Average Error: 3.9 → 2.3
Time: 26.2s
Precision: binary64
Cost: 42500
\[z > 0.5\]
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(z - 1\right) + 8}\right) \]
↓
\[\begin{array}{l} t_0 := \frac{-176.6150291621406}{z + 3}\\ t_1 := \frac{-0.13857109526572012}{z + 5}\\ t_2 := \frac{771.3234287776531}{z + 2}\\ t_3 := \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\\ t_4 := \frac{12.507343278686905}{z + 4}\\ t_5 := \frac{-1259.1392167224028}{z + 1}\\ t_6 := \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\\ \mathbf{if}\;z + -1 \leq 140:\\ \;\;\;\;\sqrt{\pi \cdot 2} \cdot \left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot \frac{\left(0.9999999999998099 + \left(\left(\left(\left(\frac{676.5203681218851}{z} + t_5\right) + t_0\right) + t_2\right) + t_4\right)\right) + \left(t_6 + \left(t_1 + t_3\right)\right)}{e^{z + 6.5}}\right)\\ \mathbf{else}:\\ \;\;\;\;e^{\mathsf{fma}\left(0.5, \log \left(\pi \cdot 2\right), \mathsf{fma}\left(z + -0.5, \log \left(z + 6.5\right), -6.5 - z\right)\right)} \cdot \left(\left(\left(\left(t_5 + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \left(t_0 + t_2\right)\right) + \left(t_4 + t_1\right)\right) + \left(t_6 + t_3\right)\right)\\ \end{array} \]
(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 (/ -176.6150291621406 (+ z 3.0)))
        (t_1 (/ -0.13857109526572012 (+ z 5.0)))
        (t_2 (/ 771.3234287776531 (+ z 2.0)))
        (t_3 (/ 9.984369578019572e-6 (+ z 6.0)))
        (t_4 (/ 12.507343278686905 (+ z 4.0)))
        (t_5 (/ -1259.1392167224028 (+ z 1.0)))
        (t_6 (/ 1.5056327351493116e-7 (+ z 7.0))))
   (if (<= (+ z -1.0) 140.0)
     (*
      (sqrt (* PI 2.0))
      (*
       (pow (+ z 6.5) (+ z -0.5))
       (/
        (+
         (+
          0.9999999999998099
          (+ (+ (+ (+ (/ 676.5203681218851 z) t_5) t_0) t_2) t_4))
         (+ t_6 (+ t_1 t_3)))
        (exp (+ z 6.5)))))
     (*
      (exp
       (fma 0.5 (log (* PI 2.0)) (fma (+ z -0.5) (log (+ z 6.5)) (- -6.5 z))))
      (+
       (+
        (+ (+ t_5 (+ 0.9999999999998099 (/ 676.5203681218851 z))) (+ t_0 t_2))
        (+ t_4 t_1))
       (+ t_6 t_3))))))
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 = -176.6150291621406 / (z + 3.0);
	double t_1 = -0.13857109526572012 / (z + 5.0);
	double t_2 = 771.3234287776531 / (z + 2.0);
	double t_3 = 9.984369578019572e-6 / (z + 6.0);
	double t_4 = 12.507343278686905 / (z + 4.0);
	double t_5 = -1259.1392167224028 / (z + 1.0);
	double t_6 = 1.5056327351493116e-7 / (z + 7.0);
	double tmp;
	if ((z + -1.0) <= 140.0) {
		tmp = sqrt((((double) M_PI) * 2.0)) * (pow((z + 6.5), (z + -0.5)) * (((0.9999999999998099 + (((((676.5203681218851 / z) + t_5) + t_0) + t_2) + t_4)) + (t_6 + (t_1 + t_3))) / exp((z + 6.5))));
	} else {
		tmp = exp(fma(0.5, log((((double) M_PI) * 2.0)), fma((z + -0.5), log((z + 6.5)), (-6.5 - z)))) * ((((t_5 + (0.9999999999998099 + (676.5203681218851 / z))) + (t_0 + t_2)) + (t_4 + t_1)) + (t_6 + t_3));
	}
	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(-176.6150291621406 / Float64(z + 3.0))
	t_1 = Float64(-0.13857109526572012 / Float64(z + 5.0))
	t_2 = Float64(771.3234287776531 / Float64(z + 2.0))
	t_3 = Float64(9.984369578019572e-6 / Float64(z + 6.0))
	t_4 = Float64(12.507343278686905 / Float64(z + 4.0))
	t_5 = Float64(-1259.1392167224028 / Float64(z + 1.0))
	t_6 = Float64(1.5056327351493116e-7 / Float64(z + 7.0))
	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(Float64(Float64(0.9999999999998099 + Float64(Float64(Float64(Float64(Float64(676.5203681218851 / z) + t_5) + t_0) + t_2) + t_4)) + Float64(t_6 + Float64(t_1 + t_3))) / exp(Float64(z + 6.5)))));
	else
		tmp = Float64(exp(fma(0.5, log(Float64(pi * 2.0)), fma(Float64(z + -0.5), log(Float64(z + 6.5)), Float64(-6.5 - z)))) * Float64(Float64(Float64(Float64(t_5 + Float64(0.9999999999998099 + Float64(676.5203681218851 / z))) + Float64(t_0 + t_2)) + Float64(t_4 + t_1)) + Float64(t_6 + t_3)));
	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[(-176.6150291621406 / N[(z + 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-0.13857109526572012 / N[(z + 5.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(771.3234287776531 / N[(z + 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(9.984369578019572e-6 / N[(z + 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(12.507343278686905 / N[(z + 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(-1259.1392167224028 / N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(1.5056327351493116e-7 / N[(z + 7.0), $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[(N[(0.9999999999998099 + N[(N[(N[(N[(N[(676.5203681218851 / z), $MachinePrecision] + t$95$5), $MachinePrecision] + t$95$0), $MachinePrecision] + t$95$2), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision] + N[(t$95$6 + N[(t$95$1 + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Exp[N[(z + 6.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Exp[N[(0.5 * N[Log[N[(Pi * 2.0), $MachinePrecision]], $MachinePrecision] + N[(N[(z + -0.5), $MachinePrecision] * N[Log[N[(z + 6.5), $MachinePrecision]], $MachinePrecision] + N[(-6.5 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(N[(N[(N[(t$95$5 + N[(0.9999999999998099 + N[(676.5203681218851 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 + t$95$2), $MachinePrecision]), $MachinePrecision] + N[(t$95$4 + t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t$95$6 + t$95$3), $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{-176.6150291621406}{z + 3}\\
t_1 := \frac{-0.13857109526572012}{z + 5}\\
t_2 := \frac{771.3234287776531}{z + 2}\\
t_3 := \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\\
t_4 := \frac{12.507343278686905}{z + 4}\\
t_5 := \frac{-1259.1392167224028}{z + 1}\\
t_6 := \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\\
\mathbf{if}\;z + -1 \leq 140:\\
\;\;\;\;\sqrt{\pi \cdot 2} \cdot \left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot \frac{\left(0.9999999999998099 + \left(\left(\left(\left(\frac{676.5203681218851}{z} + t_5\right) + t_0\right) + t_2\right) + t_4\right)\right) + \left(t_6 + \left(t_1 + t_3\right)\right)}{e^{z + 6.5}}\right)\\

\mathbf{else}:\\
\;\;\;\;e^{\mathsf{fma}\left(0.5, \log \left(\pi \cdot 2\right), \mathsf{fma}\left(z + -0.5, \log \left(z + 6.5\right), -6.5 - z\right)\right)} \cdot \left(\left(\left(\left(t_5 + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \left(t_0 + t_2\right)\right) + \left(t_4 + t_1\right)\right) + \left(t_6 + t_3\right)\right)\\


\end{array}

Error

Derivation

  1. Split input into 2 regimes

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

    1. Initial program 2.2

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

    2. Simplified2.2

      \[\leadsto \color{blue}{\sqrt{\pi \cdot 2} \cdot \left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot \frac{\left(0.9999999999998099 + \left(\left(\left(\left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z + 1}\right) + \frac{-176.6150291621406}{z + 3}\right) + \frac{771.3234287776531}{2 + z}\right) + \frac{12.507343278686905}{z + 4}\right)\right) + \left(\frac{1.5056327351493116 \cdot 10^{-7}}{z + 7} + \left(\frac{-0.13857109526572012}{z + 5} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right)\right)}{e^{z + 6.5}}\right)} \]
      Proof
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 z 13/2) (+.f64 z -1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 z) (/.f64 -3147848041806007/2500000000000 (+.f64 z 1))) (/.f64 -883075145810703/5000000000000 (+.f64 z 3))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 z (Rewrite<= metadata-eval (+.f64 -1 15/2))) (+.f64 z -1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 z) (/.f64 -3147848041806007/2500000000000 (+.f64 z 1))) (/.f64 -883075145810703/5000000000000 (+.f64 z 3))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 z (+.f64 -1 (Rewrite<= metadata-eval (+.f64 7 1/2)))) (+.f64 z -1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 z) (/.f64 -3147848041806007/2500000000000 (+.f64 z 1))) (/.f64 -883075145810703/5000000000000 (+.f64 z 3))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 z -1) (+.f64 7 1/2))) (+.f64 z -1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 z) (/.f64 -3147848041806007/2500000000000 (+.f64 z 1))) (/.f64 -883075145810703/5000000000000 (+.f64 z 3))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 z (Rewrite<= metadata-eval (neg.f64 1))) (+.f64 7 1/2)) (+.f64 z -1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 z) (/.f64 -3147848041806007/2500000000000 (+.f64 z 1))) (/.f64 -883075145810703/5000000000000 (+.f64 z 3))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (Rewrite<= sub-neg_binary64 (-.f64 z 1)) (+.f64 7 1/2)) (+.f64 z -1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 z) (/.f64 -3147848041806007/2500000000000 (+.f64 z 1))) (/.f64 -883075145810703/5000000000000 (+.f64 z 3))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2)) (+.f64 z -1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 z) (/.f64 -3147848041806007/2500000000000 (+.f64 z 1))) (/.f64 -883075145810703/5000000000000 (+.f64 z 3))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 2 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 z (Rewrite<= metadata-eval (neg.f64 1/2)))) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 z) (/.f64 -3147848041806007/2500000000000 (+.f64 z 1))) (/.f64 -883075145810703/5000000000000 (+.f64 z 3))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (Rewrite<= sub-neg_binary64 (-.f64 z 1/2))) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 z) (/.f64 -3147848041806007/2500000000000 (+.f64 z 1))) (/.f64 -883075145810703/5000000000000 (+.f64 z 3))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (-.f64 z (Rewrite<= metadata-eval (-.f64 1 1/2)))) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 z) (/.f64 -3147848041806007/2500000000000 (+.f64 z 1))) (/.f64 -883075145810703/5000000000000 (+.f64 z 3))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 1/2))) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 z) (/.f64 -3147848041806007/2500000000000 (+.f64 z 1))) (/.f64 -883075145810703/5000000000000 (+.f64 z 3))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (Rewrite<= --rgt-identity_binary64 (-.f64 z 0))) (/.f64 -3147848041806007/2500000000000 (+.f64 z 1))) (/.f64 -883075145810703/5000000000000 (+.f64 z 3))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 z (Rewrite<= metadata-eval (-.f64 1 1)))) (/.f64 -3147848041806007/2500000000000 (+.f64 z 1))) (/.f64 -883075145810703/5000000000000 (+.f64 z 3))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 z 1))) (/.f64 -883075145810703/5000000000000 (+.f64 z 3))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1)) (/.f64 -3147848041806007/2500000000000 (+.f64 z (Rewrite<= metadata-eval (neg.f64 -1))))) (/.f64 -883075145810703/5000000000000 (+.f64 z 3))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1)) (/.f64 -3147848041806007/2500000000000 (Rewrite<= sub-neg_binary64 (-.f64 z -1)))) (/.f64 -883075145810703/5000000000000 (+.f64 z 3))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1)) (/.f64 -3147848041806007/2500000000000 (-.f64 z (Rewrite<= metadata-eval (-.f64 1 2))))) (/.f64 -883075145810703/5000000000000 (+.f64 z 3))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1)) (/.f64 -3147848041806007/2500000000000 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 2)))) (/.f64 -883075145810703/5000000000000 (+.f64 z 3))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1)) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 z (Rewrite<= metadata-eval (neg.f64 -3))))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1)) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 z (neg.f64 (Rewrite<= metadata-eval (-.f64 1 4)))))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1)) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 -883075145810703/5000000000000 (Rewrite<= sub-neg_binary64 (-.f64 z (-.f64 1 4))))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1)) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 -883075145810703/5000000000000 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 4)))) (/.f64 7713234287776531/10000000000000 (+.f64 2 z))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1)) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 7713234287776531/10000000000000 (Rewrite=> +-commutative_binary64 (+.f64 z 2)))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1)) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 7713234287776531/10000000000000 (+.f64 z (Rewrite<= metadata-eval (+.f64 -1 3))))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1)) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 7713234287776531/10000000000000 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 z -1) 3)))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1)) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 7713234287776531/10000000000000 (+.f64 (+.f64 z (Rewrite<= metadata-eval (neg.f64 1))) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1)) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))) (/.f64 7713234287776531/10000000000000 (+.f64 (Rewrite<= sub-neg_binary64 (-.f64 z 1)) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (Rewrite<= associate-+r+_binary64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1)) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (+.f64 (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4)) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3))))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 18 points increase in error, 18 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1)) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3)) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4))))) (/.f64 2501468655737381/200000000000000 (+.f64 z 4)))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1)) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (+.f64 (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3)) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4)))) (/.f64 2501468655737381/200000000000000 (+.f64 z (Rewrite<= metadata-eval (neg.f64 -4)))))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1)) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (+.f64 (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3)) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4)))) (/.f64 2501468655737381/200000000000000 (+.f64 z (neg.f64 (Rewrite<= metadata-eval (-.f64 1 5))))))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1)) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (+.f64 (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3)) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4)))) (/.f64 2501468655737381/200000000000000 (Rewrite<= sub-neg_binary64 (-.f64 z (-.f64 1 5)))))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1)) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (+.f64 (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3)) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 z 1) 4)))) (/.f64 2501468655737381/200000000000000 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 5))))) (+.f64 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (+.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1)) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (+.f64 (/.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 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 11 points increase in error, 4 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 9999999999998099/10000000000000000 (+.f64 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1)) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2)))) (+.f64 (/.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 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 72 points increase in error, 56 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 (+.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2)))) (+.f64 (/.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 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 59 points increase in error, 50 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (+.f64 (Rewrite<= associate-+l+_binary64 (+.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 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z 7)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 67 points increase in error, 72 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.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 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z (Rewrite<= metadata-eval (neg.f64 -7)))) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.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 (/.f64 3764081837873279/25000000000000000000000 (+.f64 z (neg.f64 (Rewrite<= metadata-eval (-.f64 1 8))))) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.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 (/.f64 3764081837873279/25000000000000000000000 (Rewrite<= sub-neg_binary64 (-.f64 z (-.f64 1 8)))) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.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 (/.f64 3764081837873279/25000000000000000000000 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 8))) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z 5)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.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 (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z (Rewrite<= metadata-eval (neg.f64 -5)))) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.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 (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 z (neg.f64 (Rewrite<= metadata-eval (-.f64 1 6))))) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.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 (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (Rewrite<= sub-neg_binary64 (-.f64 z (-.f64 1 6)))) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.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 (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 z 6))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.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 (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z (Rewrite<= metadata-eval (neg.f64 -6))))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.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 (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6)) (/.f64 2496092394504893/250000000000000000000 (+.f64 z (neg.f64 (Rewrite<= metadata-eval (-.f64 1 7)))))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.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 (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6)) (/.f64 2496092394504893/250000000000000000000 (Rewrite<= sub-neg_binary64 (-.f64 z (-.f64 1 7))))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.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 (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8)) (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6)) (/.f64 2496092394504893/250000000000000000000 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 7)))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.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))) (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6)) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (Rewrite<= associate-+l+_binary64 (+.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 (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 z 1) 6)) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 z 1) 7)))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 z 1) 8)))) (exp.f64 (+.f64 z 13/2))))): 25 points increase in error, 28 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (+.f64 (Rewrite<= associate-+l+_binary64 (+.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))) (exp.f64 (+.f64 z 13/2))))): 22 points increase in error, 24 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (+.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))))) (exp.f64 (+.f64 z 13/2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (*.f64 1 (+.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)))) (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 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (*.f64 1 (+.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)))) (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 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (*.f64 1 (+.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)))) (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 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (*.f64 1 (+.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)))) (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 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (*.f64 1 (+.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)))) (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 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (/.f64 (*.f64 1 (+.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)))) (exp.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2)))))): 0 points increase in error, 2 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (exp.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))))))): 26 points increase in error, 34 points decrease in error
      (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (*.f64 (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (+.f64 (-.f64 z 1) 1/2)) (*.f64 (Rewrite<= exp-neg_binary64 (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)))))): 29 points increase in error, 25 points decrease in error
      (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))) (*.f64 (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)))))): 40 points increase in error, 39 points decrease in error
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.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))))): 44 points increase in error, 33 points decrease in error

    if 140 < (-.f64 z 1)

    1. Initial program 61.8

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

    2. Simplified61.8

      \[\leadsto \color{blue}{\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(z + -1\right) + 7.5\right)}^{\left(z - 0.5\right)}\right) \cdot e^{\left(-\left(z - -6\right)\right) + -0.5}\right) \cdot \left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) + \frac{-1259.1392167224028}{z - -1}\right) + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right)} \]
      Proof
      (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 z -1) 15/2) (-.f64 z 1/2))) (exp.f64 (+.f64 (neg.f64 (-.f64 z -6)) -1/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 z 0))) (/.f64 -3147848041806007/2500000000000 (-.f64 z -1))) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 z -2)) (/.f64 -883075145810703/5000000000000 (-.f64 z -3)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 -3464277381643003/25000000000000000 (-.f64 z -5)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 z (Rewrite<= metadata-eval (neg.f64 1))) 15/2) (-.f64 z 1/2))) (exp.f64 (+.f64 (neg.f64 (-.f64 z -6)) -1/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 z 0))) (/.f64 -3147848041806007/2500000000000 (-.f64 z -1))) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 z -2)) (/.f64 -883075145810703/5000000000000 (-.f64 z -3)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 -3464277381643003/25000000000000000 (-.f64 z -5)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (+.f64 (Rewrite<= sub-neg_binary64 (-.f64 z 1)) 15/2) (-.f64 z 1/2))) (exp.f64 (+.f64 (neg.f64 (-.f64 z -6)) -1/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 z 0))) (/.f64 -3147848041806007/2500000000000 (-.f64 z -1))) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 z -2)) (/.f64 -883075145810703/5000000000000 (-.f64 z -3)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 -3464277381643003/25000000000000000 (-.f64 z -5)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (+.f64 (-.f64 z 1) (Rewrite<= metadata-eval (+.f64 7 1/2))) (-.f64 z 1/2))) (exp.f64 (+.f64 (neg.f64 (-.f64 z -6)) -1/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 z 0))) (/.f64 -3147848041806007/2500000000000 (-.f64 z -1))) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 z -2)) (/.f64 -883075145810703/5000000000000 (-.f64 z -3)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 -3464277381643003/25000000000000000 (-.f64 z -5)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2)) (-.f64 z 1/2))) (exp.f64 (+.f64 (neg.f64 (-.f64 z -6)) -1/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 z 0))) (/.f64 -3147848041806007/2500000000000 (-.f64 z -1))) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 z -2)) (/.f64 -883075145810703/5000000000000 (-.f64 z -3)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 -3464277381643003/25000000000000000 (-.f64 z -5)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 2 points decrease in error
      (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (-.f64 z (Rewrite<= metadata-eval (-.f64 1 1/2))))) (exp.f64 (+.f64 (neg.f64 (-.f64 z -6)) -1/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 z 0))) (/.f64 -3147848041806007/2500000000000 (-.f64 z -1))) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 z -2)) (/.f64 -883075145810703/5000000000000 (-.f64 z -3)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 -3464277381643003/25000000000000000 (-.f64 z -5)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2) (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 1/2)))) (exp.f64 (+.f64 (neg.f64 (-.f64 z -6)) -1/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 z 0))) (/.f64 -3147848041806007/2500000000000 (-.f64 z -1))) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 z -2)) (/.f64 -883075145810703/5000000000000 (-.f64 z -3)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 -3464277381643003/25000000000000000 (-.f64 z -5)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.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 (+.f64 (neg.f64 (-.f64 z (Rewrite<= metadata-eval (-.f64 1 7)))) -1/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 z 0))) (/.f64 -3147848041806007/2500000000000 (-.f64 z -1))) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 z -2)) (/.f64 -883075145810703/5000000000000 (-.f64 z -3)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 -3464277381643003/25000000000000000 (-.f64 z -5)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.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 (+.f64 (neg.f64 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 7))) -1/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 z 0))) (/.f64 -3147848041806007/2500000000000 (-.f64 z -1))) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 z -2)) (/.f64 -883075145810703/5000000000000 (-.f64 z -3)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 -3464277381643003/25000000000000000 (-.f64 z -5)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.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 (+.f64 (neg.f64 (+.f64 (-.f64 z 1) 7)) (Rewrite<= metadata-eval (neg.f64 1/2))))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 z 0))) (/.f64 -3147848041806007/2500000000000 (-.f64 z -1))) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 z -2)) (/.f64 -883075145810703/5000000000000 (-.f64 z -3)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 -3464277381643003/25000000000000000 (-.f64 z -5)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.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 (Rewrite<= distribute-neg-in_binary64 (neg.f64 (+.f64 (+.f64 (-.f64 z 1) 7) 1/2))))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 z 0))) (/.f64 -3147848041806007/2500000000000 (-.f64 z -1))) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 z -2)) (/.f64 -883075145810703/5000000000000 (-.f64 z -3)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 -3464277381643003/25000000000000000 (-.f64 z -5)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.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 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 z (Rewrite<= metadata-eval (-.f64 1 1))))) (/.f64 -3147848041806007/2500000000000 (-.f64 z -1))) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 z -2)) (/.f64 -883075145810703/5000000000000 (-.f64 z -3)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 -3464277381643003/25000000000000000 (-.f64 z -5)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.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 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 1)))) (/.f64 -3147848041806007/2500000000000 (-.f64 z -1))) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 z -2)) (/.f64 -883075145810703/5000000000000 (-.f64 z -3)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 -3464277381643003/25000000000000000 (-.f64 z -5)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.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 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (-.f64 z (Rewrite<= metadata-eval (-.f64 1 2))))) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 z -2)) (/.f64 -883075145810703/5000000000000 (-.f64 z -3)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 -3464277381643003/25000000000000000 (-.f64 z -5)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.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 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 2)))) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 z -2)) (/.f64 -883075145810703/5000000000000 (-.f64 z -3)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 -3464277381643003/25000000000000000 (-.f64 z -5)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.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 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (+.f64 (/.f64 7713234287776531/10000000000000 (-.f64 z (Rewrite<= metadata-eval (-.f64 1 3)))) (/.f64 -883075145810703/5000000000000 (-.f64 z -3)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 -3464277381643003/25000000000000000 (-.f64 z -5)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.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 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (+.f64 (/.f64 7713234287776531/10000000000000 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 3))) (/.f64 -883075145810703/5000000000000 (-.f64 z -3)))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 -3464277381643003/25000000000000000 (-.f64 z -5)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.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 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (+.f64 (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3)) (/.f64 -883075145810703/5000000000000 (-.f64 z (Rewrite<= metadata-eval (-.f64 1 4)))))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 -3464277381643003/25000000000000000 (-.f64 z -5)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.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 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 z 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 z 1) 2))) (+.f64 (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 z 1) 3)) (/.f64 -883075145810703/5000000000000 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 4))))) (+.f64 (/.f64 2501468655737381/200000000000000 (-.f64 z -4)) (/.f64 -3464277381643003/25000000000000000 (-.f64 z -5)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.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 (Rewrite<= associate-+l+_binary64 (+.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 z -4)) (/.f64 -3464277381643003/25000000000000000 (-.f64 z -5)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 65 points increase in error, 82 points decrease in error
      (*.f64 (*.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 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 z (Rewrite<= metadata-eval (-.f64 1 5)))) (/.f64 -3464277381643003/25000000000000000 (-.f64 z -5)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.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 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 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 5))) (/.f64 -3464277381643003/25000000000000000 (-.f64 z -5)))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.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 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 z (Rewrite<= metadata-eval (-.f64 1 6)))))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.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 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 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 6))))) (+.f64 (/.f64 2496092394504893/250000000000000000000 (-.f64 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.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 (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 z -6)) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 23 points increase in error, 23 points decrease in error
      (*.f64 (*.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 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 z (Rewrite<= metadata-eval (-.f64 1 7)))) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.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 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 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (-.f64 z -7))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.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 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 z (Rewrite<= metadata-eval (-.f64 1 8))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.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 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 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 z 1) 8)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (*.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)))) (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))))): 27 points increase in error, 32 points decrease in error

    3. Taylor expanded in z around inf 61.8

      \[\leadsto \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(z + -1\right) + 7.5\right)}^{\left(z - 0.5\right)}\right) \cdot \color{blue}{e^{-\left(6.5 + z\right)}}\right) \cdot \left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) + \frac{-1259.1392167224028}{z - -1}\right) + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]

    4. Simplified61.8

      \[\leadsto \left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(z + -1\right) + 7.5\right)}^{\left(z - 0.5\right)}\right) \cdot \color{blue}{e^{-6.5 - z}}\right) \cdot \left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{z - 0}\right) + \frac{-1259.1392167224028}{z - -1}\right) + \left(\frac{771.3234287776531}{z - -2} + \frac{-176.6150291621406}{z - -3}\right)\right) + \left(\frac{12.507343278686905}{z - -4} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{z - -6} + \frac{1.5056327351493116 \cdot 10^{-7}}{z - -7}\right)\right) \]
      Proof
      (exp.f64 (-.f64 -13/2 z)): 0 points increase in error, 0 points decrease in error
      (exp.f64 (Rewrite<= unsub-neg_binary64 (+.f64 -13/2 (neg.f64 z)))): 0 points increase in error, 0 points decrease in error
      (exp.f64 (+.f64 (Rewrite<= metadata-eval (neg.f64 13/2)) (neg.f64 z))): 0 points increase in error, 0 points decrease in error
      (exp.f64 (Rewrite<= distribute-neg-in_binary64 (neg.f64 (+.f64 13/2 z)))): 0 points increase in error, 0 points decrease in error

    5. Applied egg-rr7.7

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

  4. Final simplification2.3

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

Alternatives

Alternative 1
Error2.3
Cost36164
\[\begin{array}{l} t_0 := \frac{-176.6150291621406}{z + 3}\\ t_1 := \frac{-0.13857109526572012}{z + 5}\\ t_2 := \frac{771.3234287776531}{z + 2}\\ t_3 := \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\\ t_4 := \frac{12.507343278686905}{z + 4}\\ t_5 := \sqrt{\pi \cdot 2}\\ t_6 := \frac{-1259.1392167224028}{z + 1}\\ t_7 := \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\\ \mathbf{if}\;z + -1 \leq 140:\\ \;\;\;\;t_5 \cdot \left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot \frac{\left(0.9999999999998099 + \left(\left(\left(\left(\frac{676.5203681218851}{z} + t_6\right) + t_0\right) + t_2\right) + t_4\right)\right) + \left(t_7 + \left(t_1 + t_3\right)\right)}{e^{z + 6.5}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_5 \cdot \left(e^{\mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right)} \cdot \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{z} + \left(t_6 + t_2\right)\right) + \left(\left(t_7 + \left(t_4 + t_3\right)\right) + \left(t_0 + t_1\right)\right)\right)\right)\right)\\ \end{array} \]
Alternative 2
Error2.3
Cost36164
\[\begin{array}{l} t_0 := \frac{-176.6150291621406}{z + 3}\\ t_1 := \frac{-0.13857109526572012}{z + 5}\\ t_2 := \frac{771.3234287776531}{z + 2}\\ t_3 := \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\\ t_4 := \frac{12.507343278686905}{z + 4}\\ t_5 := \sqrt{\pi \cdot 2}\\ t_6 := \frac{-1259.1392167224028}{z + 1}\\ t_7 := \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\\ \mathbf{if}\;z + -1 \leq 140:\\ \;\;\;\;t_5 \cdot \left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot \frac{\left(0.9999999999998099 + \left(\left(\left(\left(\frac{676.5203681218851}{z} + t_6\right) + t_0\right) + t_2\right) + t_4\right)\right) + \left(t_7 + \left(t_1 + t_3\right)\right)}{e^{z + 6.5}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_5 \cdot \left(e^{\mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right)} \cdot \left(\left(t_0 + \left(t_7 + \left(t_1 + \left(t_4 + t_3\right)\right)\right)\right) + \left(0.9999999999998099 + \left(\frac{676.5203681218851}{z} + \left(t_6 + t_2\right)\right)\right)\right)\right)\\ \end{array} \]
Alternative 3
Error2.3
Cost36164
\[\begin{array}{l} t_0 := \frac{-176.6150291621406}{z + 3}\\ t_1 := \frac{-0.13857109526572012}{z + 5}\\ t_2 := \frac{771.3234287776531}{z + 2}\\ t_3 := \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\\ t_4 := \frac{12.507343278686905}{z + 4}\\ t_5 := \sqrt{\pi \cdot 2}\\ t_6 := \frac{-1259.1392167224028}{z + 1}\\ t_7 := \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\\ \mathbf{if}\;z + -1 \leq 140:\\ \;\;\;\;t_5 \cdot \left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot \frac{\left(0.9999999999998099 + \left(\left(\left(\left(\frac{676.5203681218851}{z} + t_6\right) + t_0\right) + t_2\right) + t_4\right)\right) + \left(t_7 + \left(t_1 + t_3\right)\right)}{e^{z + 6.5}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_5 \cdot \left(\left(\left(t_6 + \left(t_2 + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right)\right) + \left(t_0 + \left(t_7 + \left(t_1 + \left(t_4 + t_3\right)\right)\right)\right)\right) \cdot e^{\mathsf{fma}\left(-\log \left(z + 6.5\right), 0.5 - z, -6.5 - z\right)}\right)\\ \end{array} \]
Alternative 4
Error2.3
Cost29828
\[\begin{array}{l} t_0 := \frac{-176.6150291621406}{z + 3}\\ t_1 := \frac{-0.13857109526572012}{z + 5}\\ t_2 := \frac{771.3234287776531}{z + 2}\\ t_3 := \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\\ t_4 := \frac{12.507343278686905}{z + 4}\\ t_5 := \sqrt{\pi \cdot 2}\\ t_6 := \frac{-1259.1392167224028}{z + 1}\\ t_7 := \frac{1.5056327351493116 \cdot 10^{-7}}{z + 7}\\ \mathbf{if}\;z + -1 \leq 140:\\ \;\;\;\;t_5 \cdot \left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot \frac{\left(0.9999999999998099 + \left(\left(\left(\left(\frac{676.5203681218851}{z} + t_6\right) + t_0\right) + t_2\right) + t_4\right)\right) + \left(t_7 + \left(t_1 + t_3\right)\right)}{e^{z + 6.5}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_5 \cdot \left(\left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{z} + \left(t_6 + t_2\right)\right) + \left(\left(t_7 + \left(t_4 + t_3\right)\right) + \left(t_0 + t_1\right)\right)\right)\right) \cdot e^{\left(-6.5 - z\right) + \log \left(z + 6.5\right) \cdot \left(z + -0.5\right)}\right)\\ \end{array} \]
Alternative 5
Error3.9
Cost29504
\[\sqrt{\pi \cdot 2} \cdot \left(\left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot e^{-6.5 - z}\right) \cdot \left(\left(\frac{771.3234287776531}{z + 2} + \left(\frac{-176.6150291621406}{z + 3} + \left(0.9999999999998099 + \left(\frac{676.5203681218851}{z} + \frac{-1259.1392167224028}{z + 1}\right)\right)\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \frac{-0.13857109526572012}{z + 5}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-7}}{z + 7} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right)\right)\right)\right) \]
Alternative 6
Error3.6
Cost29504
\[\sqrt{\pi \cdot 2} \cdot \left(\left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{z} + \left(\frac{-1259.1392167224028}{z + 1} + \frac{771.3234287776531}{z + 2}\right)\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-7}}{z + 7} + \left(\frac{12.507343278686905}{z + 4} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right)\right) + \left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z + 5}\right)\right)\right)\right) \cdot \frac{e^{-6.5 - z}}{{\left(z + 6.5\right)}^{\left(0.5 - z\right)}}\right) \]
Alternative 7
Error46.9
Cost28864
\[\left(e^{-6.5 - z} \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(z + -1\right) + 7.5\right)}^{\left(z + -0.5\right)}\right)\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-7}}{z + 7} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \frac{-0.13857109526572012}{z + 5}\right) + \left(0.9999999999998099 + \left(\frac{12.0895510149948}{z} + \frac{\frac{246.3374466535184}{z}}{z}\right)\right)\right)\right) \]
Alternative 8
Error46.9
Cost28864
\[\left(e^{-6.5 - z} \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(z + -1\right) + 7.5\right)}^{\left(z + -0.5\right)}\right)\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-7}}{z + 7} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \frac{-0.13857109526572012}{z + 5}\right) + \left(\left(0.9999999999998099 + \frac{12.0895510149948}{z}\right) + \frac{246.3374466535184}{z \cdot z}\right)\right)\right) \]
Alternative 9
Error49.9
Cost28736
\[\sqrt{\pi \cdot 2} \cdot \left(\frac{e^{-6.5 - z}}{{\left(z + 6.5\right)}^{\left(0.5 - z\right)}} \cdot \left(\left(\frac{-176.6150291621406}{z + 3} + \left(\frac{1.5056327351493116 \cdot 10^{-7}}{z + 7} + \left(\frac{-0.13857109526572012}{z + 5} + \left(\frac{12.507343278686905}{z + 4} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right)\right)\right)\right) + \left(0.9999999999998099 + \frac{188.7045801771354}{z}\right)\right)\right) \]
Alternative 10
Error46.9
Cost28736
\[\sqrt{\pi \cdot 2} \cdot \left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-7}}{z + 7} + \left(\frac{-0.13857109526572012}{z + 5} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right)\right) + \left(0.9999999999998099 + \left(\frac{12.507343278686905}{z + 4} + \left(\frac{12.0895510149948}{z} + \frac{246.3374466535184}{z \cdot z}\right)\right)\right)}{e^{z + 6.5}}\right) \]
Alternative 11
Error46.9
Cost28736
\[\sqrt{\pi \cdot 2} \cdot \left(\left({\left(z + 6.5\right)}^{\left(z + -0.5\right)} \cdot e^{-6.5 - z}\right) \cdot \left(\left(\left(\frac{12.507343278686905}{z + 4} + \frac{-0.13857109526572012}{z + 5}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-7}}{z + 7} + \frac{9.984369578019572 \cdot 10^{-6}}{z + 6}\right)\right) + \left(0.9999999999998099 + \left(\frac{12.0895510149948}{z} + \frac{246.3374466535184}{z \cdot z}\right)\right)\right)\right) \]
Alternative 12
Error51.5
Cost26816
\[\sqrt{\pi \cdot 2} \cdot \left(\frac{{\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z + 6.5}} \cdot \left(0.9999999999998099 + \frac{24.458333333348836}{z}\right)\right) \]
Alternative 13
Error52.0
Cost26692
\[\begin{array}{l} \mathbf{if}\;z \leq 4:\\ \;\;\;\;\sqrt{\pi \cdot \left(\frac{140824.5564565449}{z \cdot z} \cdot e^{-13}\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\pi \cdot 2} \cdot \left(0.9999999999998099 \cdot \frac{{\left(z + 6.5\right)}^{\left(z + -0.5\right)}}{e^{z + 6.5}}\right)\\ \end{array} \]
Alternative 14
Error55.5
Cost19712
\[\sqrt{\pi \cdot \left(\frac{140824.5564565449}{z \cdot z} \cdot e^{-13}\right)} \]
Alternative 15
Error55.5
Cost19584
\[\sqrt{\pi \cdot 140824.5564565449} \cdot \frac{e^{-6.5}}{z} \]

Error

Reproduce

herbie shell --seed 2022332 
(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)))))