Jmat.Real.gamma, branch z less than 0.5

Average Error: 1.7 → 0.5

Time: 1.5min

Precision: binary64

Cost: 50112

\[z \leq 0.5\]

Math

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

↓

\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{\left(z + -1\right) + -6.5} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} - \left(-0.9999999999998099 + \left(\frac{-1259.1392167224028}{z + -2} + \left(\frac{-771.3234287776531}{3 - z} + \frac{676.5203681218851}{z + -1}\right)\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{1 - \left(z + -6\right)} - \frac{-1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) + 7}\right)\right)\right)\right) \]

FPCore

(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
 (*
  (/ PI (sin (* PI z)))
  (*
   (* (sqrt (* PI 2.0)) (pow (+ (- 1.0 z) 6.5) (+ (- 1.0 z) -0.5)))
   (*
    (exp (+ (+ z -1.0) -6.5))
    (+
     (+
      (-
       (/ -0.13857109526572012 (+ (- 1.0 z) 5.0))
       (+
        -0.9999999999998099
        (+
         (/ -1259.1392167224028 (+ z -2.0))
         (+
          (/ -771.3234287776531 (- 3.0 z))
          (/ 676.5203681218851 (+ z -1.0))))))
      (+
       (/ -176.6150291621406 (+ (- 1.0 z) 3.0))
       (/ 12.507343278686905 (+ (- 1.0 z) 4.0))))
     (-
      (/ 9.984369578019572e-6 (- 1.0 (+ z -6.0)))
      (/ -1.5056327351493116e-7 (+ (- 1.0 z) 7.0))))))))

C

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) {
	return (((double) M_PI) / sin((((double) M_PI) * z))) * ((sqrt((((double) M_PI) * 2.0)) * pow(((1.0 - z) + 6.5), ((1.0 - z) + -0.5))) * (exp(((z + -1.0) + -6.5)) * ((((-0.13857109526572012 / ((1.0 - z) + 5.0)) - (-0.9999999999998099 + ((-1259.1392167224028 / (z + -2.0)) + ((-771.3234287776531 / (3.0 - z)) + (676.5203681218851 / (z + -1.0)))))) + ((-176.6150291621406 / ((1.0 - z) + 3.0)) + (12.507343278686905 / ((1.0 - z) + 4.0)))) + ((9.984369578019572e-6 / (1.0 - (z + -6.0))) - (-1.5056327351493116e-7 / ((1.0 - z) + 7.0))))));
}

Java

public static double code(double z) {
	return (Math.PI / Math.sin((Math.PI * z))) * (((Math.sqrt((Math.PI * 2.0)) * Math.pow(((((1.0 - z) - 1.0) + 7.0) + 0.5), (((1.0 - z) - 1.0) + 0.5))) * Math.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))));
}

↓

public static double code(double z) {
	return (Math.PI / Math.sin((Math.PI * z))) * ((Math.sqrt((Math.PI * 2.0)) * Math.pow(((1.0 - z) + 6.5), ((1.0 - z) + -0.5))) * (Math.exp(((z + -1.0) + -6.5)) * ((((-0.13857109526572012 / ((1.0 - z) + 5.0)) - (-0.9999999999998099 + ((-1259.1392167224028 / (z + -2.0)) + ((-771.3234287776531 / (3.0 - z)) + (676.5203681218851 / (z + -1.0)))))) + ((-176.6150291621406 / ((1.0 - z) + 3.0)) + (12.507343278686905 / ((1.0 - z) + 4.0)))) + ((9.984369578019572e-6 / (1.0 - (z + -6.0))) - (-1.5056327351493116e-7 / ((1.0 - z) + 7.0))))));
}

Python

def code(z):
	return (math.pi / math.sin((math.pi * z))) * (((math.sqrt((math.pi * 2.0)) * math.pow(((((1.0 - z) - 1.0) + 7.0) + 0.5), (((1.0 - z) - 1.0) + 0.5))) * math.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))))

↓

def code(z):
	return (math.pi / math.sin((math.pi * z))) * ((math.sqrt((math.pi * 2.0)) * math.pow(((1.0 - z) + 6.5), ((1.0 - z) + -0.5))) * (math.exp(((z + -1.0) + -6.5)) * ((((-0.13857109526572012 / ((1.0 - z) + 5.0)) - (-0.9999999999998099 + ((-1259.1392167224028 / (z + -2.0)) + ((-771.3234287776531 / (3.0 - z)) + (676.5203681218851 / (z + -1.0)))))) + ((-176.6150291621406 / ((1.0 - z) + 3.0)) + (12.507343278686905 / ((1.0 - z) + 4.0)))) + ((9.984369578019572e-6 / (1.0 - (z + -6.0))) - (-1.5056327351493116e-7 / ((1.0 - z) + 7.0))))))

Julia

function code(z)
	return Float64(Float64(pi / sin(Float64(pi * z))) * Float64(Float64(Float64(sqrt(Float64(pi * 2.0)) * (Float64(Float64(Float64(Float64(1.0 - z) - 1.0) + 7.0) + 0.5) ^ Float64(Float64(Float64(1.0 - z) - 1.0) + 0.5))) * exp(Float64(-Float64(Float64(Float64(Float64(1.0 - z) - 1.0) + 7.0) + 0.5)))) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(0.9999999999998099 + Float64(676.5203681218851 / Float64(Float64(Float64(1.0 - z) - 1.0) + 1.0))) + Float64(-1259.1392167224028 / Float64(Float64(Float64(1.0 - z) - 1.0) + 2.0))) + Float64(771.3234287776531 / Float64(Float64(Float64(1.0 - z) - 1.0) + 3.0))) + Float64(-176.6150291621406 / Float64(Float64(Float64(1.0 - z) - 1.0) + 4.0))) + Float64(12.507343278686905 / Float64(Float64(Float64(1.0 - z) - 1.0) + 5.0))) + Float64(-0.13857109526572012 / Float64(Float64(Float64(1.0 - z) - 1.0) + 6.0))) + Float64(9.984369578019572e-6 / Float64(Float64(Float64(1.0 - z) - 1.0) + 7.0))) + Float64(1.5056327351493116e-7 / Float64(Float64(Float64(1.0 - z) - 1.0) + 8.0)))))
end

↓

function code(z)
	return Float64(Float64(pi / sin(Float64(pi * z))) * Float64(Float64(sqrt(Float64(pi * 2.0)) * (Float64(Float64(1.0 - z) + 6.5) ^ Float64(Float64(1.0 - z) + -0.5))) * Float64(exp(Float64(Float64(z + -1.0) + -6.5)) * Float64(Float64(Float64(Float64(-0.13857109526572012 / Float64(Float64(1.0 - z) + 5.0)) - Float64(-0.9999999999998099 + Float64(Float64(-1259.1392167224028 / Float64(z + -2.0)) + Float64(Float64(-771.3234287776531 / Float64(3.0 - z)) + Float64(676.5203681218851 / Float64(z + -1.0)))))) + Float64(Float64(-176.6150291621406 / Float64(Float64(1.0 - z) + 3.0)) + Float64(12.507343278686905 / Float64(Float64(1.0 - z) + 4.0)))) + Float64(Float64(9.984369578019572e-6 / Float64(1.0 - Float64(z + -6.0))) - Float64(-1.5056327351493116e-7 / Float64(Float64(1.0 - z) + 7.0)))))))
end

MATLAB

function tmp = code(z)
	tmp = (pi / sin((pi * z))) * (((sqrt((pi * 2.0)) * (((((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))));
end

↓

function tmp = code(z)
	tmp = (pi / sin((pi * z))) * ((sqrt((pi * 2.0)) * (((1.0 - z) + 6.5) ^ ((1.0 - z) + -0.5))) * (exp(((z + -1.0) + -6.5)) * ((((-0.13857109526572012 / ((1.0 - z) + 5.0)) - (-0.9999999999998099 + ((-1259.1392167224028 / (z + -2.0)) + ((-771.3234287776531 / (3.0 - z)) + (676.5203681218851 / (z + -1.0)))))) + ((-176.6150291621406 / ((1.0 - z) + 3.0)) + (12.507343278686905 / ((1.0 - z) + 4.0)))) + ((9.984369578019572e-6 / (1.0 - (z + -6.0))) - (-1.5056327351493116e-7 / ((1.0 - z) + 7.0))))));
end

Wolfram

code[z_] := N[(N[(Pi / N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[Sqrt[N[(Pi * 2.0), $MachinePrecision]], $MachinePrecision] * N[Power[N[(N[(N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision] + 7.0), $MachinePrecision] + 0.5), $MachinePrecision], N[(N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision] + 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Exp[(-N[(N[(N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision] + 7.0), $MachinePrecision] + 0.5), $MachinePrecision])], $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(0.9999999999998099 + N[(676.5203681218851 / N[(N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1259.1392167224028 / N[(N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(771.3234287776531 / N[(N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision] + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-176.6150291621406 / N[(N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision] + 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(12.507343278686905 / N[(N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision] + 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.13857109526572012 / N[(N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision] + 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(9.984369578019572e-6 / N[(N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision] + 7.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision] + 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[z_] := N[(N[(Pi / N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(N[Sqrt[N[(Pi * 2.0), $MachinePrecision]], $MachinePrecision] * N[Power[N[(N[(1.0 - z), $MachinePrecision] + 6.5), $MachinePrecision], N[(N[(1.0 - z), $MachinePrecision] + -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[Exp[N[(N[(z + -1.0), $MachinePrecision] + -6.5), $MachinePrecision]], $MachinePrecision] * N[(N[(N[(N[(-0.13857109526572012 / N[(N[(1.0 - z), $MachinePrecision] + 5.0), $MachinePrecision]), $MachinePrecision] - N[(-0.9999999999998099 + N[(N[(-1259.1392167224028 / N[(z + -2.0), $MachinePrecision]), $MachinePrecision] + N[(N[(-771.3234287776531 / N[(3.0 - z), $MachinePrecision]), $MachinePrecision] + N[(676.5203681218851 / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-176.6150291621406 / N[(N[(1.0 - z), $MachinePrecision] + 3.0), $MachinePrecision]), $MachinePrecision] + N[(12.507343278686905 / N[(N[(1.0 - z), $MachinePrecision] + 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(9.984369578019572e-6 / N[(1.0 - N[(z + -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-1.5056327351493116e-7 / N[(N[(1.0 - z), $MachinePrecision] + 7.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

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. Simplified 1.4

   \[\leadsto \color{blue}{\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{1 - \left(z + -6\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) + 7}\right)\right)\right)\right)} \]
   Proof

   [Start] 1.7	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right) \]
   associate-*l* [=>] 1.7	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \color{blue}{\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot \left(e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)} \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)} \]
   associate-+l+ [=>] 1.7	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\color{blue}{\left(\left(\left(1 - z\right) - 1\right) + \left(7 + 0.5\right)\right)}}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot \left(e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)} \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right) \]
   associate-+l- [=>] 1.7	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\color{blue}{\left(\left(1 - z\right) - \left(1 - \left(7 + 0.5\right)\right)\right)}}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot \left(e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)} \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right) \]
   sub-neg [=>] 1.7	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\color{blue}{\left(\left(1 - z\right) + \left(-\left(1 - \left(7 + 0.5\right)\right)\right)\right)}}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot \left(e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)} \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right) \]
   metadata-eval [=>] 1.7	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + \left(-\left(1 - \color{blue}{7.5}\right)\right)\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot \left(e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)} \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right) \]
   metadata-eval [=>] 1.7	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + \left(-\color{blue}{-6.5}\right)\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot \left(e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)} \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right) \]
   metadata-eval [=>] 1.7	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + \color{blue}{6.5}\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot \left(e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)} \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right) \]
   associate-+l- [=>] 1.7	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\color{blue}{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}\right) \cdot \left(e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)} \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right) \]
   metadata-eval [=>] 1.7	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) - \color{blue}{0.5}\right)}\right) \cdot \left(e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)} \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right) \]
   sub-neg [=>] 1.7	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\color{blue}{\left(\left(1 - z\right) + \left(-0.5\right)\right)}}\right) \cdot \left(e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)} \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right) \]
   metadata-eval [=>] 1.7	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + \color{blue}{-0.5}\right)}\right) \cdot \left(e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)} \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right) \]
   associate-+l+ [=>] 1.7	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\color{blue}{\left(\left(\left(1 - z\right) - 1\right) + \left(7 + 0.5\right)\right)}} \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right) \]
   associate-+l- [=>] 1.7	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\color{blue}{\left(\left(1 - z\right) - \left(1 - \left(7 + 0.5\right)\right)\right)}} \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right) \]
   sub-neg [=>] 1.7	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\color{blue}{\left(\left(1 - z\right) + \left(-\left(1 - \left(7 + 0.5\right)\right)\right)\right)}} \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right) \]
   metadata-eval [=>] 1.7	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + \left(-\left(1 - \color{blue}{7.5}\right)\right)\right)} \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right) \]
   metadata-eval [=>] 1.7	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + \left(-\color{blue}{-6.5}\right)\right)} \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right) \]
   metadata-eval [=>] 1.7	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + \color{blue}{6.5}\right)} \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right) \]
   associate-+l+ [=>] 1.0	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \color{blue}{\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)}\right)\right) \]
   +-commutative [=>] 1.0	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\color{blue}{\left(\frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6} + \left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right)} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   associate-+l+ [=>] 0.5	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6} + \color{blue}{\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right)}\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   associate-+r+ [=>] 0.5	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\color{blue}{\left(\left(\frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6} + \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right)\right) + \left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right)} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   associate-+l- [=>] 0.5	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\color{blue}{\left(1 - z\right) - \left(1 - 6\right)}} + \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right)\right) + \left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   sub-neg [=>] 0.5	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\color{blue}{\left(1 - z\right) + \left(-\left(1 - 6\right)\right)}} + \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right)\right) + \left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   metadata-eval [=>] 0.5	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + \left(-\color{blue}{-5}\right)} + \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right)\right) + \left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   metadata-eval [=>] 0.5	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + \color{blue}{5}} + \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right)\right) + \left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   associate-+l+ [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(\color{blue}{\left(0.9999999999998099 + \left(\frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1} + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right)\right)} + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right)\right) + \left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   associate-+l+ [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \color{blue}{\left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1} + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right)\right)}\right) + \left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   associate-+l- [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{\color{blue}{\left(1 - z\right) - \left(1 - 1\right)}} + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   metadata-eval [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{\left(1 - z\right) - \color{blue}{0}} + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   --rgt-identity [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{\color{blue}{1 - z}} + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   associate-+l- [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\color{blue}{\left(1 - z\right) - \left(1 - 2\right)}}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   sub-neg [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\color{blue}{\left(1 - z\right) + \left(-\left(1 - 2\right)\right)}}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   metadata-eval [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + \left(-\color{blue}{-1}\right)}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   metadata-eval [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + \color{blue}{1}}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   associate-+l- [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\color{blue}{\left(1 - z\right) - \left(1 - 3\right)}}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   sub-neg [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\color{blue}{\left(1 - z\right) + \left(-\left(1 - 3\right)\right)}}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   metadata-eval [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + \left(-\color{blue}{-2}\right)}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   metadata-eval [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + \color{blue}{2}}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   associate-+l- [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right)\right) + \left(\frac{-176.6150291621406}{\color{blue}{\left(1 - z\right) - \left(1 - 4\right)}} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   sub-neg [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right)\right) + \left(\frac{-176.6150291621406}{\color{blue}{\left(1 - z\right) + \left(-\left(1 - 4\right)\right)}} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   metadata-eval [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + \left(-\color{blue}{-3}\right)} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   metadata-eval [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + \color{blue}{3}} + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   associate-+l- [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\color{blue}{\left(1 - z\right) - \left(1 - 5\right)}}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   sub-neg [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\color{blue}{\left(1 - z\right) + \left(-\left(1 - 5\right)\right)}}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   metadata-eval [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + \left(-\color{blue}{-4}\right)}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   metadata-eval [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + \color{blue}{4}}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   associate-+l- [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\color{blue}{\left(1 - z\right) - \left(1 - 7\right)}} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   associate--l- [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\color{blue}{1 - \left(z + \left(1 - 7\right)\right)}} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   +-rgt-identity [<=] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{1 - \left(\color{blue}{\left(z + 0\right)} + \left(1 - 7\right)\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   metadata-eval [<=] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{1 - \left(\left(z + \color{blue}{\left(1 - 1\right)}\right) + \left(1 - 7\right)\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   associate--l+ [<=] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{1 - \left(\color{blue}{\left(\left(z + 1\right) - 1\right)} + \left(1 - 7\right)\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   associate--l+ [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{1 - \left(\color{blue}{\left(z + \left(1 - 1\right)\right)} + \left(1 - 7\right)\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   metadata-eval [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{1 - \left(\left(z + \color{blue}{0}\right) + \left(1 - 7\right)\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   +-rgt-identity [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{1 - \left(\color{blue}{z} + \left(1 - 7\right)\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   metadata-eval [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{1 - \left(z + \color{blue}{-6}\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\right)\right) \]
   associate-+l- [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{1 - \left(z + -6\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{\color{blue}{\left(1 - z\right) - \left(1 - 8\right)}}\right)\right)\right)\right) \]
   sub-neg [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{1 - \left(z + -6\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{\color{blue}{\left(1 - z\right) + \left(-\left(1 - 8\right)\right)}}\right)\right)\right)\right) \]
   metadata-eval [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{1 - \left(z + -6\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) + \left(-\color{blue}{-7}\right)}\right)\right)\right)\right) \]
   metadata-eval [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \frac{771.3234287776531}{\left(1 - z\right) + 2}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{1 - \left(z + -6\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) + \color{blue}{7}}\right)\right)\right)\right) \]

3. Applied egg-rr 1.8

   \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{-676.5203681218851}{z + -1} + \frac{1259.1392167224028}{z + -2}\right)} - \left(1 - \frac{771.3234287776531}{3 - z}\right)\right)}\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{1 - \left(z + -6\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) + 7}\right)\right)\right)\right) \]

4. Simplified 0.5

   \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \color{blue}{\left(\frac{1259.1392167224028}{z + -2} + \left(\frac{-676.5203681218851}{z + -1} + \frac{771.3234287776531}{3 - z}\right)\right)}\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{1 - \left(z + -6\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) + 7}\right)\right)\right)\right) \]
   Proof

   [Start] 1.8	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(e^{\mathsf{log1p}\left(\frac{-676.5203681218851}{z + -1} + \frac{1259.1392167224028}{z + -2}\right)} - \left(1 - \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{1 - \left(z + -6\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) + 7}\right)\right)\right)\right) \]
   associate--r- [=>] 1.8	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \color{blue}{\left(\left(e^{\mathsf{log1p}\left(\frac{-676.5203681218851}{z + -1} + \frac{1259.1392167224028}{z + -2}\right)} - 1\right) + \frac{771.3234287776531}{3 - z}\right)}\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{1 - \left(z + -6\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) + 7}\right)\right)\right)\right) \]
   expm1-def [=>] 1.8	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{-676.5203681218851}{z + -1} + \frac{1259.1392167224028}{z + -2}\right)\right)} + \frac{771.3234287776531}{3 - z}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{1 - \left(z + -6\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) + 7}\right)\right)\right)\right) \]
   expm1-log1p [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\color{blue}{\left(\frac{-676.5203681218851}{z + -1} + \frac{1259.1392167224028}{z + -2}\right)} + \frac{771.3234287776531}{3 - z}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{1 - \left(z + -6\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) + 7}\right)\right)\right)\right) \]
   +-commutative [=>] 1.4	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \left(\color{blue}{\left(\frac{1259.1392167224028}{z + -2} + \frac{-676.5203681218851}{z + -1}\right)} + \frac{771.3234287776531}{3 - z}\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{1 - \left(z + -6\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) + 7}\right)\right)\right)\right) \]
   associate-+l+ [=>] 0.5	\[ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{-\left(\left(1 - z\right) + 6.5\right)} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(0.9999999999998099 + \color{blue}{\left(\frac{1259.1392167224028}{z + -2} + \left(\frac{-676.5203681218851}{z + -1} + \frac{771.3234287776531}{3 - z}\right)\right)}\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{1 - \left(z + -6\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) + 7}\right)\right)\right)\right) \]

5. Final simplification 0.5

   \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{\left(z + -1\right) + -6.5} \cdot \left(\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} - \left(-0.9999999999998099 + \left(\frac{-1259.1392167224028}{z + -2} + \left(\frac{-771.3234287776531}{3 - z} + \frac{676.5203681218851}{z + -1}\right)\right)\right)\right) + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{1 - \left(z + -6\right)} - \frac{-1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) + 7}\right)\right)\right)\right) \]

Alternatives

Alternative 1
Error	0.5
Cost	49856

\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot \left(e^{z + -7.5} \cdot \left(\left(0.9999999999998099 + \left(\frac{771.3234287776531}{3 - z} - \frac{\left(\frac{z}{-1259.1392167224028} + 0.0015883867116823602\right) + \left(\frac{z}{676.5203681218851} + -0.00147815209581367\right)}{\left(-0.0015883867116823602 - \frac{z}{-1259.1392167224028}\right) \cdot \left(0.00147815209581367 - \frac{z}{676.5203681218851}\right)}\right)\right) + \left(\left(\frac{12.507343278686905}{5 - z} + \left(\frac{-176.6150291621406}{4 - z} + \frac{-0.13857109526572012}{6 - z}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right)\right)\right) \]

Alternative 2
Error	0.5
Cost	49472

\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot \left(e^{z + -7.5} \cdot \left(\left(\left(\frac{12.507343278686905}{5 - z} + \left(\frac{-176.6150291621406}{4 - z} + \frac{-0.13857109526572012}{6 - z}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right) - \left(-0.9999999999998099 + \left(\frac{-771.3234287776531}{3 - z} + \frac{0.00011023461586869015 + z \cdot 0.0006839587399724899}{\left(-0.0015883867116823602 - \frac{z}{-1259.1392167224028}\right) \cdot \left(0.00147815209581367 - \frac{z}{676.5203681218851}\right)}\right)\right)\right)\right)\right) \]

Alternative 3
Error	0.5
Cost	49472

\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{\left(z + -1\right) + -6.5} \cdot \left(\frac{-0.13857109526572012}{6 - z} + \left(\left(\frac{-676.5203681218851}{z + -1} - \left(-0.9999999999998099 + \left(\frac{-771.3234287776531}{3 - z} - \frac{1259.1392167224028}{z + -2}\right)\right)\right) + \left(\left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right) + \left(\frac{12.507343278686905}{5 - z} + \frac{-176.6150291621406}{4 - z}\right)\right)\right)\right)\right)\right) \]

Alternative 4
Error	0.5
Cost	49152

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

Alternative 5
Error	0.5
Cost	49088

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

Alternative 6
Error	0.5
Cost	49088

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

Alternative 7
Error	1.1
Cost	47680

\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot \left({\left(7.5 - z\right)}^{\left(0.5 - z\right)} \cdot e^{z + -7.5}\right)\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right) + \left(263.4062807184368 - z \cdot \left(z \cdot -545.0359493463282 + -436.9000215473151\right)\right)\right)\right) \]

Alternative 8
Error	1.4
Cost	47424

\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot \left({\left(7.5 - z\right)}^{\left(0.5 - z\right)} \cdot e^{z + -7.5}\right)\right) \cdot \left(\left(\frac{-0.13857109526572012}{6 - z} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right) + \left(263.4062807184368 - z \cdot -436.9000215473151\right)\right)\right) \]

Alternative 9
Error	1.3
Cost	33856

\[\frac{1}{z} \cdot \left(\left({\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)} \cdot \left(\sqrt{\pi} \cdot \sqrt{2}\right)\right) \cdot \left(e^{-6.5 - \left(1 - z\right)} \cdot \left(263.3831869810514 + z \cdot 436.8961725563396\right)\right)\right) \]

Alternative 10
Error	1.3
Cost	33792

\[\frac{1}{z} \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(\left(263.3831869810514 + z \cdot 436.8961725563396\right) \cdot {\left(e^{-1}\right)}^{\left(7.5 - z\right)}\right)\right) \]

Alternative 11
Error	1.9
Cost	27328

\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) + 6.5\right)}^{\left(\left(1 - z\right) + -0.5\right)}\right) \cdot \left(e^{z + -7.5} \cdot \left(z \cdot -436.8961725563396 + -263.3831869810514\right)\right)\right) \cdot \frac{-1}{z} \]

Alternative 12
Error	2.5
Cost	26368

\[\frac{1}{z} \cdot \left(263.3831869810514 \cdot \left(\sqrt{\pi \cdot 2} \cdot \left(e^{-7.5} \cdot \sqrt{7.5}\right)\right)\right) \]

Reproduce

herbie shell --seed 2022356 
(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))))))