Average Error: 1.7 → 0.5
Time: 2.1min
Precision: binary64
\[z \leq 0.5\]
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right) \]
↓
\[\begin{array}{l} t_0 := 0.9999999999998099 + \frac{676.5203681218851}{1 - z}\\ t_1 := \left(1 - z\right) + 6\\ t_2 := 2 + \left(1 - z\right)\\ t_3 := \left(\left(1 - z\right) + -1\right) + 7.5\\ t_4 := \left(1 - z\right) + 3\\ t_5 := \left(1 - z\right) + 5\\ t_6 := 1 + \left(1 - z\right)\\ t_7 := \frac{-1259.1392167224028}{t_6}\\ t_8 := t_0 - t_7\\ t_9 := t_4 \cdot \left(t_8 \cdot t_2\right)\\ t_10 := \left(1 - z\right) + 4\\ t_11 := t_10 \cdot t_9\\ t_12 := t_5 \cdot t_11\\ t_13 := t_1 \cdot t_12\\ t_14 := \left(1 - z\right) + 7\\ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{\left(\sqrt{\pi \cdot 2} \cdot {t_3}^{\left(1 - z\right)}\right) \cdot \mathsf{fma}\left(1.5056327351493116 \cdot 10^{-7}, t_13, t_14 \cdot \mathsf{fma}\left(t_1, \mathsf{fma}\left(-0.13857109526572012, t_11, t_5 \cdot \mathsf{fma}\left(12.507343278686905, t_9, t_10 \cdot \mathsf{fma}\left(t_8, t_2 \cdot -176.6150291621406, t_4 \cdot \mathsf{fma}\left(\mathsf{fma}\left(t_0, t_0, t_7 \cdot \frac{1259.1392167224028}{t_6}\right), t_2, t_8 \cdot 771.3234287776531\right)\right)\right)\right), t_12 \cdot 9.984369578019572 \cdot 10^{-6}\right)\right)}{\left(\sqrt{t_3} \cdot e^{t_3}\right) \cdot \left(t_13 \cdot t_14\right)} \end{array} \]
\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^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
↓
\begin{array}{l}
t_0 := 0.9999999999998099 + \frac{676.5203681218851}{1 - z}\\
t_1 := \left(1 - z\right) + 6\\
t_2 := 2 + \left(1 - z\right)\\
t_3 := \left(\left(1 - z\right) + -1\right) + 7.5\\
t_4 := \left(1 - z\right) + 3\\
t_5 := \left(1 - z\right) + 5\\
t_6 := 1 + \left(1 - z\right)\\
t_7 := \frac{-1259.1392167224028}{t_6}\\
t_8 := t_0 - t_7\\
t_9 := t_4 \cdot \left(t_8 \cdot t_2\right)\\
t_10 := \left(1 - z\right) + 4\\
t_11 := t_10 \cdot t_9\\
t_12 := t_5 \cdot t_11\\
t_13 := t_1 \cdot t_12\\
t_14 := \left(1 - z\right) + 7\\
\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{\left(\sqrt{\pi \cdot 2} \cdot {t_3}^{\left(1 - z\right)}\right) \cdot \mathsf{fma}\left(1.5056327351493116 \cdot 10^{-7}, t_13, t_14 \cdot \mathsf{fma}\left(t_1, \mathsf{fma}\left(-0.13857109526572012, t_11, t_5 \cdot \mathsf{fma}\left(12.507343278686905, t_9, t_10 \cdot \mathsf{fma}\left(t_8, t_2 \cdot -176.6150291621406, t_4 \cdot \mathsf{fma}\left(\mathsf{fma}\left(t_0, t_0, t_7 \cdot \frac{1259.1392167224028}{t_6}\right), t_2, t_8 \cdot 771.3234287776531\right)\right)\right)\right), t_12 \cdot 9.984369578019572 \cdot 10^{-6}\right)\right)}{\left(\sqrt{t_3} \cdot e^{t_3}\right) \cdot \left(t_13 \cdot t_14\right)}
\end{array}

(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-6 (+ (- (- 1.0 z) 1.0) 7.0)))
    (/ 1.5056327351493116e-7 (+ (- (- 1.0 z) 1.0) 8.0))))))
↓
(FPCore (z)
 :precision binary64
 (let* ((t_0 (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
        (t_1 (+ (- 1.0 z) 6.0))
        (t_2 (+ 2.0 (- 1.0 z)))
        (t_3 (+ (+ (- 1.0 z) -1.0) 7.5))
        (t_4 (+ (- 1.0 z) 3.0))
        (t_5 (+ (- 1.0 z) 5.0))
        (t_6 (+ 1.0 (- 1.0 z)))
        (t_7 (/ -1259.1392167224028 t_6))
        (t_8 (- t_0 t_7))
        (t_9 (* t_4 (* t_8 t_2)))
        (t_10 (+ (- 1.0 z) 4.0))
        (t_11 (* t_10 t_9))
        (t_12 (* t_5 t_11))
        (t_13 (* t_1 t_12))
        (t_14 (+ (- 1.0 z) 7.0)))
   (*
    (/ PI (sin (* PI z)))
    (/
     (*
      (* (sqrt (* PI 2.0)) (pow t_3 (- 1.0 z)))
      (fma
       1.5056327351493116e-7
       t_13
       (*
        t_14
        (fma
         t_1
         (fma
          -0.13857109526572012
          t_11
          (*
           t_5
           (fma
            12.507343278686905
            t_9
            (*
             t_10
             (fma
              t_8
              (* t_2 -176.6150291621406)
              (*
               t_4
               (fma
                (fma t_0 t_0 (* t_7 (/ 1259.1392167224028 t_6)))
                t_2
                (* t_8 771.3234287776531))))))))
         (* t_12 9.984369578019572e-6)))))
     (* (* (sqrt t_3) (exp t_3)) (* t_13 t_14))))))
double code(double z) {
	return (((double) M_PI) / sin(((double) M_PI) * z)) * (((sqrt(((double) M_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-6 / (((1.0 - z) - 1.0) + 7.0))) + (1.5056327351493116e-7 / (((1.0 - z) - 1.0) + 8.0))));
}
↓
double code(double z) {
	double t_0 = 0.9999999999998099 + (676.5203681218851 / (1.0 - z));
	double t_1 = (1.0 - z) + 6.0;
	double t_2 = 2.0 + (1.0 - z);
	double t_3 = ((1.0 - z) + -1.0) + 7.5;
	double t_4 = (1.0 - z) + 3.0;
	double t_5 = (1.0 - z) + 5.0;
	double t_6 = 1.0 + (1.0 - z);
	double t_7 = -1259.1392167224028 / t_6;
	double t_8 = t_0 - t_7;
	double t_9 = t_4 * (t_8 * t_2);
	double t_10 = (1.0 - z) + 4.0;
	double t_11 = t_10 * t_9;
	double t_12 = t_5 * t_11;
	double t_13 = t_1 * t_12;
	double t_14 = (1.0 - z) + 7.0;
	return (((double) M_PI) / sin(((double) M_PI) * z)) * (((sqrt(((double) M_PI) * 2.0) * pow(t_3, (1.0 - z))) * fma(1.5056327351493116e-7, t_13, (t_14 * fma(t_1, fma(-0.13857109526572012, t_11, (t_5 * fma(12.507343278686905, t_9, (t_10 * fma(t_8, (t_2 * -176.6150291621406), (t_4 * fma(fma(t_0, t_0, (t_7 * (1259.1392167224028 / t_6))), t_2, (t_8 * 771.3234287776531)))))))), (t_12 * 9.984369578019572e-6))))) / ((sqrt(t_3) * exp(t_3)) * (t_13 * t_14)));
}

Error

Bits error versus z

Derivation

  1. Initial program 1.7

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

  2. Applied flip-+_binary641.0

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

  3. Applied frac-add_binary641.7

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

  4. Applied frac-add_binary641.7

    \[\leadsto \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(\color{blue}{\frac{\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) \cdot \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} \cdot \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right) + \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) \cdot 771.3234287776531\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot -176.6150291621406}{\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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\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^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right) \]

  5. Applied frac-add_binary641.0

    \[\leadsto \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(\color{blue}{\frac{\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) \cdot \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} \cdot \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right) + \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) \cdot 771.3234287776531\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot -176.6150291621406\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot 12.507343278686905}{\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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\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^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right) \]

  6. Applied frac-add_binary641.0

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

  7. Applied frac-add_binary641.0

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

  8. Applied frac-add_binary641.0

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

  9. Applied neg-sub0_binary641.0

    \[\leadsto \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^{\color{blue}{0 - \left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}}\right) \cdot \frac{\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) \cdot \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} \cdot \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right) + \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) \cdot 771.3234287776531\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot -176.6150291621406\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot 12.507343278686905\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot -0.13857109526572012\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 7\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right)\right) \cdot 9.984369578019572 \cdot 10^{-6}\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 8\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 7\right)\right) \cdot 1.5056327351493116 \cdot 10^{-7}}{\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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 7\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 8\right)}\right) \]

  10. Applied exp-diff_binary641.0

    \[\leadsto \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 \color{blue}{\frac{e^{0}}{e^{\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5}}}\right) \cdot \frac{\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) \cdot \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} \cdot \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right) + \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) \cdot 771.3234287776531\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot -176.6150291621406\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot 12.507343278686905\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot -0.13857109526572012\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 7\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right)\right) \cdot 9.984369578019572 \cdot 10^{-6}\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 8\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 7\right)\right) \cdot 1.5056327351493116 \cdot 10^{-7}}{\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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 7\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 8\right)}\right) \]

  11. Applied associate-+l-_binary641.0

    \[\leadsto \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)}^{\color{blue}{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}\right) \cdot \frac{e^{0}}{e^{\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5}}\right) \cdot \frac{\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) \cdot \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} \cdot \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right) + \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) \cdot 771.3234287776531\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot -176.6150291621406\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot 12.507343278686905\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot -0.13857109526572012\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 7\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right)\right) \cdot 9.984369578019572 \cdot 10^{-6}\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 8\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 7\right)\right) \cdot 1.5056327351493116 \cdot 10^{-7}}{\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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 7\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 8\right)}\right) \]

  12. Applied pow-sub_binary641.0

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot \color{blue}{\frac{{\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(1 - z\right)}}{{\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(1 - 0.5\right)}}}\right) \cdot \frac{e^{0}}{e^{\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5}}\right) \cdot \frac{\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) \cdot \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} \cdot \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right) + \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) \cdot 771.3234287776531\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot -176.6150291621406\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot 12.507343278686905\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot -0.13857109526572012\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 7\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right)\right) \cdot 9.984369578019572 \cdot 10^{-6}\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 8\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 7\right)\right) \cdot 1.5056327351493116 \cdot 10^{-7}}{\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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 7\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 8\right)}\right) \]

  13. Applied associate-*r/_binary641.0

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\color{blue}{\frac{\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(1 - z\right)}}{{\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(1 - 0.5\right)}}} \cdot \frac{e^{0}}{e^{\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5}}\right) \cdot \frac{\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) \cdot \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} \cdot \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right) + \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) \cdot 771.3234287776531\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot -176.6150291621406\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot 12.507343278686905\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot -0.13857109526572012\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 7\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right)\right) \cdot 9.984369578019572 \cdot 10^{-6}\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 8\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 7\right)\right) \cdot 1.5056327351493116 \cdot 10^{-7}}{\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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 7\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 8\right)}\right) \]

  14. Applied frac-times_binary641.0

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\frac{\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(1 - z\right)}\right) \cdot e^{0}}{{\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(1 - 0.5\right)} \cdot e^{\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5}}} \cdot \frac{\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) \cdot \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} \cdot \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right) + \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) \cdot 771.3234287776531\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot -176.6150291621406\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot 12.507343278686905\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot -0.13857109526572012\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 7\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right)\right) \cdot 9.984369578019572 \cdot 10^{-6}\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 8\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 7\right)\right) \cdot 1.5056327351493116 \cdot 10^{-7}}{\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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 7\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 8\right)}\right) \]

  15. Applied frac-times_binary640.5

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \color{blue}{\frac{\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(1 - z\right)}\right) \cdot e^{0}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) \cdot \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} \cdot \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right) + \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) \cdot 771.3234287776531\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot -176.6150291621406\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot 12.507343278686905\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot -0.13857109526572012\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 7\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right)\right) \cdot 9.984369578019572 \cdot 10^{-6}\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 8\right) + \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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 7\right)\right) \cdot 1.5056327351493116 \cdot 10^{-7}\right)}{\left({\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(1 - 0.5\right)} \cdot e^{\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5}\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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 7\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 8\right)\right)}} \]

  16. Simplified0.5

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{\color{blue}{\left(\sqrt{2 \cdot \pi} \cdot {\left(\left(\left(1 - z\right) + -1\right) + 7.5\right)}^{\left(1 - z\right)}\right) \cdot \mathsf{fma}\left(1.5056327351493116 \cdot 10^{-7}, \left(\left(1 - z\right) + 6\right) \cdot \left(\left(\left(1 - z\right) + 5\right) \cdot \left(\left(\left(1 - z\right) + 4\right) \cdot \left(\left(\left(1 - z\right) + 3\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) - \frac{-1259.1392167224028}{1 + \left(1 - z\right)}\right) \cdot \left(\left(1 - z\right) + 2\right)\right)\right)\right)\right), \left(\left(1 - z\right) + 7\right) \cdot \mathsf{fma}\left(\left(1 - z\right) + 6, \mathsf{fma}\left(-0.13857109526572012, \left(\left(1 - z\right) + 4\right) \cdot \left(\left(\left(1 - z\right) + 3\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) - \frac{-1259.1392167224028}{1 + \left(1 - z\right)}\right) \cdot \left(\left(1 - z\right) + 2\right)\right)\right), \left(\left(1 - z\right) + 5\right) \cdot \mathsf{fma}\left(12.507343278686905, \left(\left(1 - z\right) + 3\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) - \frac{-1259.1392167224028}{1 + \left(1 - z\right)}\right) \cdot \left(\left(1 - z\right) + 2\right)\right), \left(\left(1 - z\right) + 4\right) \cdot \mathsf{fma}\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) - \frac{-1259.1392167224028}{1 + \left(1 - z\right)}, \left(\left(1 - z\right) + 2\right) \cdot -176.6150291621406, \left(\left(1 - z\right) + 3\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}, 0.9999999999998099 + \frac{676.5203681218851}{1 - z}, \frac{1259.1392167224028}{1 + \left(1 - z\right)} \cdot \frac{-1259.1392167224028}{1 + \left(1 - z\right)}\right), \left(1 - z\right) + 2, \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) - \frac{-1259.1392167224028}{1 + \left(1 - z\right)}\right) \cdot 771.3234287776531\right)\right)\right)\right), 9.984369578019572 \cdot 10^{-6} \cdot \left(\left(\left(1 - z\right) + 5\right) \cdot \left(\left(\left(1 - z\right) + 4\right) \cdot \left(\left(\left(1 - z\right) + 3\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) - \frac{-1259.1392167224028}{1 + \left(1 - z\right)}\right) \cdot \left(\left(1 - z\right) + 2\right)\right)\right)\right)\right)\right)\right)}}{\left({\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(1 - 0.5\right)} \cdot e^{\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5}\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) \cdot \left(\left(\left(1 - z\right) - 1\right) + 3\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 4\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 5\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 6\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 7\right)\right) \cdot \left(\left(\left(1 - z\right) - 1\right) + 8\right)\right)} \]

  17. Simplified0.5

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{\left(\sqrt{2 \cdot \pi} \cdot {\left(\left(\left(1 - z\right) + -1\right) + 7.5\right)}^{\left(1 - z\right)}\right) \cdot \mathsf{fma}\left(1.5056327351493116 \cdot 10^{-7}, \left(\left(1 - z\right) + 6\right) \cdot \left(\left(\left(1 - z\right) + 5\right) \cdot \left(\left(\left(1 - z\right) + 4\right) \cdot \left(\left(\left(1 - z\right) + 3\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) - \frac{-1259.1392167224028}{1 + \left(1 - z\right)}\right) \cdot \left(\left(1 - z\right) + 2\right)\right)\right)\right)\right), \left(\left(1 - z\right) + 7\right) \cdot \mathsf{fma}\left(\left(1 - z\right) + 6, \mathsf{fma}\left(-0.13857109526572012, \left(\left(1 - z\right) + 4\right) \cdot \left(\left(\left(1 - z\right) + 3\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) - \frac{-1259.1392167224028}{1 + \left(1 - z\right)}\right) \cdot \left(\left(1 - z\right) + 2\right)\right)\right), \left(\left(1 - z\right) + 5\right) \cdot \mathsf{fma}\left(12.507343278686905, \left(\left(1 - z\right) + 3\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) - \frac{-1259.1392167224028}{1 + \left(1 - z\right)}\right) \cdot \left(\left(1 - z\right) + 2\right)\right), \left(\left(1 - z\right) + 4\right) \cdot \mathsf{fma}\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) - \frac{-1259.1392167224028}{1 + \left(1 - z\right)}, \left(\left(1 - z\right) + 2\right) \cdot -176.6150291621406, \left(\left(1 - z\right) + 3\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}, 0.9999999999998099 + \frac{676.5203681218851}{1 - z}, \frac{1259.1392167224028}{1 + \left(1 - z\right)} \cdot \frac{-1259.1392167224028}{1 + \left(1 - z\right)}\right), \left(1 - z\right) + 2, \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) - \frac{-1259.1392167224028}{1 + \left(1 - z\right)}\right) \cdot 771.3234287776531\right)\right)\right)\right), 9.984369578019572 \cdot 10^{-6} \cdot \left(\left(\left(1 - z\right) + 5\right) \cdot \left(\left(\left(1 - z\right) + 4\right) \cdot \left(\left(\left(1 - z\right) + 3\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) - \frac{-1259.1392167224028}{1 + \left(1 - z\right)}\right) \cdot \left(\left(1 - z\right) + 2\right)\right)\right)\right)\right)\right)\right)}{\color{blue}{\left(\sqrt{\left(\left(1 - z\right) + -1\right) + 7.5} \cdot e^{\left(\left(1 - z\right) + -1\right) + 7.5}\right) \cdot \left(\left(\left(1 - z\right) + 7\right) \cdot \left(\left(\left(1 - z\right) + 6\right) \cdot \left(\left(\left(1 - z\right) + 5\right) \cdot \left(\left(\left(1 - z\right) + 4\right) \cdot \left(\left(\left(1 - z\right) + 3\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) - \frac{-1259.1392167224028}{1 + \left(1 - z\right)}\right) \cdot \left(\left(1 - z\right) + 2\right)\right)\right)\right)\right)\right)\right)}} \]

  18. Final simplification0.5

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(1 - z\right) + -1\right) + 7.5\right)}^{\left(1 - z\right)}\right) \cdot \mathsf{fma}\left(1.5056327351493116 \cdot 10^{-7}, \left(\left(1 - z\right) + 6\right) \cdot \left(\left(\left(1 - z\right) + 5\right) \cdot \left(\left(\left(1 - z\right) + 4\right) \cdot \left(\left(\left(1 - z\right) + 3\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) - \frac{-1259.1392167224028}{1 + \left(1 - z\right)}\right) \cdot \left(2 + \left(1 - z\right)\right)\right)\right)\right)\right), \left(\left(1 - z\right) + 7\right) \cdot \mathsf{fma}\left(\left(1 - z\right) + 6, \mathsf{fma}\left(-0.13857109526572012, \left(\left(1 - z\right) + 4\right) \cdot \left(\left(\left(1 - z\right) + 3\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) - \frac{-1259.1392167224028}{1 + \left(1 - z\right)}\right) \cdot \left(2 + \left(1 - z\right)\right)\right)\right), \left(\left(1 - z\right) + 5\right) \cdot \mathsf{fma}\left(12.507343278686905, \left(\left(1 - z\right) + 3\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) - \frac{-1259.1392167224028}{1 + \left(1 - z\right)}\right) \cdot \left(2 + \left(1 - z\right)\right)\right), \left(\left(1 - z\right) + 4\right) \cdot \mathsf{fma}\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) - \frac{-1259.1392167224028}{1 + \left(1 - z\right)}, \left(2 + \left(1 - z\right)\right) \cdot -176.6150291621406, \left(\left(1 - z\right) + 3\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}, 0.9999999999998099 + \frac{676.5203681218851}{1 - z}, \frac{-1259.1392167224028}{1 + \left(1 - z\right)} \cdot \frac{1259.1392167224028}{1 + \left(1 - z\right)}\right), 2 + \left(1 - z\right), \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) - \frac{-1259.1392167224028}{1 + \left(1 - z\right)}\right) \cdot 771.3234287776531\right)\right)\right)\right), \left(\left(\left(1 - z\right) + 5\right) \cdot \left(\left(\left(1 - z\right) + 4\right) \cdot \left(\left(\left(1 - z\right) + 3\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) - \frac{-1259.1392167224028}{1 + \left(1 - z\right)}\right) \cdot \left(2 + \left(1 - z\right)\right)\right)\right)\right)\right) \cdot 9.984369578019572 \cdot 10^{-6}\right)\right)}{\left(\sqrt{\left(\left(1 - z\right) + -1\right) + 7.5} \cdot e^{\left(\left(1 - z\right) + -1\right) + 7.5}\right) \cdot \left(\left(\left(\left(1 - z\right) + 6\right) \cdot \left(\left(\left(1 - z\right) + 5\right) \cdot \left(\left(\left(1 - z\right) + 4\right) \cdot \left(\left(\left(1 - z\right) + 3\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) - \frac{-1259.1392167224028}{1 + \left(1 - z\right)}\right) \cdot \left(2 + \left(1 - z\right)\right)\right)\right)\right)\right)\right) \cdot \left(\left(1 - z\right) + 7\right)\right)} \]

Reproduce

herbie shell --seed 2022019 
(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-6 (+ (- (- 1.0 z) 1.0) 7.0))) (/ 1.5056327351493116e-7 (+ (- (- 1.0 z) 1.0) 8.0))))))