Jmat.Real.gamma, branch z greater than 0.5

Average Error: 4.0 → 2.4

Time: 32.7s

Precision: binary64

Cost: 51652

\[z > 0.5\]

Math

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

↓

\[\begin{array}{l} t_0 := \frac{-0.13857109526572012}{\left(z + -1\right) + 6}\\ t_1 := \frac{z}{-1259.1392167224028} + -0.0007941933558411801\\ t_2 := \frac{771.3234287776531}{\left(z + -1\right) + 3}\\ t_3 := \frac{9.984369578019572 \cdot 10^{-6}}{\left(z + -1\right) + 7}\\ t_4 := \frac{-176.6150291621406}{\left(z + -1\right) + 4}\\ t_5 := \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8}\\ t_6 := \frac{12.507343278686905}{\left(z + -1\right) + 5}\\ t_7 := 0.9999999999996197 + \frac{676.5203681218851}{z} \cdot \left(\frac{676.5203681218851}{z} + -0.9999999999998099\right)\\ \mathbf{if}\;z + -1 \leq 142:\\ \;\;\;\;\left(\left(e^{-6.5 - z} \cdot \left(\sqrt{2} \cdot \sqrt{\pi}\right)\right) \cdot {\left(z + 6.5\right)}^{\left(z + -0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z - -1}\right) + 0.9999999999998099\right) + t_2\right) + t_4\right) + t_6\right) + t_0\right) + t_3\right) + t_5\right)\\ \mathbf{else}:\\ \;\;\;\;e^{\mathsf{fma}\left(z + -0.5, \log \left(z + 6.5\right), \mathsf{fma}\left(0.5, \log \left(2 \cdot \pi\right), -6.5 - z\right)\right)} \cdot \left(t_5 + \left(t_3 + \left(t_0 + \left(t_6 + \left(t_4 + \left(t_2 + \frac{t_7 + t_1 \cdot \left(0.9999999999994297 + \frac{309629712.5173946}{{z}^{3}}\right)}{t_7 \cdot t_1}\right)\right)\right)\right)\right)\right)\\ \end{array} \]

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 (/ -0.13857109526572012 (+ (+ z -1.0) 6.0)))
        (t_1 (+ (/ z -1259.1392167224028) -0.0007941933558411801))
        (t_2 (/ 771.3234287776531 (+ (+ z -1.0) 3.0)))
        (t_3 (/ 9.984369578019572e-6 (+ (+ z -1.0) 7.0)))
        (t_4 (/ -176.6150291621406 (+ (+ z -1.0) 4.0)))
        (t_5 (/ 1.5056327351493116e-7 (+ (+ z -1.0) 8.0)))
        (t_6 (/ 12.507343278686905 (+ (+ z -1.0) 5.0)))
        (t_7
         (+
          0.9999999999996197
          (*
           (/ 676.5203681218851 z)
           (+ (/ 676.5203681218851 z) -0.9999999999998099)))))
   (if (<= (+ z -1.0) 142.0)
     (*
      (*
       (* (exp (- -6.5 z)) (* (sqrt 2.0) (sqrt PI)))
       (pow (+ z 6.5) (+ z -0.5)))
      (+
       (+
        (+
         (+
          (+
           (+
            (+
             (+ (/ 676.5203681218851 z) (/ -1259.1392167224028 (- z -1.0)))
             0.9999999999998099)
            t_2)
           t_4)
          t_6)
         t_0)
        t_3)
       t_5))
     (*
      (exp
       (fma (+ z -0.5) (log (+ z 6.5)) (fma 0.5 (log (* 2.0 PI)) (- -6.5 z))))
      (+
       t_5
       (+
        t_3
        (+
         t_0
         (+
          t_6
          (+
           t_4
           (+
            t_2
            (/
             (+
              t_7
              (* t_1 (+ 0.9999999999994297 (/ 309629712.5173946 (pow z 3.0)))))
             (* t_7 t_1))))))))))))

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 = -0.13857109526572012 / ((z + -1.0) + 6.0);
	double t_1 = (z / -1259.1392167224028) + -0.0007941933558411801;
	double t_2 = 771.3234287776531 / ((z + -1.0) + 3.0);
	double t_3 = 9.984369578019572e-6 / ((z + -1.0) + 7.0);
	double t_4 = -176.6150291621406 / ((z + -1.0) + 4.0);
	double t_5 = 1.5056327351493116e-7 / ((z + -1.0) + 8.0);
	double t_6 = 12.507343278686905 / ((z + -1.0) + 5.0);
	double t_7 = 0.9999999999996197 + ((676.5203681218851 / z) * ((676.5203681218851 / z) + -0.9999999999998099));
	double tmp;
	if ((z + -1.0) <= 142.0) {
		tmp = ((exp((-6.5 - z)) * (sqrt(2.0) * sqrt(((double) M_PI)))) * pow((z + 6.5), (z + -0.5))) * (((((((((676.5203681218851 / z) + (-1259.1392167224028 / (z - -1.0))) + 0.9999999999998099) + t_2) + t_4) + t_6) + t_0) + t_3) + t_5);
	} else {
		tmp = exp(fma((z + -0.5), log((z + 6.5)), fma(0.5, log((2.0 * ((double) M_PI))), (-6.5 - z)))) * (t_5 + (t_3 + (t_0 + (t_6 + (t_4 + (t_2 + ((t_7 + (t_1 * (0.9999999999994297 + (309629712.5173946 / pow(z, 3.0))))) / (t_7 * t_1))))))));
	}
	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(-0.13857109526572012 / Float64(Float64(z + -1.0) + 6.0))
	t_1 = Float64(Float64(z / -1259.1392167224028) + -0.0007941933558411801)
	t_2 = Float64(771.3234287776531 / Float64(Float64(z + -1.0) + 3.0))
	t_3 = Float64(9.984369578019572e-6 / Float64(Float64(z + -1.0) + 7.0))
	t_4 = Float64(-176.6150291621406 / Float64(Float64(z + -1.0) + 4.0))
	t_5 = Float64(1.5056327351493116e-7 / Float64(Float64(z + -1.0) + 8.0))
	t_6 = Float64(12.507343278686905 / Float64(Float64(z + -1.0) + 5.0))
	t_7 = Float64(0.9999999999996197 + Float64(Float64(676.5203681218851 / z) * Float64(Float64(676.5203681218851 / z) + -0.9999999999998099)))
	tmp = 0.0
	if (Float64(z + -1.0) <= 142.0)
		tmp = Float64(Float64(Float64(exp(Float64(-6.5 - z)) * Float64(sqrt(2.0) * sqrt(pi))) * (Float64(z + 6.5) ^ Float64(z + -0.5))) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(676.5203681218851 / z) + Float64(-1259.1392167224028 / Float64(z - -1.0))) + 0.9999999999998099) + t_2) + t_4) + t_6) + t_0) + t_3) + t_5));
	else
		tmp = Float64(exp(fma(Float64(z + -0.5), log(Float64(z + 6.5)), fma(0.5, log(Float64(2.0 * pi)), Float64(-6.5 - z)))) * Float64(t_5 + Float64(t_3 + Float64(t_0 + Float64(t_6 + Float64(t_4 + Float64(t_2 + Float64(Float64(t_7 + Float64(t_1 * Float64(0.9999999999994297 + Float64(309629712.5173946 / (z ^ 3.0))))) / Float64(t_7 * t_1)))))))));
	end
	return 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[(-0.13857109526572012 / N[(N[(z + -1.0), $MachinePrecision] + 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(z / -1259.1392167224028), $MachinePrecision] + -0.0007941933558411801), $MachinePrecision]}, Block[{t$95$2 = N[(771.3234287776531 / N[(N[(z + -1.0), $MachinePrecision] + 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(9.984369578019572e-6 / N[(N[(z + -1.0), $MachinePrecision] + 7.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(-176.6150291621406 / N[(N[(z + -1.0), $MachinePrecision] + 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(1.5056327351493116e-7 / N[(N[(z + -1.0), $MachinePrecision] + 8.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(12.507343278686905 / N[(N[(z + -1.0), $MachinePrecision] + 5.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(0.9999999999996197 + N[(N[(676.5203681218851 / z), $MachinePrecision] * N[(N[(676.5203681218851 / z), $MachinePrecision] + -0.9999999999998099), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z + -1.0), $MachinePrecision], 142.0], N[(N[(N[(N[Exp[N[(-6.5 - z), $MachinePrecision]], $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[Sqrt[Pi], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Power[N[(z + 6.5), $MachinePrecision], N[(z + -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(N[(676.5203681218851 / z), $MachinePrecision] + N[(-1259.1392167224028 / N[(z - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 0.9999999999998099), $MachinePrecision] + t$95$2), $MachinePrecision] + t$95$4), $MachinePrecision] + t$95$6), $MachinePrecision] + t$95$0), $MachinePrecision] + t$95$3), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision], N[(N[Exp[N[(N[(z + -0.5), $MachinePrecision] * N[Log[N[(z + 6.5), $MachinePrecision]], $MachinePrecision] + N[(0.5 * N[Log[N[(2.0 * Pi), $MachinePrecision]], $MachinePrecision] + N[(-6.5 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(t$95$5 + N[(t$95$3 + N[(t$95$0 + N[(t$95$6 + N[(t$95$4 + N[(t$95$2 + N[(N[(t$95$7 + N[(t$95$1 * N[(0.9999999999994297 + N[(309629712.5173946 / N[Power[z, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$7 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z 1) < 142

   1. Initial program 2.3

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

   2. Taylor expanded in z around inf 2.2

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

   3. Simplified 2.3

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

   4. Applied egg-rr 2.3

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

   5. Applied egg-rr 2.2

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

   if 142 < (-.f64 z 1)

   1. Initial program 64.0

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

   2. Taylor expanded in z around inf 64.0

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

   3. Simplified 64.0

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

   4. Applied egg-rr 64.0

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

   5. Applied egg-rr 7.6

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

   6. Applied egg-rr 7.6

      \[\leadsto e^{\mathsf{fma}\left(z + -0.5, \log \left(z + 6.5\right), \mathsf{fma}\left(0.5, \log \left(2 \cdot \pi\right), -6.5 - z\right)\right)} \cdot \left(\left(\left(\left(\left(\left(\color{blue}{\frac{\left(0.9999999999996197 + \frac{676.5203681218851}{z} \cdot \left(\frac{676.5203681218851}{z} - 0.9999999999998099\right)\right) + \left(\frac{z}{-1259.1392167224028} - 0.0007941933558411801\right) \cdot \left(0.9999999999994297 + \frac{309629712.5173946}{{z}^{3}}\right)}{\left(\frac{z}{-1259.1392167224028} - 0.0007941933558411801\right) \cdot \left(0.9999999999996197 + \frac{676.5203681218851}{z} \cdot \left(\frac{676.5203681218851}{z} - 0.9999999999998099\right)\right)}} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 2.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;z + -1 \leq 142:\\ \;\;\;\;\left(\left(e^{-6.5 - z} \cdot \left(\sqrt{2} \cdot \sqrt{\pi}\right)\right) \cdot {\left(z + 6.5\right)}^{\left(z + -0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z - -1}\right) + 0.9999999999998099\right) + \frac{771.3234287776531}{\left(z + -1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z + -1\right) + 4}\right) + \frac{12.507343278686905}{\left(z + -1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z + -1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z + -1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8}\right)\\ \mathbf{else}:\\ \;\;\;\;e^{\mathsf{fma}\left(z + -0.5, \log \left(z + 6.5\right), \mathsf{fma}\left(0.5, \log \left(2 \cdot \pi\right), -6.5 - z\right)\right)} \cdot \left(\frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(z + -1\right) + 7} + \left(\frac{-0.13857109526572012}{\left(z + -1\right) + 6} + \left(\frac{12.507343278686905}{\left(z + -1\right) + 5} + \left(\frac{-176.6150291621406}{\left(z + -1\right) + 4} + \left(\frac{771.3234287776531}{\left(z + -1\right) + 3} + \frac{\left(0.9999999999996197 + \frac{676.5203681218851}{z} \cdot \left(\frac{676.5203681218851}{z} + -0.9999999999998099\right)\right) + \left(\frac{z}{-1259.1392167224028} + -0.0007941933558411801\right) \cdot \left(0.9999999999994297 + \frac{309629712.5173946}{{z}^{3}}\right)}{\left(0.9999999999996197 + \frac{676.5203681218851}{z} \cdot \left(\frac{676.5203681218851}{z} + -0.9999999999998099\right)\right) \cdot \left(\frac{z}{-1259.1392167224028} + -0.0007941933558411801\right)}\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	2.4
Cost	44548

\[\begin{array}{l} t_0 := \frac{-0.13857109526572012}{\left(z + -1\right) + 6}\\ t_1 := \frac{z}{-1259.1392167224028} + -0.0007941933558411801\\ t_2 := \frac{771.3234287776531}{\left(z + -1\right) + 3}\\ t_3 := \frac{9.984369578019572 \cdot 10^{-6}}{\left(z + -1\right) + 7}\\ t_4 := \frac{-176.6150291621406}{\left(z + -1\right) + 4}\\ t_5 := \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8}\\ t_6 := \frac{12.507343278686905}{\left(z + -1\right) + 5}\\ t_7 := 0.9999999999998099 + \frac{-676.5203681218851}{z}\\ \mathbf{if}\;z + -1 \leq 142:\\ \;\;\;\;\left(\left(e^{-6.5 - z} \cdot \left(\sqrt{2} \cdot \sqrt{\pi}\right)\right) \cdot {\left(z + 6.5\right)}^{\left(z + -0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z - -1}\right) + 0.9999999999998099\right) + t_2\right) + t_4\right) + t_6\right) + t_0\right) + t_3\right) + t_5\right)\\ \mathbf{else}:\\ \;\;\;\;e^{\mathsf{fma}\left(z + -0.5, \log \left(z + 6.5\right), \mathsf{fma}\left(0.5, \log \left(2 \cdot \pi\right), -6.5 - z\right)\right)} \cdot \left(t_5 + \left(t_3 + \left(t_0 + \left(t_6 + \left(t_4 + \left(t_2 + \frac{t_7 + t_1 \cdot \left(0.9999999999996197 + \frac{-457679.80848377093}{z \cdot z}\right)}{t_1 \cdot t_7}\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 2
Error	2.4
Cost	44420

\[\begin{array}{l} t_0 := \frac{-0.13857109526572012}{\left(z + -1\right) + 6}\\ t_1 := \frac{12.507343278686905}{\left(z + -1\right) + 5}\\ t_2 := 0.9999999999998099 + \frac{-676.5203681218851}{z}\\ t_3 := \frac{771.3234287776531}{\left(z + -1\right) + 3}\\ t_4 := \frac{9.984369578019572 \cdot 10^{-6}}{\left(z + -1\right) + 7}\\ t_5 := \frac{-176.6150291621406}{\left(z + -1\right) + 4}\\ t_6 := \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8}\\ \mathbf{if}\;z + -1 \leq 142:\\ \;\;\;\;\left(\left(e^{-6.5 - z} \cdot \left(\sqrt{2} \cdot \sqrt{\pi}\right)\right) \cdot {\left(z + 6.5\right)}^{\left(z + -0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z - -1}\right) + 0.9999999999998099\right) + t_3\right) + t_5\right) + t_1\right) + t_0\right) + t_4\right) + t_6\right)\\ \mathbf{else}:\\ \;\;\;\;e^{\mathsf{fma}\left(z + -0.5, \log \left(z + 6.5\right), \mathsf{fma}\left(0.5, \log \left(2 \cdot \pi\right), -6.5 - z\right)\right)} \cdot \left(t_6 + \left(t_4 + \left(t_0 + \left(t_1 + \left(t_5 + \left(t_3 + \frac{-1259.1392167224028 \cdot t_2 + \left(0.9999999999996197 + \frac{-457679.80848377093}{z \cdot z}\right) \cdot \left(z - -1\right)}{t_2 \cdot \left(z - -1\right)}\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 3
Error	2.4
Cost	43268

\[\begin{array}{l} t_0 := \frac{12.507343278686905}{\left(z + -1\right) + 5}\\ t_1 := \frac{-1259.1392167224028}{z - -1}\\ t_2 := \frac{-0.13857109526572012}{\left(z + -1\right) + 6}\\ t_3 := \frac{771.3234287776531}{\left(z + -1\right) + 3}\\ t_4 := \frac{9.984369578019572 \cdot 10^{-6}}{\left(z + -1\right) + 7}\\ t_5 := \frac{-176.6150291621406}{\left(z + -1\right) + 4}\\ t_6 := \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8}\\ \mathbf{if}\;z + -1 \leq 142:\\ \;\;\;\;\left(\left(e^{-6.5 - z} \cdot \left(\sqrt{2} \cdot \sqrt{\pi}\right)\right) \cdot {\left(z + 6.5\right)}^{\left(z + -0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(\frac{676.5203681218851}{z} + t_1\right) + 0.9999999999998099\right) + t_3\right) + t_5\right) + t_0\right) + t_2\right) + t_4\right) + t_6\right)\\ \mathbf{else}:\\ \;\;\;\;e^{\mathsf{fma}\left(z + -0.5, \log \left(z + 6.5\right), \mathsf{fma}\left(0.5, \log \left(2 \cdot \pi\right), -6.5 - z\right)\right)} \cdot \left(t_6 + \left(t_4 + \left(t_2 + \left(t_0 + \left(t_5 + \left(t_3 + \left(\left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) + t_1\right)\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 4
Error	2.4
Cost	43012

\[\begin{array}{l} t_0 := \frac{-0.13857109526572012}{\left(z + -1\right) + 6}\\ t_1 := \frac{9.984369578019572 \cdot 10^{-6}}{\left(z + -1\right) + 7}\\ t_2 := \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8}\\ t_3 := \left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z - -1}\right) + 0.9999999999998099\\ t_4 := \frac{12.507343278686905}{\left(z + -1\right) + 5}\\ \mathbf{if}\;z + -1 \leq 142:\\ \;\;\;\;\left(\left(e^{-6.5 - z} \cdot \left(\sqrt{2} \cdot \sqrt{\pi}\right)\right) \cdot {\left(z + 6.5\right)}^{\left(z + -0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(t_3 + \frac{771.3234287776531}{\left(z + -1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z + -1\right) + 4}\right) + t_4\right) + t_0\right) + t_1\right) + t_2\right)\\ \mathbf{else}:\\ \;\;\;\;e^{\mathsf{fma}\left(z + -0.5, \log \left(z + 6.5\right), \mathsf{fma}\left(0.5, \log \left(2 \cdot \pi\right), -6.5 - z\right)\right)} \cdot \left(t_2 + \left(t_1 + \left(t_0 + \left(t_4 + \left(t_3 + \left(\frac{-176.6150291621406}{z - -3} + \frac{771.3234287776531}{z + 2}\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 5
Error	4.0
Cost	36672

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

Alternative 6
Error	4.0
Cost	31296

\[\begin{array}{l} t_0 := \left(z + -1\right) + 7\\ \left(\left(\sqrt{2 \cdot \pi} \cdot {\left(t_0 + 0.5\right)}^{\left(\left(z + -1\right) + 0.5\right)}\right) \cdot \frac{1}{e^{\left(z + -1\right) + 7.5}}\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{t_0} + \left(\frac{-0.13857109526572012}{\left(z + -1\right) + 6} + \left(\frac{12.507343278686905}{\left(z + -1\right) + 5} + \left(\frac{-176.6150291621406}{\left(z + -1\right) + 4} + \left(\frac{771.3234287776531}{\left(z + -1\right) + 3} + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 + \left(z + -1\right)}\right) + \frac{-1259.1392167224028}{\left(z + -1\right) + 2}\right)\right)\right)\right)\right)\right)\right) \end{array} \]

Alternative 7
Error	4.0
Cost	30656

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

Alternative 8
Error	4.0
Cost	30272

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

Alternative 9
Error	4.1
Cost	29504

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

Alternative 10
Error	4.1
Cost	29504

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

Alternative 11
Error	49.4
Cost	29120

\[{\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot \left(\frac{\sqrt{2 \cdot \pi}}{e^{z + 6.5}} \cdot \left(\frac{-176.6150291621406}{z - -3} + \left(\left(\frac{-0.13857109526572012}{z + 5} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right) + \left(\frac{771.3234287776531}{z + 2} + \left(\frac{1209.1098436076552}{z \cdot z} + \left(0.9999999999998099 + \frac{-570.1115053218308}{z}\right)\right)\right)\right)\right)\right) \]

Alternative 12
Error	53.1
Cost	28480

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

Alternative 13
Error	53.5
Cost	28352

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

Alternative 14
Error	54.0
Cost	26560

\[\frac{\sqrt{2 \cdot \pi} \cdot \left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot 327.76232546796365\right)}{e^{z + 6.5}} \]

Alternative 15
Error	54.0
Cost	26560

\[{\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot \left(\frac{\sqrt{2 \cdot \pi}}{e^{z + 6.5}} \cdot 327.76232546796365\right) \]

Alternative 16
Error	56.1
Cost	26432

\[{\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot \left(327.76232546796365 \cdot \frac{\sqrt{2 \cdot \pi}}{e^{6.5}}\right) \]

Alternative 17
Error	57.1
Cost	26240

\[\left(\frac{\sqrt{2 \cdot \pi}}{e^{z + 6.5}} \cdot 327.76232546796365\right) \cdot \sqrt{0.15384615384615385} \]

Reproduce

herbie shell --seed 2022284 
(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)))))