0 z) 1.0) 3.0))) (/ -176.6150291621406 (+ (- (- 1.0 z) 1.0) 4.0))) (/ 12.507343278686905 (+ (- (- 1.0 z) 1.0) 5.0))) (/ -0.13857109526572012 (+ (- (- 1.0 z) 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- (- 1.0 z) 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- (- 1.0 z) 1.0) 8.0))))))