Jmat.Real.gamma, branch z greater than 0.5

Average Error: 4.0 → 2.3

Time: 42.6s

Precision: binary64

Cost: 31236

\[z > 0.5\]

Math

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

↓

\[\begin{array}{l} t_0 := \frac{-1259.1392167224028}{z + 1}\\ \mathbf{if}\;z - 1 \leq 140:\\ \;\;\;\;\left(\left(\left(\left(t_0 + \frac{771.3234287776531}{2 + z}\right) + \left(0.9999999999998099 + \frac{338.26018406094255}{z}\right)\right) - \left(\frac{176.6150291621406}{z + 3} - \frac{338.26018406094255}{z}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \frac{-0.13857109526572012}{z + 5}\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right) \cdot \frac{\sqrt{\pi \cdot 2} \cdot {\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z + 6.5}}\\ \mathbf{else}:\\ \;\;\;\;\left(e^{-6.5 - \left(z + \log \left(z - -6.5\right) \cdot \left(0.5 - z\right)\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left(\left(\left(\left(\left(\frac{771.3234287776531}{-2 - z} + \left(\left(\frac{-676.5203681218851}{z} + -0.9999999999998099\right) + \left(2 \cdot \left(\left(0.9999999999998099 - \frac{-676.5203681218851}{z}\right) + \frac{771.3234287776531}{z + 2}\right) - \left(\frac{-176.6150291621406}{-3 - z} - t_0\right)\right)\right)\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\\ \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (*
  (*
   (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
   (exp (- (+ (+ (- z 1.0) 7.0) 0.5))))
  (+
   (+
    (+
     (+
      (+
       (+
        (+
         (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- z 1.0) 1.0)))
         (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))
        (/ 771.3234287776531 (+ (- z 1.0) 3.0)))
       (/ -176.6150291621406 (+ (- z 1.0) 4.0)))
      (/ 12.507343278686905 (+ (- z 1.0) 5.0)))
     (/ -0.13857109526572012 (+ (- z 1.0) 6.0)))
    (/ 9.984369578019572e-6 (+ (- z 1.0) 7.0)))
   (/ 1.5056327351493116e-7 (+ (- z 1.0) 8.0)))))

↓

(FPCore (z)
 :precision binary64
 (let* ((t_0 (/ -1259.1392167224028 (+ z 1.0))))
   (if (<= (- z 1.0) 140.0)
     (*
      (+
       (-
        (+
         (+ t_0 (/ 771.3234287776531 (+ 2.0 z)))
         (+ 0.9999999999998099 (/ 338.26018406094255 z)))
        (- (/ 176.6150291621406 (+ z 3.0)) (/ 338.26018406094255 z)))
       (+
        (+ (/ 12.507343278686905 (+ z 4.0)) (/ -0.13857109526572012 (+ z 5.0)))
        (+
         (/ 9.984369578019572e-6 (+ z 6.0))
         (/ 1.5056327351493116e-7 (+ z 7.0)))))
      (/ (* (sqrt (* PI 2.0)) (pow (+ z 6.5) (+ z -0.5))) (exp (+ z 6.5))))
     (*
      (* (exp (- -6.5 (+ z (* (log (- z -6.5)) (- 0.5 z))))) (sqrt (* 2.0 PI)))
      (+
       (+
        (+
         (+
          (+
           (/ 771.3234287776531 (- -2.0 z))
           (+
            (+ (/ -676.5203681218851 z) -0.9999999999998099)
            (-
             (*
              2.0
              (+
               (- 0.9999999999998099 (/ -676.5203681218851 z))
               (/ 771.3234287776531 (+ z 2.0))))
             (- (/ -176.6150291621406 (- -3.0 z)) t_0))))
          (/ 12.507343278686905 (+ (- z 1.0) 5.0)))
         (/ -0.13857109526572012 (+ (- z 1.0) 6.0)))
        (/ 9.984369578019572e-6 (+ (- z 1.0) 7.0)))
       (/ 1.5056327351493116e-7 (+ (- z 1.0) 8.0)))))))

C

double code(double z) {
	return ((sqrt((((double) M_PI) * 2.0)) * pow((((z - 1.0) + 7.0) + 0.5), ((z - 1.0) + 0.5))) * exp(-(((z - 1.0) + 7.0) + 0.5))) * ((((((((0.9999999999998099 + (676.5203681218851 / ((z - 1.0) + 1.0))) + (-1259.1392167224028 / ((z - 1.0) + 2.0))) + (771.3234287776531 / ((z - 1.0) + 3.0))) + (-176.6150291621406 / ((z - 1.0) + 4.0))) + (12.507343278686905 / ((z - 1.0) + 5.0))) + (-0.13857109526572012 / ((z - 1.0) + 6.0))) + (9.984369578019572e-6 / ((z - 1.0) + 7.0))) + (1.5056327351493116e-7 / ((z - 1.0) + 8.0)));
}

↓

double code(double z) {
	double t_0 = -1259.1392167224028 / (z + 1.0);
	double tmp;
	if ((z - 1.0) <= 140.0) {
		tmp = ((((t_0 + (771.3234287776531 / (2.0 + z))) + (0.9999999999998099 + (338.26018406094255 / z))) - ((176.6150291621406 / (z + 3.0)) - (338.26018406094255 / z))) + (((12.507343278686905 / (z + 4.0)) + (-0.13857109526572012 / (z + 5.0))) + ((9.984369578019572e-6 / (z + 6.0)) + (1.5056327351493116e-7 / (z + 7.0))))) * ((sqrt((((double) M_PI) * 2.0)) * pow((z + 6.5), (z + -0.5))) / exp((z + 6.5)));
	} else {
		tmp = (exp((-6.5 - (z + (log((z - -6.5)) * (0.5 - z))))) * sqrt((2.0 * ((double) M_PI)))) * ((((((771.3234287776531 / (-2.0 - z)) + (((-676.5203681218851 / z) + -0.9999999999998099) + ((2.0 * ((0.9999999999998099 - (-676.5203681218851 / z)) + (771.3234287776531 / (z + 2.0)))) - ((-176.6150291621406 / (-3.0 - z)) - t_0)))) + (12.507343278686905 / ((z - 1.0) + 5.0))) + (-0.13857109526572012 / ((z - 1.0) + 6.0))) + (9.984369578019572e-6 / ((z - 1.0) + 7.0))) + (1.5056327351493116e-7 / ((z - 1.0) + 8.0)));
	}
	return tmp;
}

Java

public static double code(double z) {
	return ((Math.sqrt((Math.PI * 2.0)) * Math.pow((((z - 1.0) + 7.0) + 0.5), ((z - 1.0) + 0.5))) * Math.exp(-(((z - 1.0) + 7.0) + 0.5))) * ((((((((0.9999999999998099 + (676.5203681218851 / ((z - 1.0) + 1.0))) + (-1259.1392167224028 / ((z - 1.0) + 2.0))) + (771.3234287776531 / ((z - 1.0) + 3.0))) + (-176.6150291621406 / ((z - 1.0) + 4.0))) + (12.507343278686905 / ((z - 1.0) + 5.0))) + (-0.13857109526572012 / ((z - 1.0) + 6.0))) + (9.984369578019572e-6 / ((z - 1.0) + 7.0))) + (1.5056327351493116e-7 / ((z - 1.0) + 8.0)));
}

↓

public static double code(double z) {
	double t_0 = -1259.1392167224028 / (z + 1.0);
	double tmp;
	if ((z - 1.0) <= 140.0) {
		tmp = ((((t_0 + (771.3234287776531 / (2.0 + z))) + (0.9999999999998099 + (338.26018406094255 / z))) - ((176.6150291621406 / (z + 3.0)) - (338.26018406094255 / z))) + (((12.507343278686905 / (z + 4.0)) + (-0.13857109526572012 / (z + 5.0))) + ((9.984369578019572e-6 / (z + 6.0)) + (1.5056327351493116e-7 / (z + 7.0))))) * ((Math.sqrt((Math.PI * 2.0)) * Math.pow((z + 6.5), (z + -0.5))) / Math.exp((z + 6.5)));
	} else {
		tmp = (Math.exp((-6.5 - (z + (Math.log((z - -6.5)) * (0.5 - z))))) * Math.sqrt((2.0 * Math.PI))) * ((((((771.3234287776531 / (-2.0 - z)) + (((-676.5203681218851 / z) + -0.9999999999998099) + ((2.0 * ((0.9999999999998099 - (-676.5203681218851 / z)) + (771.3234287776531 / (z + 2.0)))) - ((-176.6150291621406 / (-3.0 - z)) - t_0)))) + (12.507343278686905 / ((z - 1.0) + 5.0))) + (-0.13857109526572012 / ((z - 1.0) + 6.0))) + (9.984369578019572e-6 / ((z - 1.0) + 7.0))) + (1.5056327351493116e-7 / ((z - 1.0) + 8.0)));
	}
	return tmp;
}

Python

def code(z):
	return ((math.sqrt((math.pi * 2.0)) * math.pow((((z - 1.0) + 7.0) + 0.5), ((z - 1.0) + 0.5))) * math.exp(-(((z - 1.0) + 7.0) + 0.5))) * ((((((((0.9999999999998099 + (676.5203681218851 / ((z - 1.0) + 1.0))) + (-1259.1392167224028 / ((z - 1.0) + 2.0))) + (771.3234287776531 / ((z - 1.0) + 3.0))) + (-176.6150291621406 / ((z - 1.0) + 4.0))) + (12.507343278686905 / ((z - 1.0) + 5.0))) + (-0.13857109526572012 / ((z - 1.0) + 6.0))) + (9.984369578019572e-6 / ((z - 1.0) + 7.0))) + (1.5056327351493116e-7 / ((z - 1.0) + 8.0)))

↓

def code(z):
	t_0 = -1259.1392167224028 / (z + 1.0)
	tmp = 0
	if (z - 1.0) <= 140.0:
		tmp = ((((t_0 + (771.3234287776531 / (2.0 + z))) + (0.9999999999998099 + (338.26018406094255 / z))) - ((176.6150291621406 / (z + 3.0)) - (338.26018406094255 / z))) + (((12.507343278686905 / (z + 4.0)) + (-0.13857109526572012 / (z + 5.0))) + ((9.984369578019572e-6 / (z + 6.0)) + (1.5056327351493116e-7 / (z + 7.0))))) * ((math.sqrt((math.pi * 2.0)) * math.pow((z + 6.5), (z + -0.5))) / math.exp((z + 6.5)))
	else:
		tmp = (math.exp((-6.5 - (z + (math.log((z - -6.5)) * (0.5 - z))))) * math.sqrt((2.0 * math.pi))) * ((((((771.3234287776531 / (-2.0 - z)) + (((-676.5203681218851 / z) + -0.9999999999998099) + ((2.0 * ((0.9999999999998099 - (-676.5203681218851 / z)) + (771.3234287776531 / (z + 2.0)))) - ((-176.6150291621406 / (-3.0 - z)) - t_0)))) + (12.507343278686905 / ((z - 1.0) + 5.0))) + (-0.13857109526572012 / ((z - 1.0) + 6.0))) + (9.984369578019572e-6 / ((z - 1.0) + 7.0))) + (1.5056327351493116e-7 / ((z - 1.0) + 8.0)))
	return tmp

Julia

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

↓

function code(z)
	t_0 = Float64(-1259.1392167224028 / Float64(z + 1.0))
	tmp = 0.0
	if (Float64(z - 1.0) <= 140.0)
		tmp = Float64(Float64(Float64(Float64(Float64(t_0 + Float64(771.3234287776531 / Float64(2.0 + z))) + Float64(0.9999999999998099 + Float64(338.26018406094255 / z))) - Float64(Float64(176.6150291621406 / Float64(z + 3.0)) - Float64(338.26018406094255 / z))) + Float64(Float64(Float64(12.507343278686905 / Float64(z + 4.0)) + Float64(-0.13857109526572012 / Float64(z + 5.0))) + Float64(Float64(9.984369578019572e-6 / Float64(z + 6.0)) + Float64(1.5056327351493116e-7 / Float64(z + 7.0))))) * Float64(Float64(sqrt(Float64(pi * 2.0)) * (Float64(z + 6.5) ^ Float64(z + -0.5))) / exp(Float64(z + 6.5))));
	else
		tmp = Float64(Float64(exp(Float64(-6.5 - Float64(z + Float64(log(Float64(z - -6.5)) * Float64(0.5 - z))))) * sqrt(Float64(2.0 * pi))) * Float64(Float64(Float64(Float64(Float64(Float64(771.3234287776531 / Float64(-2.0 - z)) + Float64(Float64(Float64(-676.5203681218851 / z) + -0.9999999999998099) + Float64(Float64(2.0 * Float64(Float64(0.9999999999998099 - Float64(-676.5203681218851 / z)) + Float64(771.3234287776531 / Float64(z + 2.0)))) - Float64(Float64(-176.6150291621406 / Float64(-3.0 - z)) - t_0)))) + Float64(12.507343278686905 / Float64(Float64(z - 1.0) + 5.0))) + Float64(-0.13857109526572012 / Float64(Float64(z - 1.0) + 6.0))) + Float64(9.984369578019572e-6 / Float64(Float64(z - 1.0) + 7.0))) + Float64(1.5056327351493116e-7 / Float64(Float64(z - 1.0) + 8.0))));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(z)
	t_0 = -1259.1392167224028 / (z + 1.0);
	tmp = 0.0;
	if ((z - 1.0) <= 140.0)
		tmp = ((((t_0 + (771.3234287776531 / (2.0 + z))) + (0.9999999999998099 + (338.26018406094255 / z))) - ((176.6150291621406 / (z + 3.0)) - (338.26018406094255 / z))) + (((12.507343278686905 / (z + 4.0)) + (-0.13857109526572012 / (z + 5.0))) + ((9.984369578019572e-6 / (z + 6.0)) + (1.5056327351493116e-7 / (z + 7.0))))) * ((sqrt((pi * 2.0)) * ((z + 6.5) ^ (z + -0.5))) / exp((z + 6.5)));
	else
		tmp = (exp((-6.5 - (z + (log((z - -6.5)) * (0.5 - z))))) * sqrt((2.0 * pi))) * ((((((771.3234287776531 / (-2.0 - z)) + (((-676.5203681218851 / z) + -0.9999999999998099) + ((2.0 * ((0.9999999999998099 - (-676.5203681218851 / z)) + (771.3234287776531 / (z + 2.0)))) - ((-176.6150291621406 / (-3.0 - z)) - t_0)))) + (12.507343278686905 / ((z - 1.0) + 5.0))) + (-0.13857109526572012 / ((z - 1.0) + 6.0))) + (9.984369578019572e-6 / ((z - 1.0) + 7.0))) + (1.5056327351493116e-7 / ((z - 1.0) + 8.0)));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[z_] := Block[{t$95$0 = N[(-1259.1392167224028 / N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z - 1.0), $MachinePrecision], 140.0], N[(N[(N[(N[(N[(t$95$0 + N[(771.3234287776531 / N[(2.0 + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.9999999999998099 + N[(338.26018406094255 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(176.6150291621406 / N[(z + 3.0), $MachinePrecision]), $MachinePrecision] - N[(338.26018406094255 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(12.507343278686905 / N[(z + 4.0), $MachinePrecision]), $MachinePrecision] + N[(-0.13857109526572012 / N[(z + 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(9.984369578019572e-6 / N[(z + 6.0), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(z + 7.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[Sqrt[N[(Pi * 2.0), $MachinePrecision]], $MachinePrecision] * N[Power[N[(z + 6.5), $MachinePrecision], N[(z + -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[Exp[N[(z + 6.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Exp[N[(-6.5 - N[(z + N[(N[Log[N[(z - -6.5), $MachinePrecision]], $MachinePrecision] * N[(0.5 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(2.0 * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(N[(N[(771.3234287776531 / N[(-2.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(-676.5203681218851 / z), $MachinePrecision] + -0.9999999999998099), $MachinePrecision] + N[(N[(2.0 * N[(N[(0.9999999999998099 - N[(-676.5203681218851 / z), $MachinePrecision]), $MachinePrecision] + N[(771.3234287776531 / N[(z + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(-176.6150291621406 / N[(-3.0 - z), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(12.507343278686905 / N[(N[(z - 1.0), $MachinePrecision] + 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.13857109526572012 / N[(N[(z - 1.0), $MachinePrecision] + 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(9.984369578019572e-6 / N[(N[(z - 1.0), $MachinePrecision] + 7.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(N[(z - 1.0), $MachinePrecision] + 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z 1) < 140

   1. Initial program 2.2

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

   2. Simplified 2.4

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

      [Start] 2.2	\[ \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \]
      rational_best-simplify-1 [=>] 2.2	\[ \color{blue}{\left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right)} \]
      exponential-simplify-2 [=>] 2.2	\[ \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot \color{blue}{\frac{1}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}}}\right) \]
      rational_best-simplify-55 [=>] 2.2	\[ \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \cdot \color{blue}{\left(1 \cdot \frac{\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}}{e^{\left(\left(z - 1\right) + 7\right) + 0.5}}\right)} \]

   3. Applied egg-rr 2.2

      \[\leadsto \left(\color{blue}{\left(\left(\frac{338.26018406094255}{z} + \left(0.9999999999998099 + \left(\frac{-1259.1392167224028}{z + 1} + \frac{771.3234287776531}{2 + z}\right)\right)\right) - \left(\frac{176.6150291621406}{z + 3} - \frac{338.26018406094255}{z}\right)\right)} + \left(\left(\frac{12.507343278686905}{z + 4} + \frac{-0.13857109526572012}{z + 5}\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right) \cdot \frac{\sqrt{\pi \cdot 2} \cdot {\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z + 6.5}} \]

   4. Simplified 2.2

      \[\leadsto \left(\color{blue}{\left(\left(\left(\frac{-1259.1392167224028}{z + 1} + \frac{771.3234287776531}{2 + z}\right) + \left(0.9999999999998099 + \frac{338.26018406094255}{z}\right)\right) - \left(\frac{176.6150291621406}{z + 3} - \frac{338.26018406094255}{z}\right)\right)} + \left(\left(\frac{12.507343278686905}{z + 4} + \frac{-0.13857109526572012}{z + 5}\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right) \cdot \frac{\sqrt{\pi \cdot 2} \cdot {\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z + 6.5}} \]
      Proof

      [Start] 2.2

      \[ \left(\left(\left(\frac{338.26018406094255}{z} + \left(0.9999999999998099 + \left(\frac{-1259.1392167224028}{z + 1} + \frac{771.3234287776531}{2 + z}\right)\right)\right) - \left(\frac{176.6150291621406}{z + 3} - \frac{338.26018406094255}{z}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \frac{-0.13857109526572012}{z + 5}\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right) \cdot \frac{\sqrt{\pi \cdot 2} \cdot {\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z + 6.5}} \]

      rational_best-simplify-47 [=>] 2.2

      \[ \left(\left(\color{blue}{\left(\left(\frac{-1259.1392167224028}{z + 1} + \frac{771.3234287776531}{2 + z}\right) + \left(0.9999999999998099 + \frac{338.26018406094255}{z}\right)\right)} - \left(\frac{176.6150291621406}{z + 3} - \frac{338.26018406094255}{z}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \frac{-0.13857109526572012}{z + 5}\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right) \cdot \frac{\sqrt{\pi \cdot 2} \cdot {\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z + 6.5}} \]

   if 140 < (-.f64 z 1)

   1. Initial program 60.2

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

   2. Taylor expanded in z around -inf 60.5

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

   3. Simplified 7.8

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

      [Start] 60.5	\[ \left(\left(\sqrt{2} \cdot \left(e^{-1 \cdot \left(\log \left(6.5 - -1 \cdot z\right) \cdot \left(-1 \cdot z + 0.5\right)\right)} \cdot e^{-1 \cdot z - 6.5}\right)\right) \cdot \sqrt{\pi}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \]
      rational_best-simplify-1 [=>] 60.5	\[ \color{blue}{\left(\sqrt{\pi} \cdot \left(\sqrt{2} \cdot \left(e^{-1 \cdot \left(\log \left(6.5 - -1 \cdot z\right) \cdot \left(-1 \cdot z + 0.5\right)\right)} \cdot e^{-1 \cdot z - 6.5}\right)\right)\right)} \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \]
      rational_best-simplify-50 [=>] 60.5	\[ \color{blue}{\left(\left(e^{-1 \cdot \left(\log \left(6.5 - -1 \cdot z\right) \cdot \left(-1 \cdot z + 0.5\right)\right)} \cdot e^{-1 \cdot z - 6.5}\right) \cdot \left(\sqrt{2} \cdot \sqrt{\pi}\right)\right)} \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \]

   4. Applied egg-rr 7.8

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

   5. Applied egg-rr 7.8

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

   6. Simplified 7.8

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

      [Start] 7.8	\[ \left(e^{-6.5 - \left(z + \log \left(z - -6.5\right) \cdot \left(0.5 - z\right)\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 - \frac{-676.5203681218851}{z}\right) + \frac{771.3234287776531}{z + 2}\right) \cdot 2 - \left(\frac{-176.6150291621406}{-3 - z} - \frac{-1259.1392167224028}{z + 1}\right)\right) + \left(\left(-0.9999999999998099 + \frac{-676.5203681218851}{z}\right) + \frac{771.3234287776531}{-2 - z}\right)\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \]
      rational_best-simplify-47 [=>] 7.8	\[ \left(e^{-6.5 - \left(z + \log \left(z - -6.5\right) \cdot \left(0.5 - z\right)\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left(\left(\left(\left(\color{blue}{\left(\frac{771.3234287776531}{-2 - z} + \left(\left(-0.9999999999998099 + \frac{-676.5203681218851}{z}\right) + \left(\left(\left(0.9999999999998099 - \frac{-676.5203681218851}{z}\right) + \frac{771.3234287776531}{z + 2}\right) \cdot 2 - \left(\frac{-176.6150291621406}{-3 - z} - \frac{-1259.1392167224028}{z + 1}\right)\right)\right)\right)} + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \]
      rational_best-simplify-3 [=>] 7.8	\[ \left(e^{-6.5 - \left(z + \log \left(z - -6.5\right) \cdot \left(0.5 - z\right)\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left(\left(\left(\left(\left(\frac{771.3234287776531}{-2 - z} + \left(\color{blue}{\left(\frac{-676.5203681218851}{z} + -0.9999999999998099\right)} + \left(\left(\left(0.9999999999998099 - \frac{-676.5203681218851}{z}\right) + \frac{771.3234287776531}{z + 2}\right) \cdot 2 - \left(\frac{-176.6150291621406}{-3 - z} - \frac{-1259.1392167224028}{z + 1}\right)\right)\right)\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \]
      rational_best-simplify-1 [=>] 7.8	\[ \left(e^{-6.5 - \left(z + \log \left(z - -6.5\right) \cdot \left(0.5 - z\right)\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left(\left(\left(\left(\left(\frac{771.3234287776531}{-2 - z} + \left(\left(\frac{-676.5203681218851}{z} + -0.9999999999998099\right) + \left(\color{blue}{2 \cdot \left(\left(0.9999999999998099 - \frac{-676.5203681218851}{z}\right) + \frac{771.3234287776531}{z + 2}\right)} - \left(\frac{-176.6150291621406}{-3 - z} - \frac{-1259.1392167224028}{z + 1}\right)\right)\right)\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \]

3. Recombined 2 regimes into one program.

4. Final simplification 2.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - 1 \leq 140:\\ \;\;\;\;\left(\left(\left(\left(\frac{-1259.1392167224028}{z + 1} + \frac{771.3234287776531}{2 + z}\right) + \left(0.9999999999998099 + \frac{338.26018406094255}{z}\right)\right) - \left(\frac{176.6150291621406}{z + 3} - \frac{338.26018406094255}{z}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \frac{-0.13857109526572012}{z + 5}\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right) \cdot \frac{\sqrt{\pi \cdot 2} \cdot {\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z + 6.5}}\\ \mathbf{else}:\\ \;\;\;\;\left(e^{-6.5 - \left(z + \log \left(z - -6.5\right) \cdot \left(0.5 - z\right)\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left(\left(\left(\left(\left(\frac{771.3234287776531}{-2 - z} + \left(\left(\frac{-676.5203681218851}{z} + -0.9999999999998099\right) + \left(2 \cdot \left(\left(0.9999999999998099 - \frac{-676.5203681218851}{z}\right) + \frac{771.3234287776531}{z + 2}\right) - \left(\frac{-176.6150291621406}{-3 - z} - \frac{-1259.1392167224028}{z + 1}\right)\right)\right)\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	2.4
Cost	44224

\[\begin{array}{l} t_0 := {\left(6.5 + z\right)}^{\left(\frac{z}{2} + -0.25\right)}\\ \left(\frac{t_0 \cdot \left(t_0 \cdot e^{-z}\right)}{e^{6.5}} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \end{array} \]

Alternative 2
Error	2.5
Cost	30596

\[\begin{array}{l} t_0 := \frac{-88.3075145810703}{z + 3}\\ \mathbf{if}\;z \leq 145:\\ \;\;\;\;\left(\left(\left(\left(\frac{-1259.1392167224028}{z + 1} + \frac{771.3234287776531}{2 + z}\right) + \left(0.9999999999998099 + \frac{338.26018406094255}{z}\right)\right) - \left(\frac{176.6150291621406}{z + 3} - \frac{338.26018406094255}{z}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \frac{-0.13857109526572012}{z + 5}\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right) \cdot \frac{\sqrt{\pi \cdot 2} \cdot {\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z + 6.5}}\\ \mathbf{else}:\\ \;\;\;\;\left(e^{-6.5 - \left(z + \log \left(z - -6.5\right) \cdot \left(0.5 - z\right)\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left(\left(\left(\left(\left(t_0 - \left(\frac{-1259.1392167224028}{-1 - z} - \left(\frac{771.3234287776531}{z + 2} + \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 + t_0\right)\right)\right)\right)\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\\ \end{array} \]

Alternative 3
Error	2.5
Cost	30212

\[\begin{array}{l} t_0 := \frac{-1259.1392167224028}{z + 1}\\ \mathbf{if}\;z \leq 145:\\ \;\;\;\;\left(\left(\left(\left(t_0 + \frac{771.3234287776531}{2 + z}\right) + \left(0.9999999999998099 + \frac{338.26018406094255}{z}\right)\right) - \left(\frac{176.6150291621406}{z + 3} - \frac{338.26018406094255}{z}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \frac{-0.13857109526572012}{z + 5}\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right) \cdot \frac{\sqrt{\pi \cdot 2} \cdot {\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z + 6.5}}\\ \mathbf{else}:\\ \;\;\;\;\left(e^{-6.5 - \left(z + \log \left(z - -6.5\right) \cdot \left(0.5 - z\right)\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left(\left(\left(\left(\left(t_0 + \left(0.9999999999998099 + \left(\frac{-176.6150291621406}{z + 3} + \left(\frac{676.5203681218851}{z} + \frac{771.3234287776531}{z + 2}\right)\right)\right)\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\\ \end{array} \]

Alternative 4
Error	2.5
Cost	30212

\[\begin{array}{l} t_0 := \frac{-1259.1392167224028}{z + 1}\\ \mathbf{if}\;z \leq 145:\\ \;\;\;\;\left(\left(\left(\left(t_0 + \frac{771.3234287776531}{2 + z}\right) + \left(0.9999999999998099 + \frac{338.26018406094255}{z}\right)\right) - \left(\frac{176.6150291621406}{z + 3} - \frac{338.26018406094255}{z}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \frac{-0.13857109526572012}{z + 5}\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right) \cdot \frac{\sqrt{\pi \cdot 2} \cdot {\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z + 6.5}}\\ \mathbf{else}:\\ \;\;\;\;\left(e^{-6.5 - \left(z + \log \left(z - -6.5\right) \cdot \left(0.5 - z\right)\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left(\left(\left(\left(\left(t_0 + \left(\frac{676.5203681218851}{z} + \left(\frac{771.3234287776531}{z + 2} + \left(0.9999999999998099 + \frac{-176.6150291621406}{z + 3}\right)\right)\right)\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\\ \end{array} \]

Alternative 5
Error	2.5
Cost	30212

\[\begin{array}{l} \mathbf{if}\;z \leq 145:\\ \;\;\;\;\left(\left(\left(\left(\frac{-1259.1392167224028}{z + 1} + \frac{771.3234287776531}{2 + z}\right) + \left(0.9999999999998099 + \frac{338.26018406094255}{z}\right)\right) - \left(\frac{176.6150291621406}{z + 3} - \frac{338.26018406094255}{z}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \frac{-0.13857109526572012}{z + 5}\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right) \cdot \frac{\sqrt{\pi \cdot 2} \cdot {\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z + 6.5}}\\ \mathbf{else}:\\ \;\;\;\;\left(e^{-6.5 - \left(z + \log \left(z - -6.5\right) \cdot \left(0.5 - z\right)\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left(\left(\left(\left(\left(\left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 + \frac{771.3234287776531}{z + 2}\right)\right) - \left(\frac{-176.6150291621406}{-3 - z} + \frac{-1259.1392167224028}{-1 - z}\right)\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right)\\ \end{array} \]

Alternative 6
Error	2.5
Cost	29892

\[\begin{array}{l} t_0 := \sqrt{\pi \cdot 2}\\ t_1 := \frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\\ t_2 := \frac{-1259.1392167224028}{z + 1}\\ t_3 := \frac{12.507343278686905}{z + 4} + \frac{-0.13857109526572012}{z + 5}\\ t_4 := \frac{771.3234287776531}{2 + z}\\ \mathbf{if}\;z \leq 145:\\ \;\;\;\;\left(\left(\left(\left(t_2 + t_4\right) + \left(0.9999999999998099 + \frac{338.26018406094255}{z}\right)\right) - \left(\frac{176.6150291621406}{z + 3} - \frac{338.26018406094255}{z}\right)\right) + \left(t_3 + t_1\right)\right) \cdot \frac{t_0 \cdot {\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z + 6.5}}\\ \mathbf{else}:\\ \;\;\;\;\left(t_0 \cdot e^{-6.5 - \left(z + \log \left(z - -6.5\right) \cdot \left(0.5 - z\right)\right)}\right) \cdot \left(\left(\left(\left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 + t_2\right)\right) + \left(t_4 + \frac{-176.6150291621406}{z + 3}\right)\right) + t_3\right) + t_1\right)\\ \end{array} \]

Alternative 7
Error	2.5
Cost	29764

\[\begin{array}{l} t_0 := \frac{-1259.1392167224028}{z + 1}\\ t_1 := \frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\\ t_2 := \frac{12.507343278686905}{z + 4} + \frac{-0.13857109526572012}{z + 5}\\ t_3 := \sqrt{\pi \cdot 2}\\ \mathbf{if}\;z \leq 145:\\ \;\;\;\;\left(\left(\left(\frac{176.6150291621406}{-3 - z} + \left(0.49999999999990496 + \left(\left(\frac{676.5203681218851}{z} + t_0\right) - \frac{-771.3234287776531}{z - -2}\right)\right)\right) + 0.49999999999990496\right) + \left(t_2 + t_1\right)\right) \cdot \left(t_3 \cdot \frac{{\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z + 6.5}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t_3 \cdot e^{-6.5 - \left(z + \log \left(z - -6.5\right) \cdot \left(0.5 - z\right)\right)}\right) \cdot \left(\left(\left(\left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 + t_0\right)\right) + \left(\frac{771.3234287776531}{2 + z} + \frac{-176.6150291621406}{z + 3}\right)\right) + t_2\right) + t_1\right)\\ \end{array} \]

Alternative 8
Error	2.5
Cost	29700

\[\begin{array}{l} t_0 := \frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\\ t_1 := \frac{12.507343278686905}{z + 4} + \frac{-0.13857109526572012}{z + 5}\\ t_2 := \sqrt{\pi \cdot 2}\\ \mathbf{if}\;z \leq 145:\\ \;\;\;\;\left(\left(\left(\frac{676.5203681218851}{z} - \left(\frac{771.3234287776531}{-2 - z} + \frac{-1259.1392167224028}{-1 - z}\right)\right) - \left(-0.9999999999998099 + \frac{-176.6150291621406}{-3 - z}\right)\right) + \left(t_1 + t_0\right)\right) \cdot \left(t_2 \cdot \frac{{\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z + 6.5}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t_2 \cdot e^{-6.5 - \left(z + \log \left(z - -6.5\right) \cdot \left(0.5 - z\right)\right)}\right) \cdot \left(\left(\left(\left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 + \frac{-1259.1392167224028}{z + 1}\right)\right) + \left(\frac{771.3234287776531}{2 + z} + \frac{-176.6150291621406}{z + 3}\right)\right) + t_1\right) + t_0\right)\\ \end{array} \]

Alternative 9
Error	4.1
Cost	29504

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

Alternative 10
Error	4.1
Cost	29504

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

Alternative 11
Error	4.0
Cost	29504

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

Alternative 12
Error	4.0
Cost	29504

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

Alternative 13
Error	4.0
Cost	29504

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

Alternative 14
Error	4.0
Cost	29504

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

Alternative 15
Error	3.9
Cost	29504

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

Alternative 16
Error	3.9
Cost	29504

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

Alternative 17
Error	3.9
Cost	29504

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

Alternative 18
Error	49.4
Cost	29440

\[\left(e^{-6.5 - \left(z + \log \left(z - -6.5\right) \cdot \left(0.5 - z\right)\right)} \cdot \sqrt{2 \cdot \pi}\right) \cdot \left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{188.7045801771354}{z}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \]

Alternative 19
Error	49.9
Cost	28736

\[\left(\left(\frac{-176.6150291621406}{z + 3} - \left(-0.9999999999998099 - \frac{188.7045801771354}{z}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \frac{-0.13857109526572012}{z + 5}\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right) \cdot \frac{\sqrt{\pi \cdot 2} \cdot {\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z + 6.5}} \]

Alternative 20
Error	51.7
Cost	28352

\[\left(\left(0.9999999999998099 + \frac{12.0895510149948}{z}\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \frac{-0.13857109526572012}{z + 5}\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right) \cdot \left(\sqrt{\pi \cdot 2} \cdot \frac{{\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z + 6.5}}\right) \]

Alternative 21
Error	52.9
Cost	28096

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

Alternative 22
Error	55.9
Cost	27968

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

Alternative 23
Error	57.3
Cost	19584

\[4.099123286189028 \cdot \frac{\sqrt{\pi \cdot 0.3076923076923077}}{e^{6.5}} \]

Reproduce

herbie shell --seed 2023100 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z greater than 0.5"
  :precision binary64
  :pre (> z 0.5)
  (* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- z 1.0) 1.0))) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-6 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-7 (+ (- z 1.0) 8.0)))))