?

Average Accuracy: 94.0% → 96.5%
Time: 48.1s
Precision: binary64
Cost: 91332

?

\[z > 0.5\]
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \]
↓
\[\begin{array}{l} t_0 := \frac{-0.13857109526572012}{z + 5}\\ t_1 := \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\\ t_2 := \frac{-176.6150291621406}{z + 3}\\ t_3 := \frac{12.507343278686905}{z + 4}\\ t_4 := \mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right)\\ t_5 := \frac{771.3234287776531}{z + 2}\\ t_6 := \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\\ \mathbf{if}\;z + -1 \leq 140:\\ \;\;\;\;\sqrt{\pi \cdot 2} \cdot \left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot \left(e^{-6.5 - z} \cdot \left(\left(0.9999999999998099 + \left(t_5 + \frac{\mathsf{fma}\left(z, -1259.1392167224028, \mathsf{fma}\left(676.5203681218851, z, 676.5203681218851\right)\right)}{\mathsf{fma}\left(z, z, z\right)}\right)\right) + \left(\left(\left(t_0 + t_6\right) + \left(t_2 + t_3\right)\right) + t_1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\sqrt[3]{t_4 \cdot \left(t_4 \cdot t_4\right)}}\right)\right) \cdot \left(\left(\left(\frac{\left(\frac{1373039.4254510517}{z \cdot z} + \left(\frac{309629712.5173946}{{z}^{3}} + \left(\frac{2029.5611043648837}{z} + 0.9999999999994297\right)\right)\right) + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 + \frac{1259.1392167224028}{z + 1}\right)\right)} + \left(t_5 + t_2\right)\right) + \left(t_0 + t_3\right)\right) + \left(t_6 + t_1\right)\right)\\ \end{array} \]
(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 5.0)))
        (t_1 (/ 1.5056327351493116e-7 (+ z 7.0)))
        (t_2 (/ -176.6150291621406 (+ z 3.0)))
        (t_3 (/ 12.507343278686905 (+ z 4.0)))
        (t_4 (fma (- (log (+ z 6.5))) (- 0.5 z) (- -6.5 z)))
        (t_5 (/ 771.3234287776531 (+ z 2.0)))
        (t_6 (/ 9.984369578019572e-6 (+ z 6.0))))
   (if (<= (+ z -1.0) 140.0)
     (*
      (sqrt (* PI 2.0))
      (*
       (pow (+ z 6.5) (+ z -0.5))
       (*
        (exp (- -6.5 z))
        (+
         (+
          0.9999999999998099
          (+
           t_5
           (/
            (fma
             z
             -1259.1392167224028
             (fma 676.5203681218851 z 676.5203681218851))
            (fma z z z))))
         (+ (+ (+ t_0 t_6) (+ t_2 t_3)) t_1)))))
     (*
      (* (sqrt 2.0) (* (sqrt PI) (exp (cbrt (* t_4 (* t_4 t_4))))))
      (+
       (+
        (+
         (/
          (+
           (+
            (/ 1373039.4254510517 (* z z))
            (+
             (/ 309629712.5173946 (pow z 3.0))
             (+ (/ 2029.5611043648837 z) 0.9999999999994297)))
           (/ -1996279061.5505414 (pow (+ z 1.0) 3.0)))
          (+
           (/ (/ 1585431.567088306 (+ z 1.0)) (+ z 1.0))
           (*
            (+ 0.9999999999998099 (/ 676.5203681218851 z))
            (+
             (/ 676.5203681218851 z)
             (+ 0.9999999999998099 (/ 1259.1392167224028 (+ z 1.0)))))))
         (+ t_5 t_2))
        (+ t_0 t_3))
       (+ t_6 t_1))))))
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 + 5.0);
	double t_1 = 1.5056327351493116e-7 / (z + 7.0);
	double t_2 = -176.6150291621406 / (z + 3.0);
	double t_3 = 12.507343278686905 / (z + 4.0);
	double t_4 = fma(-log((z + 6.5)), (0.5 - z), (-6.5 - z));
	double t_5 = 771.3234287776531 / (z + 2.0);
	double t_6 = 9.984369578019572e-6 / (z + 6.0);
	double tmp;
	if ((z + -1.0) <= 140.0) {
		tmp = sqrt((((double) M_PI) * 2.0)) * (pow((z + 6.5), (z + -0.5)) * (exp((-6.5 - z)) * ((0.9999999999998099 + (t_5 + (fma(z, -1259.1392167224028, fma(676.5203681218851, z, 676.5203681218851)) / fma(z, z, z)))) + (((t_0 + t_6) + (t_2 + t_3)) + t_1))));
	} else {
		tmp = (sqrt(2.0) * (sqrt(((double) M_PI)) * exp(cbrt((t_4 * (t_4 * t_4)))))) * (((((((1373039.4254510517 / (z * z)) + ((309629712.5173946 / pow(z, 3.0)) + ((2029.5611043648837 / z) + 0.9999999999994297))) + (-1996279061.5505414 / pow((z + 1.0), 3.0))) / (((1585431.567088306 / (z + 1.0)) / (z + 1.0)) + ((0.9999999999998099 + (676.5203681218851 / z)) * ((676.5203681218851 / z) + (0.9999999999998099 + (1259.1392167224028 / (z + 1.0))))))) + (t_5 + t_2)) + (t_0 + t_3)) + (t_6 + t_1));
	}
	return tmp;
}

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(z + 5.0))
	t_1 = Float64(1.5056327351493116e-7 / Float64(z + 7.0))
	t_2 = Float64(-176.6150291621406 / Float64(z + 3.0))
	t_3 = Float64(12.507343278686905 / Float64(z + 4.0))
	t_4 = fma(Float64(-log(Float64(z + 6.5))), Float64(0.5 - z), Float64(-6.5 - z))
	t_5 = Float64(771.3234287776531 / Float64(z + 2.0))
	t_6 = Float64(9.984369578019572e-6 / Float64(z + 6.0))
	tmp = 0.0
	if (Float64(z + -1.0) <= 140.0)
		tmp = Float64(sqrt(Float64(pi * 2.0)) * Float64((Float64(z + 6.5) ^ Float64(z + -0.5)) * Float64(exp(Float64(-6.5 - z)) * Float64(Float64(0.9999999999998099 + Float64(t_5 + Float64(fma(z, -1259.1392167224028, fma(676.5203681218851, z, 676.5203681218851)) / fma(z, z, z)))) + Float64(Float64(Float64(t_0 + t_6) + Float64(t_2 + t_3)) + t_1)))));
	else
		tmp = Float64(Float64(sqrt(2.0) * Float64(sqrt(pi) * exp(cbrt(Float64(t_4 * Float64(t_4 * t_4)))))) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(1373039.4254510517 / Float64(z * z)) + Float64(Float64(309629712.5173946 / (z ^ 3.0)) + Float64(Float64(2029.5611043648837 / z) + 0.9999999999994297))) + Float64(-1996279061.5505414 / (Float64(z + 1.0) ^ 3.0))) / Float64(Float64(Float64(1585431.567088306 / Float64(z + 1.0)) / Float64(z + 1.0)) + Float64(Float64(0.9999999999998099 + Float64(676.5203681218851 / z)) * Float64(Float64(676.5203681218851 / z) + Float64(0.9999999999998099 + Float64(1259.1392167224028 / Float64(z + 1.0))))))) + Float64(t_5 + t_2)) + Float64(t_0 + t_3)) + Float64(t_6 + t_1)));
	end
	return tmp
end

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[(z + 5.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.5056327351493116e-7 / N[(z + 7.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-176.6150291621406 / N[(z + 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(12.507343278686905 / N[(z + 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[((-N[Log[N[(z + 6.5), $MachinePrecision]], $MachinePrecision]) * N[(0.5 - z), $MachinePrecision] + N[(-6.5 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(771.3234287776531 / N[(z + 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(9.984369578019572e-6 / N[(z + 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z + -1.0), $MachinePrecision], 140.0], N[(N[Sqrt[N[(Pi * 2.0), $MachinePrecision]], $MachinePrecision] * N[(N[Power[N[(z + 6.5), $MachinePrecision], N[(z + -0.5), $MachinePrecision]], $MachinePrecision] * N[(N[Exp[N[(-6.5 - z), $MachinePrecision]], $MachinePrecision] * N[(N[(0.9999999999998099 + N[(t$95$5 + N[(N[(z * -1259.1392167224028 + N[(676.5203681218851 * z + 676.5203681218851), $MachinePrecision]), $MachinePrecision] / N[(z * z + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t$95$0 + t$95$6), $MachinePrecision] + N[(t$95$2 + t$95$3), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Sqrt[Pi], $MachinePrecision] * N[Exp[N[Power[N[(t$95$4 * N[(t$95$4 * t$95$4), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(1373039.4254510517 / N[(z * z), $MachinePrecision]), $MachinePrecision] + N[(N[(309629712.5173946 / N[Power[z, 3.0], $MachinePrecision]), $MachinePrecision] + N[(N[(2029.5611043648837 / z), $MachinePrecision] + 0.9999999999994297), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1996279061.5505414 / N[Power[N[(z + 1.0), $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(1585431.567088306 / N[(z + 1.0), $MachinePrecision]), $MachinePrecision] / N[(z + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(0.9999999999998099 + N[(676.5203681218851 / z), $MachinePrecision]), $MachinePrecision] * N[(N[(676.5203681218851 / z), $MachinePrecision] + N[(0.9999999999998099 + N[(1259.1392167224028 / N[(z + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$5 + t$95$2), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 + t$95$3), $MachinePrecision]), $MachinePrecision] + N[(t$95$6 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

\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}{z + 5}\\
t_1 := \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\\
t_2 := \frac{-176.6150291621406}{z + 3}\\
t_3 := \frac{12.507343278686905}{z + 4}\\
t_4 := \mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right)\\
t_5 := \frac{771.3234287776531}{z + 2}\\
t_6 := \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\\
\mathbf{if}\;z + -1 \leq 140:\\
\;\;\;\;\sqrt{\pi \cdot 2} \cdot \left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot \left(e^{-6.5 - z} \cdot \left(\left(0.9999999999998099 + \left(t_5 + \frac{\mathsf{fma}\left(z, -1259.1392167224028, \mathsf{fma}\left(676.5203681218851, z, 676.5203681218851\right)\right)}{\mathsf{fma}\left(z, z, z\right)}\right)\right) + \left(\left(\left(t_0 + t_6\right) + \left(t_2 + t_3\right)\right) + t_1\right)\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\sqrt[3]{t_4 \cdot \left(t_4 \cdot t_4\right)}}\right)\right) \cdot \left(\left(\left(\frac{\left(\frac{1373039.4254510517}{z \cdot z} + \left(\frac{309629712.5173946}{{z}^{3}} + \left(\frac{2029.5611043648837}{z} + 0.9999999999994297\right)\right)\right) + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 + \frac{1259.1392167224028}{z + 1}\right)\right)} + \left(t_5 + t_2\right)\right) + \left(t_0 + t_3\right)\right) + \left(t_6 + t_1\right)\right)\\


\end{array}

Error?

Derivation?

  1. Split input into 2 regimes

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

    1. Initial program 96.5%

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

    2. Simplified96.6%

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

      [Start]96.5

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

      associate-*l* [=>]96.5

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

      associate-*l* [=>]96.5

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

    3. Applied egg-rr96.6%

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

      [Start]96.6

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

      frac-add [=>]96.6

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

    4. Simplified96.8%

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

      [Start]96.6

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

      +-commutative [=>]96.6

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

      fma-def [=>]96.8

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

      distribute-lft-in [=>]96.8

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

      metadata-eval [=>]96.8

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

      fma-def [=>]96.8

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

      distribute-rgt-in [=>]96.7

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

      *-lft-identity [=>]96.7

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

      fma-def [=>]96.8

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

    if 140 < (-.f64 z 1)

    1. Initial program 4.1%

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

    2. Simplified4.1%

      \[\leadsto \color{blue}{\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(z + -1\right) + 7.5\right)}^{\left(z - 0.5\right)}\right) \cdot e^{\left(-\left(z - -6\right)\right) + -0.5}\right) \cdot \left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) + \frac{-1259.1392167224028}{z - -1}\right) + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right)} \]
      Proof

      [Start]4.1

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

    3. Taylor expanded in z around -inf 3.7%

      \[\leadsto \color{blue}{\left(\left(\sqrt{2} \cdot \left(e^{-1 \cdot \left(\log \left(6.5 - -1 \cdot z\right) \cdot \left(-1 \cdot z + 0.5\right)\right)} \cdot e^{-1 \cdot z - 6.5}\right)\right) \cdot \sqrt{\pi}\right)} \cdot \left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) + \frac{-1259.1392167224028}{z - -1}\right) + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

    4. Simplified88.2%

      \[\leadsto \color{blue}{\left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right)} \cdot \left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) + \frac{-1259.1392167224028}{z - -1}\right) + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]
      Proof

      [Start]3.7

      \[ \left(\left(\sqrt{2} \cdot \left(e^{-1 \cdot \left(\log \left(6.5 - -1 \cdot z\right) \cdot \left(-1 \cdot z + 0.5\right)\right)} \cdot e^{-1 \cdot z - 6.5}\right)\right) \cdot \sqrt{\pi}\right) \cdot \left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) + \frac{-1259.1392167224028}{z - -1}\right) + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      associate-*l* [=>]3.7

      \[ \color{blue}{\left(\sqrt{2} \cdot \left(\left(e^{-1 \cdot \left(\log \left(6.5 - -1 \cdot z\right) \cdot \left(-1 \cdot z + 0.5\right)\right)} \cdot e^{-1 \cdot z - 6.5}\right) \cdot \sqrt{\pi}\right)\right)} \cdot \left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) + \frac{-1259.1392167224028}{z - -1}\right) + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      *-commutative [=>]3.7

      \[ \left(\sqrt{2} \cdot \color{blue}{\left(\sqrt{\pi} \cdot \left(e^{-1 \cdot \left(\log \left(6.5 - -1 \cdot z\right) \cdot \left(-1 \cdot z + 0.5\right)\right)} \cdot e^{-1 \cdot z - 6.5}\right)\right)}\right) \cdot \left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) + \frac{-1259.1392167224028}{z - -1}\right) + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      prod-exp [=>]87.9

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot \color{blue}{e^{-1 \cdot \left(\log \left(6.5 - -1 \cdot z\right) \cdot \left(-1 \cdot z + 0.5\right)\right) + \left(-1 \cdot z - 6.5\right)}}\right)\right) \cdot \left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) + \frac{-1259.1392167224028}{z - -1}\right) + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      associate-*r* [=>]87.9

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\color{blue}{\left(-1 \cdot \log \left(6.5 - -1 \cdot z\right)\right) \cdot \left(-1 \cdot z + 0.5\right)} + \left(-1 \cdot z - 6.5\right)}\right)\right) \cdot \left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) + \frac{-1259.1392167224028}{z - -1}\right) + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      fma-def [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\color{blue}{\mathsf{fma}\left(-1 \cdot \log \left(6.5 - -1 \cdot z\right), -1 \cdot z + 0.5, -1 \cdot z - 6.5\right)}}\right)\right) \cdot \left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) + \frac{-1259.1392167224028}{z - -1}\right) + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

    5. Applied egg-rr88.2%

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

      [Start]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) + \frac{-1259.1392167224028}{z - -1}\right) + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      flip3-+ [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\color{blue}{\frac{{\left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right)}^{3} + {\left(\frac{-1259.1392167224028}{z - -1}\right)}^{3}}{\left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) \cdot \left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - \left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) \cdot \frac{-1259.1392167224028}{z - -1}\right)}} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      --rgt-identity [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{{\left(0.9999999999998099 + \frac{676.5203681218851}{\color{blue}{z}}\right)}^{3} + {\left(\frac{-1259.1392167224028}{z - -1}\right)}^{3}}{\left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) \cdot \left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - \left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) \cdot \frac{-1259.1392167224028}{z - -1}\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      sub-neg [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{{\left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)}^{3} + {\left(\frac{-1259.1392167224028}{\color{blue}{z + \left(--1\right)}}\right)}^{3}}{\left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) \cdot \left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - \left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) \cdot \frac{-1259.1392167224028}{z - -1}\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      metadata-eval [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{{\left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)}^{3} + {\left(\frac{-1259.1392167224028}{z + \color{blue}{1}}\right)}^{3}}{\left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) \cdot \left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - \left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) \cdot \frac{-1259.1392167224028}{z - -1}\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      --rgt-identity [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{{\left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)}^{3} + {\left(\frac{-1259.1392167224028}{z + 1}\right)}^{3}}{\left(0.9999999999998099 + \frac{676.5203681218851}{\color{blue}{z}}\right) \cdot \left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - \left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) \cdot \frac{-1259.1392167224028}{z - -1}\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      --rgt-identity [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{{\left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)}^{3} + {\left(\frac{-1259.1392167224028}{z + 1}\right)}^{3}}{\left(0.9999999999998099 + \frac{676.5203681218851}{z}\right) \cdot \left(0.9999999999998099 + \frac{676.5203681218851}{\color{blue}{z}}\right) + \left(\frac{-1259.1392167224028}{z - -1} \cdot \frac{-1259.1392167224028}{z - -1} - \left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) \cdot \frac{-1259.1392167224028}{z - -1}\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

    6. Simplified88.2%

      \[\leadsto \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\color{blue}{\frac{{\left(\frac{676.5203681218851}{z} + 0.9999999999998099\right)}^{3} + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)}} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]
      Proof

      [Start]88.2

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

      +-commutative [=>]88.2

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

      cube-div [=>]88.2

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

      metadata-eval [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{{\left(\frac{676.5203681218851}{z} + 0.9999999999998099\right)}^{3} + \frac{\color{blue}{-1996279061.5505414}}{{\left(z + 1\right)}^{3}}}{\left(0.9999999999998099 + \frac{676.5203681218851}{z}\right) \cdot \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right) + \left(\frac{-1259.1392167224028}{z + 1} \cdot \frac{-1259.1392167224028}{z + 1} - \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right) \cdot \frac{-1259.1392167224028}{z + 1}\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      +-commutative [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{{\left(\frac{676.5203681218851}{z} + 0.9999999999998099\right)}^{3} + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\color{blue}{\left(\frac{-1259.1392167224028}{z + 1} \cdot \frac{-1259.1392167224028}{z + 1} - \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right) \cdot \frac{-1259.1392167224028}{z + 1}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right) \cdot \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)}} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      cancel-sign-sub-inv [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{{\left(\frac{676.5203681218851}{z} + 0.9999999999998099\right)}^{3} + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\color{blue}{\left(\frac{-1259.1392167224028}{z + 1} \cdot \frac{-1259.1392167224028}{z + 1} + \left(-\left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) \cdot \frac{-1259.1392167224028}{z + 1}\right)} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right) \cdot \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      associate-+l+ [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{{\left(\frac{676.5203681218851}{z} + 0.9999999999998099\right)}^{3} + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\color{blue}{\frac{-1259.1392167224028}{z + 1} \cdot \frac{-1259.1392167224028}{z + 1} + \left(\left(-\left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) \cdot \frac{-1259.1392167224028}{z + 1} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right) \cdot \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right)}} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

    7. Taylor expanded in z around 0 88.2%

      \[\leadsto \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{\color{blue}{\left(0.9999999999994297 + \left(309629712.5173946 \cdot \frac{1}{{z}^{3}} + \left(2029.5611043648837 \cdot \frac{1}{z} + 1373039.4254510517 \cdot \frac{1}{{z}^{2}}\right)\right)\right)} + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

    8. Simplified88.2%

      \[\leadsto \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{\color{blue}{\left(\frac{1373039.4254510517}{z \cdot z} + \left(\frac{309629712.5173946}{{z}^{3}} + \left(\frac{2029.5611043648837}{z} + 0.9999999999994297\right)\right)\right)} + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]
      Proof

      [Start]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{\left(0.9999999999994297 + \left(309629712.5173946 \cdot \frac{1}{{z}^{3}} + \left(2029.5611043648837 \cdot \frac{1}{z} + 1373039.4254510517 \cdot \frac{1}{{z}^{2}}\right)\right)\right) + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      associate-+r+ [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{\color{blue}{\left(\left(0.9999999999994297 + 309629712.5173946 \cdot \frac{1}{{z}^{3}}\right) + \left(2029.5611043648837 \cdot \frac{1}{z} + 1373039.4254510517 \cdot \frac{1}{{z}^{2}}\right)\right)} + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      associate-+r+ [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{\color{blue}{\left(\left(\left(0.9999999999994297 + 309629712.5173946 \cdot \frac{1}{{z}^{3}}\right) + 2029.5611043648837 \cdot \frac{1}{z}\right) + 1373039.4254510517 \cdot \frac{1}{{z}^{2}}\right)} + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      +-commutative [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{\color{blue}{\left(1373039.4254510517 \cdot \frac{1}{{z}^{2}} + \left(\left(0.9999999999994297 + 309629712.5173946 \cdot \frac{1}{{z}^{3}}\right) + 2029.5611043648837 \cdot \frac{1}{z}\right)\right)} + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      +-commutative [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{\left(1373039.4254510517 \cdot \frac{1}{{z}^{2}} + \left(\color{blue}{\left(309629712.5173946 \cdot \frac{1}{{z}^{3}} + 0.9999999999994297\right)} + 2029.5611043648837 \cdot \frac{1}{z}\right)\right) + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      associate-+r+ [<=]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{\left(1373039.4254510517 \cdot \frac{1}{{z}^{2}} + \color{blue}{\left(309629712.5173946 \cdot \frac{1}{{z}^{3}} + \left(0.9999999999994297 + 2029.5611043648837 \cdot \frac{1}{z}\right)\right)}\right) + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      associate-*r/ [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{\left(\color{blue}{\frac{1373039.4254510517 \cdot 1}{{z}^{2}}} + \left(309629712.5173946 \cdot \frac{1}{{z}^{3}} + \left(0.9999999999994297 + 2029.5611043648837 \cdot \frac{1}{z}\right)\right)\right) + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      metadata-eval [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{\left(\frac{\color{blue}{1373039.4254510517}}{{z}^{2}} + \left(309629712.5173946 \cdot \frac{1}{{z}^{3}} + \left(0.9999999999994297 + 2029.5611043648837 \cdot \frac{1}{z}\right)\right)\right) + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      unpow2 [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{\left(\frac{1373039.4254510517}{\color{blue}{z \cdot z}} + \left(309629712.5173946 \cdot \frac{1}{{z}^{3}} + \left(0.9999999999994297 + 2029.5611043648837 \cdot \frac{1}{z}\right)\right)\right) + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      associate-*r/ [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{\left(\frac{1373039.4254510517}{z \cdot z} + \left(\color{blue}{\frac{309629712.5173946 \cdot 1}{{z}^{3}}} + \left(0.9999999999994297 + 2029.5611043648837 \cdot \frac{1}{z}\right)\right)\right) + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      metadata-eval [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{\left(\frac{1373039.4254510517}{z \cdot z} + \left(\frac{\color{blue}{309629712.5173946}}{{z}^{3}} + \left(0.9999999999994297 + 2029.5611043648837 \cdot \frac{1}{z}\right)\right)\right) + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      +-commutative [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{\left(\frac{1373039.4254510517}{z \cdot z} + \left(\frac{309629712.5173946}{{z}^{3}} + \color{blue}{\left(2029.5611043648837 \cdot \frac{1}{z} + 0.9999999999994297\right)}\right)\right) + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      associate-*r/ [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{\left(\frac{1373039.4254510517}{z \cdot z} + \left(\frac{309629712.5173946}{{z}^{3}} + \left(\color{blue}{\frac{2029.5611043648837 \cdot 1}{z}} + 0.9999999999994297\right)\right)\right) + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      metadata-eval [=>]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{\left(\frac{1373039.4254510517}{z \cdot z} + \left(\frac{309629712.5173946}{{z}^{3}} + \left(\frac{\color{blue}{2029.5611043648837}}{z} + 0.9999999999994297\right)\right)\right) + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

    9. Applied egg-rr86.9%

      \[\leadsto \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\color{blue}{\sqrt[3]{\left(\mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right) \cdot \mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right)\right) \cdot \mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right)}}}\right)\right) \cdot \left(\left(\left(\frac{\left(\frac{1373039.4254510517}{z \cdot z} + \left(\frac{309629712.5173946}{{z}^{3}} + \left(\frac{2029.5611043648837}{z} + 0.9999999999994297\right)\right)\right) + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]
      Proof

      [Start]88.2

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\left(\frac{\left(\frac{1373039.4254510517}{z \cdot z} + \left(\frac{309629712.5173946}{{z}^{3}} + \left(\frac{2029.5611043648837}{z} + 0.9999999999994297\right)\right)\right) + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      add-cbrt-cube [=>]86.9

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\color{blue}{\sqrt[3]{\left(\mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right) \cdot \mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)\right) \cdot \mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}}}\right)\right) \cdot \left(\left(\left(\frac{\left(\frac{1373039.4254510517}{z \cdot z} + \left(\frac{309629712.5173946}{{z}^{3}} + \left(\frac{2029.5611043648837}{z} + 0.9999999999994297\right)\right)\right) + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      +-commutative [=>]86.9

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\sqrt[3]{\left(\mathsf{fma}\left(-\log \color{blue}{\left(z + 6.5\right)}, 0.5 - z, -6.5 - z\right) \cdot \mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)\right) \cdot \mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}}\right)\right) \cdot \left(\left(\left(\frac{\left(\frac{1373039.4254510517}{z \cdot z} + \left(\frac{309629712.5173946}{{z}^{3}} + \left(\frac{2029.5611043648837}{z} + 0.9999999999994297\right)\right)\right) + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      +-commutative [=>]86.9

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\sqrt[3]{\left(\mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right) \cdot \mathsf{fma}\left(-\log \color{blue}{\left(z + 6.5\right)}, 0.5 - z, -6.5 - z\right)\right) \cdot \mathsf{fma}\left(-\log \left(6.5 + z\right), 0.5 - z, -6.5 - z\right)}}\right)\right) \cdot \left(\left(\left(\frac{\left(\frac{1373039.4254510517}{z \cdot z} + \left(\frac{309629712.5173946}{{z}^{3}} + \left(\frac{2029.5611043648837}{z} + 0.9999999999994297\right)\right)\right) + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

      +-commutative [=>]86.9

      \[ \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\sqrt[3]{\left(\mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right) \cdot \mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right)\right) \cdot \mathsf{fma}\left(-\log \color{blue}{\left(z + 6.5\right)}, 0.5 - z, -6.5 - z\right)}}\right)\right) \cdot \left(\left(\left(\frac{\left(\frac{1373039.4254510517}{z \cdot z} + \left(\frac{309629712.5173946}{{z}^{3}} + \left(\frac{2029.5611043648837}{z} + 0.9999999999994297\right)\right)\right) + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 - \frac{-1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]
  3. Recombined 2 regimes into one program.

  4. Final simplification96.5%

    \[\leadsto \begin{array}{l} \mathbf{if}\;z + -1 \leq 140:\\ \;\;\;\;\sqrt{\pi \cdot 2} \cdot \left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot \left(e^{-6.5 - z} \cdot \left(\left(0.9999999999998099 + \left(\frac{771.3234287776531}{z + 2} + \frac{\mathsf{fma}\left(z, -1259.1392167224028, \mathsf{fma}\left(676.5203681218851, z, 676.5203681218851\right)\right)}{\mathsf{fma}\left(z, z, z\right)}\right)\right) + \left(\left(\left(\frac{-0.13857109526572012}{z + 5} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right) + \left(\frac{-176.6150291621406}{z + 3} + \frac{12.507343278686905}{z + 4}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\sqrt[3]{\mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right) \cdot \left(\mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right) \cdot \mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right)\right)}}\right)\right) \cdot \left(\left(\left(\frac{\left(\frac{1373039.4254510517}{z \cdot z} + \left(\frac{309629712.5173946}{{z}^{3}} + \left(\frac{2029.5611043648837}{z} + 0.9999999999994297\right)\right)\right) + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 + \frac{1259.1392167224028}{z + 1}\right)\right)} + \left(\frac{771.3234287776531}{z + 2} + \frac{-176.6150291621406}{z + 3}\right)\right) + \left(\frac{-0.13857109526572012}{z + 5} + \frac{12.507343278686905}{z + 4}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy96.5%
Cost69828
\[\begin{array}{l} t_0 := \frac{12.507343278686905}{z + 4}\\ t_1 := \frac{-0.13857109526572012}{z + 5}\\ t_2 := \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\\ t_3 := \frac{771.3234287776531}{z + 2}\\ t_4 := \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\\ t_5 := \frac{-176.6150291621406}{z + 3}\\ t_6 := 0.9999999999998099 + \left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z + 1}\right)\\ \mathbf{if}\;z + -1 \leq 140:\\ \;\;\;\;\sqrt{\pi \cdot 2} \cdot \left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot \left(e^{-6.5 - z} \cdot \left(\left(0.9999999999998099 + \left(t_3 + \frac{\mathsf{fma}\left(z, -1259.1392167224028, \mathsf{fma}\left(676.5203681218851, z, 676.5203681218851\right)\right)}{\mathsf{fma}\left(z, z, z\right)}\right)\right) + \left(\left(\left(t_1 + t_4\right) + \left(t_5 + t_0\right)\right) + t_2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(t_4 + t_2\right) + \left(\left(t_1 + t_0\right) + \frac{\mathsf{log1p}\left(\mathsf{expm1}\left({t_6}^{2} - {\left(t_3 + t_5\right)}^{2}\right)\right)}{t_6 + \left(\frac{-771.3234287776531}{z + 2} - t_5\right)}\right)\right)\\ \end{array} \]
Alternative 2
Accuracy96.5%
Cost63300
\[\begin{array}{l} t_0 := \frac{12.507343278686905}{z + 4}\\ t_1 := \frac{-0.13857109526572012}{z + 5}\\ t_2 := \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\\ t_3 := \sqrt[3]{0.9999999999998099 + \left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z + 1}\right)}\\ t_4 := \frac{-176.6150291621406}{z + 3}\\ t_5 := \frac{771.3234287776531}{z + 2}\\ t_6 := \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\\ \mathbf{if}\;z + -1 \leq 140:\\ \;\;\;\;\sqrt{\pi \cdot 2} \cdot \left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot \left(e^{-6.5 - z} \cdot \left(\left(0.9999999999998099 + \left(t_5 + \frac{\mathsf{fma}\left(z, -1259.1392167224028, \mathsf{fma}\left(676.5203681218851, z, 676.5203681218851\right)\right)}{\mathsf{fma}\left(z, z, z\right)}\right)\right) + \left(\left(\left(t_1 + t_6\right) + \left(t_4 + t_0\right)\right) + t_2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(t_6 + t_2\right) + \left(\left(t_1 + t_0\right) + \left(\left(t_5 + t_4\right) + t_3 \cdot \left(t_3 \cdot t_3\right)\right)\right)\right)\\ \end{array} \]
Alternative 3
Accuracy96.5%
Cost57924
\[\begin{array}{l} t_0 := \frac{12.507343278686905}{z + 4}\\ t_1 := \frac{-0.13857109526572012}{z + 5}\\ t_2 := \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\\ t_3 := \frac{-176.6150291621406}{z + 3}\\ t_4 := \frac{771.3234287776531}{z + 2}\\ t_5 := \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\\ \mathbf{if}\;z + -1 \leq 140:\\ \;\;\;\;\sqrt{\pi \cdot 2} \cdot \left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot \left(e^{-6.5 - z} \cdot \left(\left(0.9999999999998099 + \left(t_4 + \frac{\mathsf{fma}\left(z, -1259.1392167224028, \mathsf{fma}\left(676.5203681218851, z, 676.5203681218851\right)\right)}{\mathsf{fma}\left(z, z, z\right)}\right)\right) + \left(\left(\left(t_1 + t_5\right) + \left(t_3 + t_0\right)\right) + t_2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\frac{\left(\frac{1373039.4254510517}{z \cdot z} + \left(\frac{309629712.5173946}{{z}^{3}} + \left(\frac{2029.5611043648837}{z} + 0.9999999999994297\right)\right)\right) + \frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}}}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right) \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 + \frac{1259.1392167224028}{z + 1}\right)\right)} + \left(t_4 + t_3\right)\right) + \left(t_1 + t_0\right)\right) + \left(t_5 + t_2\right)\right) \cdot \left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right)}\right)\right)\\ \end{array} \]
Alternative 4
Accuracy96.5%
Cost55428
\[\begin{array}{l} t_0 := \frac{12.507343278686905}{z + 4}\\ t_1 := \frac{-0.13857109526572012}{z + 5}\\ t_2 := \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\\ t_3 := \frac{-176.6150291621406}{z + 3}\\ t_4 := \frac{771.3234287776531}{z + 2}\\ t_5 := \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\\ \mathbf{if}\;z + -1 \leq 140:\\ \;\;\;\;\sqrt{\pi \cdot 2} \cdot \left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot \left(e^{-6.5 - z} \cdot \left(\left(0.9999999999998099 + \left(t_4 + \frac{\mathsf{fma}\left(z, -1259.1392167224028, \mathsf{fma}\left(676.5203681218851, z, 676.5203681218851\right)\right)}{\mathsf{fma}\left(z, z, z\right)}\right)\right) + \left(\left(\left(t_1 + t_5\right) + \left(t_3 + t_0\right)\right) + t_2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{2} \cdot \left(e^{\mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right)} \cdot {\left(\sqrt[3]{\sqrt{\pi}}\right)}^{3}\right)\right) \cdot \left(\left(t_5 + t_2\right) + \left(\left(t_1 + t_0\right) + \left(\left(t_4 + t_3\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{z}\right) + \frac{-1259.1392167224028}{z + 1}\right)\right)\right)\right)\\ \end{array} \]
Alternative 5
Accuracy96.5%
Cost51588
\[\begin{array}{l} t_0 := \frac{12.507343278686905}{z + 4}\\ t_1 := 0.9999999999998099 + \frac{676.5203681218851}{z}\\ t_2 := \frac{-0.13857109526572012}{z + 5}\\ t_3 := \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\\ t_4 := \frac{-176.6150291621406}{z + 3}\\ t_5 := \frac{771.3234287776531}{z + 2}\\ t_6 := \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\\ \mathbf{if}\;z + -1 \leq 140:\\ \;\;\;\;\sqrt{\pi \cdot 2} \cdot \left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot \left(e^{-6.5 - z} \cdot \left(\left(0.9999999999998099 + \left(t_5 + \frac{\mathsf{fma}\left(z, -1259.1392167224028, \mathsf{fma}\left(676.5203681218851, z, 676.5203681218851\right)\right)}{\mathsf{fma}\left(z, z, z\right)}\right)\right) + \left(\left(\left(t_2 + t_6\right) + \left(t_4 + t_0\right)\right) + t_3\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(t_6 + t_3\right) + \left(\left(t_2 + t_0\right) + \left(\left(t_5 + t_4\right) + \frac{\frac{-1996279061.5505414}{{\left(z + 1\right)}^{3}} + t_1 \cdot \left(t_1 \cdot t_1\right)}{\frac{\frac{1585431.567088306}{z + 1}}{z + 1} + t_1 \cdot \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 + \frac{1259.1392167224028}{z + 1}\right)\right)}\right)\right)\right)\\ \end{array} \]
Alternative 6
Accuracy96.5%
Cost48964
\[\begin{array}{l} t_0 := \frac{12.507343278686905}{z + 4}\\ t_1 := \frac{-0.13857109526572012}{z + 5}\\ t_2 := \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\\ t_3 := 0.9999999999998099 + \left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z + 1}\right)\\ t_4 := \frac{-176.6150291621406}{z + 3}\\ t_5 := \frac{-771.3234287776531}{z + 2} - t_4\\ t_6 := \frac{771.3234287776531}{z + 2}\\ t_7 := \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\\ \mathbf{if}\;z + -1 \leq 140:\\ \;\;\;\;\sqrt{\pi \cdot 2} \cdot \left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot \left(e^{-6.5 - z} \cdot \left(\left(0.9999999999998099 + \left(t_6 + \frac{\mathsf{fma}\left(z, -1259.1392167224028, \mathsf{fma}\left(676.5203681218851, z, 676.5203681218851\right)\right)}{\mathsf{fma}\left(z, z, z\right)}\right)\right) + \left(\left(\left(t_1 + t_7\right) + \left(t_4 + t_0\right)\right) + t_2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(t_7 + t_2\right) + \left(\left(t_1 + t_0\right) + \frac{t_3 \cdot \left(0.9999999999998099 + \frac{676.5203681218851 \cdot \left(z + 1\right) + z \cdot -1259.1392167224028}{z \cdot \left(z + 1\right)}\right) + \left(t_6 + t_4\right) \cdot t_5}{t_3 + t_5}\right)\right)\\ \end{array} \]
Alternative 7
Accuracy96.4%
Cost46020
\[\begin{array}{l} t_0 := \frac{-176.6150291621406}{z + 3}\\ t_1 := \frac{-771.3234287776531}{z + 2} - t_0\\ t_2 := \left(z + -1\right) + 7\\ t_3 := 0.9999999999998099 + \left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z + 1}\right)\\ \mathbf{if}\;z + -1 \leq 140:\\ \;\;\;\;\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(0.5 + t_2\right)}^{\left(\left(z + -1\right) + 0.5\right)}\right) \cdot e^{-0.5 + \left(-7 + \left(1 - z\right)\right)}\right) \cdot \left(\left(\left(\left(\left(\left(t_3 + \frac{771.3234287776531}{\left(z + -1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z + -1\right) + 4}\right) + \frac{12.507343278686905}{\left(z + -1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z + -1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t_2}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right) + \left(\left(\frac{-0.13857109526572012}{z + 5} + \frac{12.507343278686905}{z + 4}\right) + \frac{t_3 \cdot \left(0.9999999999998099 + \frac{676.5203681218851 \cdot \left(z + 1\right) + z \cdot -1259.1392167224028}{z \cdot \left(z + 1\right)}\right) + \left(\frac{771.3234287776531}{z + 2} + t_0\right) \cdot t_1}{t_3 + t_1}\right)\right)\\ \end{array} \]
Alternative 8
Accuracy96.4%
Cost42564
\[\begin{array}{l} t_0 := \left(z + -1\right) + 7\\ t_1 := 0.9999999999998099 + \left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z + 1}\right)\\ \mathbf{if}\;z + -1 \leq 140:\\ \;\;\;\;\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(0.5 + t_0\right)}^{\left(\left(z + -1\right) + 0.5\right)}\right) \cdot e^{-0.5 + \left(-7 + \left(1 - z\right)\right)}\right) \cdot \left(\left(\left(\left(\left(\left(t_1 + \frac{771.3234287776531}{\left(z + -1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z + -1\right) + 4}\right) + \frac{12.507343278686905}{\left(z + -1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z + -1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t_0}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right) + \left(\left(\frac{-0.13857109526572012}{z + 5} + \frac{12.507343278686905}{z + 4}\right) + \left(\left(\frac{771.3234287776531}{z + 2} + \frac{-176.6150291621406}{z + 3}\right) + t_1\right)\right)\right)\\ \end{array} \]
Alternative 9
Accuracy96.4%
Cost42564
\[\begin{array}{l} t_0 := \left(z + -1\right) + 7\\ t_1 := \frac{-1259.1392167224028}{z + 1}\\ \mathbf{if}\;z + -1 \leq 140:\\ \;\;\;\;\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(0.5 + t_0\right)}^{\left(\left(z + -1\right) + 0.5\right)}\right) \cdot e^{-0.5 + \left(-7 + \left(1 - z\right)\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \left(\frac{676.5203681218851}{z} + t_1\right)\right) + \frac{771.3234287776531}{\left(z + -1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z + -1\right) + 4}\right) + \frac{12.507343278686905}{\left(z + -1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z + -1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t_0}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right) + \left(\left(\frac{-0.13857109526572012}{z + 5} + \frac{12.507343278686905}{z + 4}\right) + \left(\left(\frac{771.3234287776531}{z + 2} + \frac{-176.6150291621406}{z + 3}\right) + \left(\frac{676.5203681218851}{z} + \left(0.9999999999998099 + t_1\right)\right)\right)\right)\right)\\ \end{array} \]
Alternative 10
Accuracy96.4%
Cost42564
\[\begin{array}{l} t_0 := \left(z + -1\right) + 7\\ t_1 := \frac{-1259.1392167224028}{z + 1}\\ \mathbf{if}\;z + -1 \leq 140:\\ \;\;\;\;\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(0.5 + t_0\right)}^{\left(\left(z + -1\right) + 0.5\right)}\right) \cdot e^{-0.5 + \left(-7 + \left(1 - z\right)\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \left(\frac{676.5203681218851}{z} + t_1\right)\right) + \frac{771.3234287776531}{\left(z + -1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z + -1\right) + 4}\right) + \frac{12.507343278686905}{\left(z + -1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z + -1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t_0}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{2} \cdot \left(\sqrt{\pi} \cdot e^{\mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right)}\right)\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right) + \left(\left(\frac{-0.13857109526572012}{z + 5} + \frac{12.507343278686905}{z + 4}\right) + \left(\left(\frac{771.3234287776531}{z + 2} + \frac{-176.6150291621406}{z + 3}\right) + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{z}\right) + t_1\right)\right)\right)\right)\\ \end{array} \]
Alternative 11
Accuracy96.4%
Cost36164
\[\begin{array}{l} t_0 := \left(z + -1\right) + 7\\ t_1 := \frac{-1259.1392167224028}{z + 1}\\ t_2 := \sqrt{\pi \cdot 2}\\ \mathbf{if}\;z + -1 \leq 140:\\ \;\;\;\;\left(\left(t_2 \cdot {\left(0.5 + t_0\right)}^{\left(\left(z + -1\right) + 0.5\right)}\right) \cdot e^{-0.5 + \left(-7 + \left(1 - z\right)\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \left(\frac{676.5203681218851}{z} + t_1\right)\right) + \frac{771.3234287776531}{\left(z + -1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z + -1\right) + 4}\right) + \frac{12.507343278686905}{\left(z + -1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z + -1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t_0}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot \left(e^{\mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right)} \cdot \left(\left(0.9999999999998099 + \frac{676.5203681218851}{z}\right) + \left(\left(t_1 + \left(\frac{-176.6150291621406}{z + 3} + \left(\frac{771.3234287776531}{z + 2} + \frac{12.507343278686905}{z + 4}\right)\right)\right) + \left(\frac{-0.13857109526572012}{z + 5} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right)\right)\right)\\ \end{array} \]
Alternative 12
Accuracy96.4%
Cost31172
\[\begin{array}{l} t_0 := \left(z + -1\right) + 7\\ t_1 := \frac{-1259.1392167224028}{z + 1}\\ t_2 := \sqrt{\pi \cdot 2}\\ \mathbf{if}\;z + -1 \leq 140:\\ \;\;\;\;\left(\left(t_2 \cdot {\left(0.5 + t_0\right)}^{\left(\left(z + -1\right) + 0.5\right)}\right) \cdot e^{-0.5 + \left(-7 + \left(1 - z\right)\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \left(\frac{676.5203681218851}{z} + t_1\right)\right) + \frac{771.3234287776531}{\left(z + -1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z + -1\right) + 4}\right) + \frac{12.507343278686905}{\left(z + -1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z + -1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t_0}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{z}\right) + \left(\left(t_1 + \left(\frac{-176.6150291621406}{z + 3} + \left(\frac{771.3234287776531}{z + 2} + \frac{12.507343278686905}{z + 4}\right)\right)\right) + \left(\frac{-0.13857109526572012}{z + 5} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right)\right) \cdot e^{\left(-6.5 - z\right) + \left(z + -0.5\right) \cdot \log \left(z + 6.5\right)}\right)\\ \end{array} \]
Alternative 13
Accuracy96.2%
Cost29700
\[\begin{array}{l} t_0 := \frac{771.3234287776531}{z + 2}\\ t_1 := \frac{-176.6150291621406}{z + 3}\\ t_2 := \frac{12.507343278686905}{z + 4}\\ t_3 := \frac{-0.13857109526572012}{z + 5}\\ t_4 := \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\\ t_5 := \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\\ t_6 := \sqrt{\pi \cdot 2}\\ t_7 := \frac{-1259.1392167224028}{z + 1}\\ \mathbf{if}\;z \leq 145:\\ \;\;\;\;t_6 \cdot \left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot \left(e^{-6.5 - z} \cdot \left(\left(\left(\left(t_3 + t_5\right) + \left(t_1 + t_2\right)\right) + t_4\right) + \left(0.9999999999998099 + \left(t_0 + \left(\frac{676.5203681218851}{z} + t_7\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_6 \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{z}\right) + \left(\left(t_7 + \left(t_1 + \left(t_0 + t_2\right)\right)\right) + \left(t_3 + \left(t_5 + t_4\right)\right)\right)\right) \cdot e^{\left(-6.5 - z\right) + \left(z + -0.5\right) \cdot \log \left(z + 6.5\right)}\right)\\ \end{array} \]
Alternative 14
Accuracy94.1%
Cost29504
\[\sqrt{\pi \cdot 2} \cdot \left(\left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot e^{-6.5 - z}\right) \cdot \left(\left(0.9999999999998099 + \left(\left(\frac{771.3234287776531}{z + 2} + \frac{-176.6150291621406}{z + 3}\right) + \left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z + 1}\right)\right)\right) + \left(\left(\frac{-0.13857109526572012}{z + 5} + \frac{12.507343278686905}{z + 4}\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right)\right) \]
Alternative 15
Accuracy94.2%
Cost29504
\[\sqrt{\pi \cdot 2} \cdot \left(\left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot e^{-6.5 - z}\right) \cdot \left(\left(0.9999999999998099 + \left(\frac{676.5203681218851}{z} + \left(\frac{771.3234287776531}{z + 2} + \frac{-1259.1392167224028}{z + 1}\right)\right)\right) + \left(\frac{-0.13857109526572012}{z + 5} + \left(\left(\frac{-176.6150291621406}{z + 3} + \frac{12.507343278686905}{z + 4}\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right)\right)\right) \]
Alternative 16
Accuracy94.2%
Cost29504
\[\sqrt{\pi \cdot 2} \cdot \left(\left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot e^{-6.5 - z}\right) \cdot \left(\left(0.9999999999998099 + \left(\frac{771.3234287776531}{z + 2} + \left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z + 1}\right)\right)\right) + \left(\left(\frac{-0.13857109526572012}{z + 5} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right) + \left(\frac{-176.6150291621406}{z + 3} + \left(\frac{12.507343278686905}{z + 4} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right)\right)\right) \]
Alternative 17
Accuracy94.1%
Cost29504
\[\sqrt{\pi \cdot 2} \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{z}\right) + \left(\left(\frac{-1259.1392167224028}{z + 1} + \left(\frac{-176.6150291621406}{z + 3} + \left(\frac{771.3234287776531}{z + 2} + \frac{12.507343278686905}{z + 4}\right)\right)\right) + \left(\frac{-0.13857109526572012}{z + 5} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right)\right) \cdot \frac{e^{-6.5 - z}}{{\left(z + 6.5\right)}^{\left(0.5 - z\right)}}\right) \]
Alternative 18
Accuracy27.0%
Cost28992
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(z + -1\right) + 7.5\right)}^{\left(z + -0.5\right)}\right) \cdot e^{-0.5 + \left(-6 - z\right)}\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right) + \left(\left(\frac{-0.13857109526572012}{z + 5} + \frac{12.507343278686905}{z + 4}\right) + \left(0.9999999999998099 + \left(\frac{12.0895510149948}{z} + \frac{246.3374466535184}{z \cdot z}\right)\right)\right)\right) \]
Alternative 19
Accuracy27.0%
Cost28992
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(z + -1\right) + 7.5\right)}^{\left(z + -0.5\right)}\right) \cdot e^{-0.5 + \left(-6 - z\right)}\right) \cdot \left(\left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right) + \left(\left(\frac{-0.13857109526572012}{z + 5} + \frac{12.507343278686905}{z + 4}\right) + \left(\left(0.9999999999998099 + \frac{12.0895510149948}{z}\right) + \frac{246.3374466535184}{z \cdot z}\right)\right)\right) \]
Alternative 20
Accuracy27.0%
Cost28736
\[\sqrt{\pi \cdot 2} \cdot \left(\left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot e^{-6.5 - z}\right) \cdot \left(\left(\left(\frac{-0.13857109526572012}{z + 5} + \frac{12.507343278686905}{z + 4}\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right) + \left(0.9999999999998099 + \left(\frac{12.0895510149948}{z} + \frac{246.3374466535184}{z \cdot z}\right)\right)\right)\right) \]
Alternative 21
Accuracy25.7%
Cost27200
\[\sqrt{\pi \cdot 2} \cdot \left(\left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot e^{-6.5 - z}\right) \cdot \left(0.9999999999998099 + \left(\frac{24.458333333348836}{z} + \frac{197.000868054939}{z \cdot z}\right)\right)\right) \]
Alternative 22
Accuracy25.7%
Cost27200
\[\sqrt{\pi \cdot 2} \cdot \left(\frac{{\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z + 6.5}} \cdot \left(0.9999999999998099 + \left(\frac{24.458333333348836}{z} + \frac{197.000868054939}{z \cdot z}\right)\right)\right) \]
Alternative 23
Accuracy25.7%
Cost27200
\[\sqrt{\pi \cdot 2} \cdot \left(\left(\left(0.9999999999998099 + \frac{24.458333333348836}{z}\right) + \frac{197.000868054939}{z \cdot z}\right) \cdot \frac{{\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z + 6.5}}\right) \]
Alternative 24
Accuracy19.7%
Cost26816
\[\sqrt{\pi \cdot 2} \cdot \left(\left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot e^{-6.5 - z}\right) \cdot \left(0.9999999999998099 + \frac{24.458333333348836}{z}\right)\right) \]
Alternative 25
Accuracy19.4%
Cost26756
\[\begin{array}{l} \mathbf{if}\;z \leq 3.96:\\ \;\;\;\;\sqrt{140824.5564565449 \cdot \left(\frac{\pi}{z} \cdot \frac{e^{-13}}{z}\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\pi \cdot 2} \cdot \left(0.9999999999998099 \cdot e^{\left(-6.5 - z\right) + \left(z + -0.5\right) \cdot \log \left(z + 6.5\right)}\right)\\ \end{array} \]
Alternative 26
Accuracy18.8%
Cost26692
\[\begin{array}{l} \mathbf{if}\;z \leq 3.96:\\ \;\;\;\;\sqrt{140824.5564565449 \cdot \left(\frac{\pi}{z} \cdot \frac{e^{-13}}{z}\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\pi \cdot 2} \cdot \left(0.9999999999998099 \cdot \left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot e^{-6.5 - z}\right)\right)\\ \end{array} \]
Alternative 27
Accuracy13.1%
Cost19712
\[\sqrt{140824.5564565449 \cdot \left(\frac{\pi}{z} \cdot \frac{e^{-13}}{z}\right)} \]

Error

Reproduce?

herbie shell --seed 2023126 
(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)))))