Jmat.Real.gamma, branch z greater than 0.5

Average Error: 3.9 → 2.8

Time: 35.6s

Precision: binary64

Cost: 77828

\[z > 0.5\]

Math

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

↓

\[\begin{array}{l} t_0 := \frac{-676.5203681218851}{z} + \frac{1259.1392167224028}{z + 1}\\ t_1 := \left(z + -1\right) + 7\\ t_2 := \sqrt[3]{\pi \cdot 2}\\ \mathbf{if}\;z + -1 \leq 150:\\ \;\;\;\;\left(\left(\left(\sqrt{{t_2}^{2}} \cdot \sqrt{t_2}\right) \cdot {\left(t_1 + 0.5\right)}^{\left(\left(z + -1\right) + 0.5\right)}\right) \cdot \left(e^{-6 - z} \cdot e^{-0.5}\right)\right) \cdot \left(\left(\left(\left(\left(\left(\frac{0.9999999999996197 + \frac{\mathsf{fma}\left(-1259.1392167224028, -z, \left(z + 1\right) \cdot -676.5203681218851\right)}{z \cdot \left(-1 - z\right)} \cdot t_0}{0.9999999999998099 + t_0} + \frac{771.3234287776531}{\left(z + -1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z + -1\right) + 4}\right) + \frac{12.507343278686905}{\left(z + -1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z + -1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t_1}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\pi \cdot 2} \cdot \left(\left(\left(\left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) + \left(\frac{-1259.1392167224028}{z + 1} + \frac{771.3234287776531}{z + 2}\right)\right) + \left(\frac{-176.6150291621406}{z + 3} + \left(\left(\frac{-0.13857109526572012}{z + 5} + \left(\frac{12.507343278686905}{z + 4} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right) \cdot e^{\left(z + -0.5\right) \cdot \log \left(z + 6.5\right) + \left(-6.5 - z\right)}\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (z)
 :precision binary64
 (let* ((t_0 (+ (/ -676.5203681218851 z) (/ 1259.1392167224028 (+ z 1.0))))
        (t_1 (+ (+ z -1.0) 7.0))
        (t_2 (cbrt (* PI 2.0))))
   (if (<= (+ z -1.0) 150.0)
     (*
      (*
       (*
        (* (sqrt (pow t_2 2.0)) (sqrt t_2))
        (pow (+ t_1 0.5) (+ (+ z -1.0) 0.5)))
       (* (exp (- -6.0 z)) (exp -0.5)))
      (+
       (+
        (+
         (+
          (+
           (+
            (/
             (+
              0.9999999999996197
              (*
               (/
                (fma
                 -1259.1392167224028
                 (- z)
                 (* (+ z 1.0) -676.5203681218851))
                (* z (- -1.0 z)))
               t_0))
             (+ 0.9999999999998099 t_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 t_1))
       (/ 1.5056327351493116e-7 (+ (+ z -1.0) 8.0))))
     (*
      (sqrt (* PI 2.0))
      (*
       (+
        (+
         (+ (/ 676.5203681218851 z) 0.9999999999998099)
         (+ (/ -1259.1392167224028 (+ z 1.0)) (/ 771.3234287776531 (+ z 2.0))))
        (+
         (/ -176.6150291621406 (+ z 3.0))
         (+
          (+
           (/ -0.13857109526572012 (+ z 5.0))
           (+
            (/ 12.507343278686905 (+ z 4.0))
            (/ 9.984369578019572e-6 (+ z 6.0))))
          (/ 1.5056327351493116e-7 (+ z 7.0)))))
       (exp (+ (* (+ z -0.5) (log (+ z 6.5))) (- -6.5 z))))))))

C

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

↓

double code(double z) {
	double t_0 = (-676.5203681218851 / z) + (1259.1392167224028 / (z + 1.0));
	double t_1 = (z + -1.0) + 7.0;
	double t_2 = cbrt((((double) M_PI) * 2.0));
	double tmp;
	if ((z + -1.0) <= 150.0) {
		tmp = (((sqrt(pow(t_2, 2.0)) * sqrt(t_2)) * pow((t_1 + 0.5), ((z + -1.0) + 0.5))) * (exp((-6.0 - z)) * exp(-0.5))) * ((((((((0.9999999999996197 + ((fma(-1259.1392167224028, -z, ((z + 1.0) * -676.5203681218851)) / (z * (-1.0 - z))) * t_0)) / (0.9999999999998099 + t_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 / t_1)) + (1.5056327351493116e-7 / ((z + -1.0) + 8.0)));
	} else {
		tmp = sqrt((((double) M_PI) * 2.0)) * (((((676.5203681218851 / z) + 0.9999999999998099) + ((-1259.1392167224028 / (z + 1.0)) + (771.3234287776531 / (z + 2.0)))) + ((-176.6150291621406 / (z + 3.0)) + (((-0.13857109526572012 / (z + 5.0)) + ((12.507343278686905 / (z + 4.0)) + (9.984369578019572e-6 / (z + 6.0)))) + (1.5056327351493116e-7 / (z + 7.0))))) * exp((((z + -0.5) * log((z + 6.5))) + (-6.5 - z))));
	}
	return tmp;
}

Julia

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

↓

function code(z)
	t_0 = Float64(Float64(-676.5203681218851 / z) + Float64(1259.1392167224028 / Float64(z + 1.0)))
	t_1 = Float64(Float64(z + -1.0) + 7.0)
	t_2 = cbrt(Float64(pi * 2.0))
	tmp = 0.0
	if (Float64(z + -1.0) <= 150.0)
		tmp = Float64(Float64(Float64(Float64(sqrt((t_2 ^ 2.0)) * sqrt(t_2)) * (Float64(t_1 + 0.5) ^ Float64(Float64(z + -1.0) + 0.5))) * Float64(exp(Float64(-6.0 - z)) * exp(-0.5))) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(0.9999999999996197 + Float64(Float64(fma(-1259.1392167224028, Float64(-z), Float64(Float64(z + 1.0) * -676.5203681218851)) / Float64(z * Float64(-1.0 - z))) * t_0)) / Float64(0.9999999999998099 + t_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 / t_1)) + Float64(1.5056327351493116e-7 / Float64(Float64(z + -1.0) + 8.0))));
	else
		tmp = Float64(sqrt(Float64(pi * 2.0)) * Float64(Float64(Float64(Float64(Float64(676.5203681218851 / z) + 0.9999999999998099) + Float64(Float64(-1259.1392167224028 / Float64(z + 1.0)) + Float64(771.3234287776531 / Float64(z + 2.0)))) + Float64(Float64(-176.6150291621406 / Float64(z + 3.0)) + Float64(Float64(Float64(-0.13857109526572012 / Float64(z + 5.0)) + Float64(Float64(12.507343278686905 / Float64(z + 4.0)) + Float64(9.984369578019572e-6 / Float64(z + 6.0)))) + Float64(1.5056327351493116e-7 / Float64(z + 7.0))))) * exp(Float64(Float64(Float64(z + -0.5) * log(Float64(z + 6.5))) + Float64(-6.5 - z)))));
	end
	return tmp
end

Wolfram

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

↓

code[z_] := Block[{t$95$0 = N[(N[(-676.5203681218851 / z), $MachinePrecision] + N[(1259.1392167224028 / N[(z + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(z + -1.0), $MachinePrecision] + 7.0), $MachinePrecision]}, Block[{t$95$2 = N[Power[N[(Pi * 2.0), $MachinePrecision], 1/3], $MachinePrecision]}, If[LessEqual[N[(z + -1.0), $MachinePrecision], 150.0], N[(N[(N[(N[(N[Sqrt[N[Power[t$95$2, 2.0], $MachinePrecision]], $MachinePrecision] * N[Sqrt[t$95$2], $MachinePrecision]), $MachinePrecision] * N[Power[N[(t$95$1 + 0.5), $MachinePrecision], N[(N[(z + -1.0), $MachinePrecision] + 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[Exp[N[(-6.0 - z), $MachinePrecision]], $MachinePrecision] * N[Exp[-0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(0.9999999999996197 + N[(N[(N[(-1259.1392167224028 * (-z) + N[(N[(z + 1.0), $MachinePrecision] * -676.5203681218851), $MachinePrecision]), $MachinePrecision] / N[(z * N[(-1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision] / N[(0.9999999999998099 + t$95$0), $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 / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(N[(z + -1.0), $MachinePrecision] + 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[N[(Pi * 2.0), $MachinePrecision]], $MachinePrecision] * N[(N[(N[(N[(N[(676.5203681218851 / z), $MachinePrecision] + 0.9999999999998099), $MachinePrecision] + N[(N[(-1259.1392167224028 / N[(z + 1.0), $MachinePrecision]), $MachinePrecision] + N[(771.3234287776531 / N[(z + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-176.6150291621406 / N[(z + 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(-0.13857109526572012 / N[(z + 5.0), $MachinePrecision]), $MachinePrecision] + N[(N[(12.507343278686905 / N[(z + 4.0), $MachinePrecision]), $MachinePrecision] + N[(9.984369578019572e-6 / N[(z + 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(z + 7.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Exp[N[(N[(N[(z + -0.5), $MachinePrecision] * N[Log[N[(z + 6.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(-6.5 - z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z 1) < 150

   1. Initial program 2.7

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

   2. Applied egg-rr 2.8

      \[\leadsto \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\color{blue}{\frac{0.9999999999996197 - \left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z - -1}\right) \cdot \left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z - -1}\right)}{0.9999999999998099 - \left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z - -1}\right)}} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \]

   3. Applied egg-rr 2.7

      \[\leadsto \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\frac{0.9999999999996197 - \color{blue}{\frac{\mathsf{fma}\left(-1259.1392167224028, -z, \left(z + 1\right) \cdot -676.5203681218851\right)}{\left(z + 1\right) \cdot \left(-z\right)}} \cdot \left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z - -1}\right)}{0.9999999999998099 - \left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z - -1}\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \]

   4. Applied egg-rr 2.7

      \[\leadsto \left(\left(\color{blue}{\left(\sqrt{{\left(\sqrt[3]{\pi \cdot 2}\right)}^{2}} \cdot \sqrt{\sqrt[3]{\pi \cdot 2}}\right)} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\frac{0.9999999999996197 - \frac{\mathsf{fma}\left(-1259.1392167224028, -z, \left(z + 1\right) \cdot -676.5203681218851\right)}{\left(z + 1\right) \cdot \left(-z\right)} \cdot \left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z - -1}\right)}{0.9999999999998099 - \left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z - -1}\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \]

   5. Applied egg-rr 2.7

      \[\leadsto \left(\left(\left(\sqrt{{\left(\sqrt[3]{\pi \cdot 2}\right)}^{2}} \cdot \sqrt{\sqrt[3]{\pi \cdot 2}}\right) \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot \color{blue}{\left(e^{-\left(z + 6\right)} \cdot e^{-0.5}\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\frac{0.9999999999996197 - \frac{\mathsf{fma}\left(-1259.1392167224028, -z, \left(z + 1\right) \cdot -676.5203681218851\right)}{\left(z + 1\right) \cdot \left(-z\right)} \cdot \left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z - -1}\right)}{0.9999999999998099 - \left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z - -1}\right)} + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \]

   if 150 < (-.f64 z 1)

   1. Initial program 64.0

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

   2. Simplified 64.0

      \[\leadsto \color{blue}{\sqrt{\pi \cdot 2} \cdot \left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{z}\right) + \left(\frac{-1259.1392167224028}{z + 1} + \frac{771.3234287776531}{2 + z}\right)\right) + \left(\frac{-176.6150291621406}{z + 3} + \left(\left(\frac{-0.13857109526572012}{z + 5} + \left(\frac{12.507343278686905}{z - -4} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right) \cdot \frac{{\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z + 6.5}}\right)} \]
      Proof
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 z)) (+.f64 (/.f64 -3147848041806007/2500000000000 (+.f64 z 1)) (/.f64 7713234287776531/10000000000000 (+.f64 2 z)))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 z 3)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (Rewrite<= --rgt-identity_binary64 (-.f64 z 0)))) (+.f64 (/.f64 -3147848041806007/2500000000000 (+.f64 z 1)) (/.f64 7713234287776531/10000000000000 (+.f64 2 z)))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 z 3)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 z (Rewrite<= metadata-eval (-.f64 1 1))))) (+.f64 (/.f64 -3147848041806007/2500000000000 (+.f64 z 1)) (/.f64 7713234287776531/10000000000000 (+.f64 2 z)))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 z 3)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 1)))) (+.f64 (/.f64 -3147848041806007/2500000000000 (+.f64 z 1)) (/.f64 7713234287776531/10000000000000 (+.f64 2 z)))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 z 3)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (+.f64 (/.f64 -3147848041806007/2500000000000 (+.f64 z (Rewrite<= metadata-eval (neg.f64 -1)))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z)))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 z 3)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (+.f64 (/.f64 -3147848041806007/2500000000000 (Rewrite<= sub-neg_binary64 (-.f64 z -1))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z)))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 z 3)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (+.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 z (Rewrite<= metadata-eval (-.f64 1 2)))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z)))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 z 3)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (+.f64 (/.f64 -3147848041806007/2500000000000 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z)))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 z 3)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (+.f64 (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2)) (/.f64 7713234287776531/10000000000000 (Rewrite=> +-commutative_binary64 (+.f64 z 2))))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 z 3)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (+.f64 (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2)) (/.f64 7713234287776531/10000000000000 (+.f64 z (Rewrite<= metadata-eval (+.f64 -1 3)))))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 z 3)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (+.f64 (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2)) (/.f64 7713234287776531/10000000000000 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 z -1) 3))))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 z 3)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (+.f64 (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2)) (/.f64 7713234287776531/10000000000000 (+.f64 (+.f64 z (Rewrite<= metadata-eval (neg.f64 1))) 3)))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 z 3)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (+.f64 (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2)) (/.f64 7713234287776531/10000000000000 (+.f64 (Rewrite<= sub-neg_binary64 (-.f64 z 1)) 3)))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 z 3)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3)))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 z 3)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 5 points increase in error, 4 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 z (Rewrite<= metadata-eval (neg.f64 -3)))) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 z (neg.f64 (Rewrite<= metadata-eval (-.f64 1 4))))) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (+.f64 (/.f64 -883075145810703/5000000000000 (Rewrite<= sub-neg_binary64 (-.f64 z (-.f64 1 4)))) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (+.f64 (/.f64 -883075145810703/5000000000000 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 4))) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z (Rewrite<= metadata-eval (neg.f64 -5)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z (neg.f64 (Rewrite<= metadata-eval (-.f64 1 6))))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (Rewrite<= sub-neg_binary64 (-.f64 z (-.f64 1 6)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 6))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6)) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z (Rewrite<= metadata-eval (-.f64 1 5)))) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6)) (+.f64 (/.f64 2501468655737381/200000000000000 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 5))) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6)) (+.f64 (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z (Rewrite<= metadata-eval (neg.f64 -6)))))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6)) (+.f64 (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z (neg.f64 (Rewrite<= metadata-eval (-.f64 1 7))))))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6)) (+.f64 (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5)) (/.f64 2496092394504893/250000000000000000000 (Rewrite<= sub-neg_binary64 (-.f64 z (-.f64 1 7)))))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4)) (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6)) (+.f64 (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5)) (/.f64 2496092394504893/250000000000000000000 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 7))))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4)) (+.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6)) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4)) (+.f64 (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5)) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6)))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4)) (+.f64 (+.f64 (+.f64 (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5)) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z (Rewrite<= metadata-eval (neg.f64 -7))))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4)) (+.f64 (+.f64 (+.f64 (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5)) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 z (neg.f64 (Rewrite<= metadata-eval (-.f64 1 8)))))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4)) (+.f64 (+.f64 (+.f64 (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5)) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (Rewrite<= sub-neg_binary64 (-.f64 z (-.f64 1 8))))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4)) (+.f64 (+.f64 (+.f64 (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5)) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 8)))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4)) (Rewrite<= associate-+r+_binary64 (+.f64 (+.f64 (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5)) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7)) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 1 points increase in error, 2 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (+.f64 (+.f64 (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5)) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7)) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8)))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 31 points increase in error, 33 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (+.f64 (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5)) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7)) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 28 points increase in error, 26 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7)) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8)))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 27 points increase in error, 24 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8)))) (/.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 28 points increase in error, 19 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))) (/.f64 (pow.f64 (+.f64 z (Rewrite<= metadata-eval (+.f64 -1 15/2))) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))) (/.f64 (pow.f64 (+.f64 z (+.f64 -1 (Rewrite<= metadata-eval (+.f64 7 1/2)))) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))) (/.f64 (pow.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 z -1) (+.f64 7 1/2))) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))) (/.f64 (pow.f64 (+.f64 (+.f64 z (Rewrite<= metadata-eval (neg.f64 1))) (+.f64 7 1/2)) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))) (/.f64 (pow.f64 (+.f64 (Rewrite<= sub-neg_binary64 (-.f64 z 1)) (+.f64 7 1/2)) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))) (/.f64 (pow.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2)) (+.f64 z -1/2)) (exp.f64 (+.f64 z 13/2))))): 7 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))) (/.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 z (Rewrite<= metadata-eval (neg.f64 1/2)))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))) (/.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (Rewrite<= sub-neg_binary64 (-.f64 z 1/2))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))) (/.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (-.f64 z (Rewrite<= metadata-eval (-.f64 1 1/2)))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))) (/.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 1/2))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))) (/.f64 (Rewrite<= *-rgt-identity_binary64 (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) 1)) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))) (/.f64 (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) 1) (exp.f64 (+.f64 z (Rewrite<= metadata-eval (+.f64 -1 15/2))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))) (/.f64 (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) 1) (exp.f64 (+.f64 z (+.f64 -1 (Rewrite<= metadata-eval (+.f64 7 1/2)))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))) (/.f64 (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) 1) (exp.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 z -1) (+.f64 7 1/2))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))) (/.f64 (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) 1) (exp.f64 (+.f64 (+.f64 z (Rewrite<= metadata-eval (neg.f64 1))) (+.f64 7 1/2)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))) (/.f64 (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) 1) (exp.f64 (+.f64 (Rewrite<= sub-neg_binary64 (-.f64 z 1)) (+.f64 7 1/2)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))) (/.f64 (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) 1) (exp.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2)))))): 2 points increase in error, 5 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))) (Rewrite<= associate-*r/_binary64 (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 1 (exp.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2))))))): 24 points increase in error, 28 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (Rewrite<= exp-neg_binary64 (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2))))))): 22 points increase in error, 23 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8)))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2))))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))))): 45 points increase in error, 49 points decrease in error
      (*.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2))))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8)))): 24 points increase in error, 32 points decrease in error

   3. Applied egg-rr 7.7

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

4. Final simplification 2.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;z + -1 \leq 150:\\ \;\;\;\;\left(\left(\left(\sqrt{{\left(\sqrt[3]{\pi \cdot 2}\right)}^{2}} \cdot \sqrt{\sqrt[3]{\pi \cdot 2}}\right) \cdot {\left(\left(\left(z + -1\right) + 7\right) + 0.5\right)}^{\left(\left(z + -1\right) + 0.5\right)}\right) \cdot \left(e^{-6 - z} \cdot e^{-0.5}\right)\right) \cdot \left(\left(\left(\left(\left(\left(\frac{0.9999999999996197 + \frac{\mathsf{fma}\left(-1259.1392167224028, -z, \left(z + 1\right) \cdot -676.5203681218851\right)}{z \cdot \left(-1 - z\right)} \cdot \left(\frac{-676.5203681218851}{z} + \frac{1259.1392167224028}{z + 1}\right)}{0.9999999999998099 + \left(\frac{-676.5203681218851}{z} + \frac{1259.1392167224028}{z + 1}\right)} + \frac{771.3234287776531}{\left(z + -1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z + -1\right) + 4}\right) + \frac{12.507343278686905}{\left(z + -1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z + -1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z + -1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\pi \cdot 2} \cdot \left(\left(\left(\left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) + \left(\frac{-1259.1392167224028}{z + 1} + \frac{771.3234287776531}{z + 2}\right)\right) + \left(\frac{-176.6150291621406}{z + 3} + \left(\left(\frac{-0.13857109526572012}{z + 5} + \left(\frac{12.507343278686905}{z + 4} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right) \cdot e^{\left(z + -0.5\right) \cdot \log \left(z + 6.5\right) + \left(-6.5 - z\right)}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	2.3
Cost	69764

\[\begin{array}{l} t_0 := \frac{771.3234287776531}{\left(z + -1\right) + 3}\\ t_1 := \sqrt{\pi \cdot 2}\\ t_2 := \frac{12.507343278686905}{\left(z + -1\right) + 5}\\ t_3 := \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8}\\ t_4 := \frac{-176.6150291621406}{\left(z + -1\right) + 4}\\ t_5 := \left(z + -1\right) + 7\\ t_6 := \frac{9.984369578019572 \cdot 10^{-6}}{t_5}\\ t_7 := \frac{-0.13857109526572012}{\left(z + -1\right) + 6}\\ t_8 := \frac{-676.5203681218851}{z} + \frac{1259.1392167224028}{z + 1}\\ \mathbf{if}\;\left(e^{-0.5 + \left(\left(1 - z\right) + -7\right)} \cdot \left({\left(t_5 + 0.5\right)}^{\left(\left(z + -1\right) + 0.5\right)} \cdot t_1\right)\right) \cdot \left(t_3 + \left(t_6 + \left(t_7 + \left(t_2 + \left(t_4 + \left(t_0 + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 + \left(z + -1\right)}\right) + \frac{-1259.1392167224028}{\left(z + -1\right) + 2}\right)\right)\right)\right)\right)\right)\right) \leq 5 \cdot 10^{+232}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\frac{0.9999999999996197 + \frac{\mathsf{fma}\left(-1259.1392167224028, -z, \left(z + 1\right) \cdot -676.5203681218851\right)}{z \cdot \left(-1 - z\right)} \cdot t_8}{0.9999999999998099 + t_8} + t_0\right) + t_4\right) + t_2\right) + t_7\right) + t_6\right) + t_3\right) \cdot \frac{t_1 \cdot {\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z + 6.5}}\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \left(\left(\left(\left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) + \left(\frac{-1259.1392167224028}{z + 1} + \frac{771.3234287776531}{z + 2}\right)\right) + \left(\frac{-176.6150291621406}{z + 3} + \left(\left(\frac{-0.13857109526572012}{z + 5} + \left(\frac{12.507343278686905}{z + 4} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right) \cdot e^{\left(z + -0.5\right) \cdot \log \left(z + 6.5\right) + \left(-6.5 - z\right)}\right)\\ \end{array} \]

Alternative 2
Error	2.3
Cost	68548

\[\begin{array}{l} t_0 := \frac{771.3234287776531}{\left(z + -1\right) + 3}\\ t_1 := \frac{-0.13857109526572012}{\left(z + -1\right) + 6}\\ t_2 := \sqrt{\pi \cdot 2}\\ t_3 := \frac{12.507343278686905}{\left(z + -1\right) + 5}\\ t_4 := \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8}\\ t_5 := \left(z + -1\right) + 7\\ t_6 := \frac{9.984369578019572 \cdot 10^{-6}}{t_5}\\ t_7 := \frac{-1259.1392167224028}{z + 1}\\ t_8 := {\left(t_5 + 0.5\right)}^{\left(\left(z + -1\right) + 0.5\right)} \cdot t_2\\ t_9 := \frac{-176.6150291621406}{\left(z + -1\right) + 4}\\ \mathbf{if}\;\left(e^{-0.5 + \left(\left(1 - z\right) + -7\right)} \cdot t_8\right) \cdot \left(t_4 + \left(t_6 + \left(t_1 + \left(t_3 + \left(t_9 + \left(t_0 + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 + \left(z + -1\right)}\right) + \frac{-1259.1392167224028}{\left(z + -1\right) + 2}\right)\right)\right)\right)\right)\right)\right) \leq 5 \cdot 10^{+232}:\\ \;\;\;\;\left(\left(e^{-6 - z} \cdot e^{-0.5}\right) \cdot t_8\right) \cdot \left(t_4 + \left(t_6 + \left(t_1 + \left(t_3 + \left(t_9 + \left(t_0 + \left(\left(\frac{676.5203681218851}{z} + t_7\right) + 0.9999999999998099\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot \left(\left(\left(\left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) + \left(t_7 + \frac{771.3234287776531}{z + 2}\right)\right) + \left(\frac{-176.6150291621406}{z + 3} + \left(\left(\frac{-0.13857109526572012}{z + 5} + \left(\frac{12.507343278686905}{z + 4} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right) \cdot e^{\left(z + -0.5\right) \cdot \log \left(z + 6.5\right) + \left(-6.5 - z\right)}\right)\\ \end{array} \]

Alternative 3
Error	2.4
Cost	67268

\[\begin{array}{l} t_0 := \left(z + -1\right) + 7\\ t_1 := \left(\left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) + \left(\frac{-1259.1392167224028}{z + 1} + \frac{771.3234287776531}{z + 2}\right)\right) + \left(\frac{-176.6150291621406}{z + 3} + \left(\left(\frac{-0.13857109526572012}{z + 5} + \left(\frac{12.507343278686905}{z + 4} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\\ t_2 := \sqrt{\pi \cdot 2}\\ \mathbf{if}\;\left(e^{-0.5 + \left(\left(1 - z\right) + -7\right)} \cdot \left({\left(t_0 + 0.5\right)}^{\left(\left(z + -1\right) + 0.5\right)} \cdot t_2\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{t_0} + \left(\frac{-0.13857109526572012}{\left(z + -1\right) + 6} + \left(\frac{12.507343278686905}{\left(z + -1\right) + 5} + \left(\frac{-176.6150291621406}{\left(z + -1\right) + 4} + \left(\frac{771.3234287776531}{\left(z + -1\right) + 3} + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 + \left(z + -1\right)}\right) + \frac{-1259.1392167224028}{\left(z + -1\right) + 2}\right)\right)\right)\right)\right)\right)\right) \leq 5 \cdot 10^{+232}:\\ \;\;\;\;t_2 \cdot \left(t_1 \cdot \frac{{\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z} \cdot e^{6.5}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot \left(t_1 \cdot e^{\left(z + -0.5\right) \cdot \log \left(z + 6.5\right) + \left(-6.5 - z\right)}\right)\\ \end{array} \]

Alternative 4
Error	2.8
Cost	65220

\[\begin{array}{l} t_0 := \left(z + -1\right) + 7\\ t_1 := \frac{-676.5203681218851}{z} + \frac{1259.1392167224028}{z + 1}\\ \mathbf{if}\;z + -1 \leq 150:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\frac{0.9999999999996197 + \frac{\mathsf{fma}\left(-1259.1392167224028, -z, \left(z + 1\right) \cdot -676.5203681218851\right)}{z \cdot \left(-1 - z\right)} \cdot t_1}{0.9999999999998099 + t_1} + \frac{771.3234287776531}{\left(z + -1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z + -1\right) + 4}\right) + \frac{12.507343278686905}{\left(z + -1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z + -1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t_0}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8}\right) \cdot \left(\left({\left(t_0 + 0.5\right)}^{\left(\left(z + -1\right) + 0.5\right)} \cdot \left(\sqrt{{\left(\sqrt[3]{\pi \cdot 2}\right)}^{2}} \cdot {\left(\pi \cdot 2\right)}^{0.16666666666666666}\right)\right) \cdot e^{-0.5 + \left(\left(1 - z\right) + -7\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\pi \cdot 2} \cdot \left(\left(\left(\left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) + \left(\frac{-1259.1392167224028}{z + 1} + \frac{771.3234287776531}{z + 2}\right)\right) + \left(\frac{-176.6150291621406}{z + 3} + \left(\left(\frac{-0.13857109526572012}{z + 5} + \left(\frac{12.507343278686905}{z + 4} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right) \cdot e^{\left(z + -0.5\right) \cdot \log \left(z + 6.5\right) + \left(-6.5 - z\right)}\right)\\ \end{array} \]

Alternative 5
Error	2.4
Cost	64324

\[\begin{array}{l} t_0 := \frac{771.3234287776531}{\left(z + -1\right) + 3}\\ t_1 := \frac{-0.13857109526572012}{\left(z + -1\right) + 6}\\ t_2 := \frac{12.507343278686905}{\left(z + -1\right) + 5}\\ t_3 := \frac{z}{-1259.1392167224028} + -0.0007941933558411801\\ t_4 := \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8}\\ t_5 := \frac{-176.6150291621406}{\left(z + -1\right) + 4}\\ t_6 := \left(z + -1\right) + 7\\ t_7 := \frac{9.984369578019572 \cdot 10^{-6}}{t_6}\\ t_8 := \left(z + -1\right) + 7.5\\ t_9 := \frac{-1259.1392167224028}{z + 1}\\ t_10 := \sqrt{\pi \cdot 2}\\ t_11 := \frac{-676.5203681218851 \cdot t_3 - z}{z \cdot t_3}\\ \mathbf{if}\;\left(e^{-0.5 + \left(\left(1 - z\right) + -7\right)} \cdot \left({\left(t_6 + 0.5\right)}^{\left(\left(z + -1\right) + 0.5\right)} \cdot t_10\right)\right) \cdot \left(t_4 + \left(t_7 + \left(t_1 + \left(t_2 + \left(t_5 + \left(t_0 + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 + \left(z + -1\right)}\right) + \frac{-1259.1392167224028}{\left(z + -1\right) + 2}\right)\right)\right)\right)\right)\right)\right) \leq 5 \cdot 10^{+232}:\\ \;\;\;\;\frac{t_10 \cdot {t_8}^{\left(z + -0.5\right)}}{e^{t_8}} \cdot \left(t_4 + \left(t_7 + \left(t_1 + \left(t_2 + \left(t_5 + \left(t_0 + \frac{0.9999999999996197 + \left(\frac{676.5203681218851}{z} + t_9\right) \cdot t_11}{0.9999999999998099 + t_11}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_10 \cdot \left(\left(\left(\left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) + \left(t_9 + \frac{771.3234287776531}{z + 2}\right)\right) + \left(\frac{-176.6150291621406}{z + 3} + \left(\left(\frac{-0.13857109526572012}{z + 5} + \left(\frac{12.507343278686905}{z + 4} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right) \cdot e^{\left(z + -0.5\right) \cdot \log \left(z + 6.5\right) + \left(-6.5 - z\right)}\right)\\ \end{array} \]

Alternative 6
Error	2.3
Cost	62276

\[\begin{array}{l} t_0 := \frac{771.3234287776531}{\left(z + -1\right) + 3}\\ t_1 := \frac{-0.13857109526572012}{\left(z + -1\right) + 6}\\ t_2 := \sqrt{\pi \cdot 2}\\ t_3 := \frac{12.507343278686905}{\left(z + -1\right) + 5}\\ t_4 := \frac{-1259.1392167224028}{z + 1}\\ t_5 := \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8}\\ t_6 := \frac{-176.6150291621406}{\left(z + -1\right) + 4}\\ t_7 := \left(z + -1\right) + 7\\ t_8 := e^{-0.5 + \left(\left(1 - z\right) + -7\right)} \cdot \left({\left(t_7 + 0.5\right)}^{\left(\left(z + -1\right) + 0.5\right)} \cdot t_2\right)\\ t_9 := \frac{9.984369578019572 \cdot 10^{-6}}{t_7}\\ \mathbf{if}\;t_8 \cdot \left(t_5 + \left(t_9 + \left(t_1 + \left(t_3 + \left(t_6 + \left(t_0 + \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 + \left(z + -1\right)}\right) + \frac{-1259.1392167224028}{\left(z + -1\right) + 2}\right)\right)\right)\right)\right)\right)\right) \leq 5 \cdot 10^{+232}:\\ \;\;\;\;t_8 \cdot \left(t_5 + \left(t_9 + \left(t_1 + \left(t_3 + \left(t_6 + \left(t_0 + \left(\left(\frac{676.5203681218851}{z} + t_4\right) + 0.9999999999998099\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot \left(\left(\left(\left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) + \left(t_4 + \frac{771.3234287776531}{z + 2}\right)\right) + \left(\frac{-176.6150291621406}{z + 3} + \left(\left(\frac{-0.13857109526572012}{z + 5} + \left(\frac{12.507343278686905}{z + 4} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right) \cdot e^{\left(z + -0.5\right) \cdot \log \left(z + 6.5\right) + \left(-6.5 - z\right)}\right)\\ \end{array} \]

Alternative 7
Error	2.8
Cost	39300

\[\begin{array}{l} t_0 := \left(z + -1\right) + 7\\ t_1 := \sqrt{\pi \cdot 2}\\ t_2 := \frac{-676.5203681218851}{z} + \frac{1259.1392167224028}{z + 1}\\ \mathbf{if}\;z + -1 \leq 150:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\frac{0.9999999999996197 + \frac{\mathsf{fma}\left(-1259.1392167224028, -z, \left(z + 1\right) \cdot -676.5203681218851\right)}{z \cdot \left(-1 - z\right)} \cdot t_2}{0.9999999999998099 + t_2} + \frac{771.3234287776531}{\left(z + -1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z + -1\right) + 4}\right) + \frac{12.507343278686905}{\left(z + -1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z + -1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t_0}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z + -1\right) + 8}\right) \cdot \left(e^{-0.5 + \left(\left(1 - z\right) + -7\right)} \cdot \left({\left(t_0 + 0.5\right)}^{\left(\left(z + -1\right) + 0.5\right)} \cdot t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \left(\left(\left(\left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) + \left(\frac{-1259.1392167224028}{z + 1} + \frac{771.3234287776531}{z + 2}\right)\right) + \left(\frac{-176.6150291621406}{z + 3} + \left(\left(\frac{-0.13857109526572012}{z + 5} + \left(\frac{12.507343278686905}{z + 4} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\right) \cdot e^{\left(z + -0.5\right) \cdot \log \left(z + 6.5\right) + \left(-6.5 - z\right)}\right)\\ \end{array} \]

Alternative 8
Error	2.4
Cost	29700

\[\begin{array}{l} t_0 := \sqrt{\pi \cdot 2}\\ t_1 := \left(\left(\frac{676.5203681218851}{z} + 0.9999999999998099\right) + \left(\frac{-1259.1392167224028}{z + 1} + \frac{771.3234287776531}{z + 2}\right)\right) + \left(\frac{-176.6150291621406}{z + 3} + \left(\left(\frac{-0.13857109526572012}{z + 5} + \left(\frac{12.507343278686905}{z + 4} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\right)\\ \mathbf{if}\;z \leq 137.05897260552334:\\ \;\;\;\;t_0 \cdot \left(t_1 \cdot \left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot e^{-6.5 - z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left(t_1 \cdot e^{\left(z + -0.5\right) \cdot \log \left(z + 6.5\right) + \left(-6.5 - z\right)}\right)\\ \end{array} \]

Alternative 9
Error	3.8
Cost	29504

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

Alternative 10
Error	48.9
Cost	29252

\[\begin{array}{l} t_0 := 0.9999999999998099 + \frac{188.7045801771354}{z}\\ t_1 := \sqrt{\pi \cdot 2}\\ t_2 := \frac{{\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z + 6.5}}\\ t_3 := \frac{-176.6150291621406}{z + 3} + \left(\left(\frac{-0.13857109526572012}{z + 5} + \left(\frac{12.507343278686905}{z + 4} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right)\\ \mathbf{if}\;z \leq 13.297409425904254:\\ \;\;\;\;t_1 \cdot \left(\left(t_3 + t_0\right) \cdot t_2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \left(t_2 \cdot \left(t_3 + \left(t_0 + \frac{-283.5076408329034}{z \cdot z}\right)\right)\right)\\ \end{array} \]

Alternative 11
Error	50.0
Cost	28736

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

Alternative 12
Error	53.4
Cost	28608

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

Alternative 13
Error	56.3
Cost	28420

\[\begin{array}{l} t_0 := \sqrt{\pi \cdot 2}\\ t_1 := \frac{\sqrt{0.15384615384615385}}{e^{6.5}}\\ t_2 := \left(\frac{-0.13857109526572012}{z + 5} + \left(\frac{12.507343278686905}{z + 4} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\\ \mathbf{if}\;z \leq 3:\\ \;\;\;\;t_0 \cdot \left(\left(0.9999999999998099 + \left(t_2 + \left(\frac{529.8450874864218}{z \cdot z} + \frac{-176.6150291621406}{z}\right)\right)\right) \cdot t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left(t_1 \cdot \left(0.9999999999998099 + \left(t_2 + \left(z \cdot 19.623892129126734 + -58.8716763873802\right)\right)\right)\right)\\ \end{array} \]

Alternative 14
Error	59.6
Cost	28032

\[\sqrt{\pi \cdot 2} \cdot \left(\frac{\sqrt{0.15384615384615385}}{e^{6.5}} \cdot \left(0.9999999999998099 + \left(\left(\left(\frac{-0.13857109526572012}{z + 5} + \left(\frac{12.507343278686905}{z + 4} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right) + \left(z \cdot 19.623892129126734 + -58.8716763873802\right)\right)\right)\right) \]

Alternative 15
Error	63.1
Cost	27904

\[\sqrt{\pi \cdot 2} \cdot \left(\frac{\sqrt{0.15384615384615385}}{e^{6.5}} \cdot \left(0.9999999999998099 + \left(\left(\left(\frac{-0.13857109526572012}{z + 5} + \left(\frac{12.507343278686905}{z + 4} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\right) + \frac{-176.6150291621406}{z}\right)\right)\right) \]

Alternative 16
Error	63.1
Cost	27648

\[\sqrt{\pi \cdot 2} \cdot \left(\frac{\sqrt{0.15384615384615385}}{e^{6.5}} \cdot \left(0.9999999999998099 + \left(-58.8716763873802 + \left(\frac{1.5056327351493116 \cdot 10^{-7}}{z + 7} + \left(\frac{-0.13857109526572012}{z + 5} + \left(\frac{12.507343278686905}{z + 4} + \frac{9.984369578019572 \cdot 10^{-6}}{z}\right)\right)\right)\right)\right)\right) \]

Alternative 17
Error	63.1
Cost	27520

\[\sqrt{\pi \cdot 2} \cdot \left(\frac{\sqrt{0.15384615384615385}}{e^{6.5}} \cdot \left(0.9999999999998099 + \left(-58.8716763873802 + \left(\frac{1.5056327351493116 \cdot 10^{-7}}{z + 7} + \left(\frac{-0.13857109526572012}{z + 5} + \left(\frac{12.507343278686905}{z + 4} + 1.6640615963365953 \cdot 10^{-6}\right)\right)\right)\right)\right)\right) \]

Reproduce

herbie shell --seed 2022296 
(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)))))