Jmat.Real.gamma, branch z less than 0.5

Percentage Accurate: 96.6% → 99.3%

Time: 10.1s

Alternatives: 14

Speedup: 2.0×

• could not determine a ground truth

  1. z = -16501236284.469276

Specification

\[z \leq 0.5\]

Math

\[\begin{array}{l} t_0 := \left(1 - z\right) - 1\\ t_1 := t\_0 + 7\\ t_2 := t\_1 + 0.5\\ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {t\_2}^{\left(t\_0 + 0.5\right)}\right) \cdot e^{-t\_2}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{t\_0 + 1}\right) + \frac{-1259.1392167224028}{t\_0 + 2}\right) + \frac{771.3234287776531}{t\_0 + 3}\right) + \frac{-176.6150291621406}{t\_0 + 4}\right) + \frac{12.507343278686905}{t\_0 + 5}\right) + \frac{-0.13857109526572012}{t\_0 + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t\_1}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{t\_0 + 8}\right)\right) \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (- (- 1.0 z) 1.0)) (t_1 (+ t_0 7.0)) (t_2 (+ t_1 0.5)))
   (*
    (/ PI (sin (* PI z)))
    (*
     (* (* (sqrt (* PI 2.0)) (pow t_2 (+ t_0 0.5))) (exp (- t_2)))
     (+
      (+
       (+
        (+
         (+
          (+
           (+
            (+ 0.9999999999998099 (/ 676.5203681218851 (+ t_0 1.0)))
            (/ -1259.1392167224028 (+ t_0 2.0)))
           (/ 771.3234287776531 (+ t_0 3.0)))
          (/ -176.6150291621406 (+ t_0 4.0)))
         (/ 12.507343278686905 (+ t_0 5.0)))
        (/ -0.13857109526572012 (+ t_0 6.0)))
       (/ 9.984369578019572e-6 t_1))
      (/ 1.5056327351493116e-7 (+ t_0 8.0)))))))

C

double code(double z) {
	double t_0 = (1.0 - z) - 1.0;
	double t_1 = t_0 + 7.0;
	double t_2 = t_1 + 0.5;
	return (((double) M_PI) / sin((((double) M_PI) * z))) * (((sqrt((((double) M_PI) * 2.0)) * pow(t_2, (t_0 + 0.5))) * exp(-t_2)) * ((((((((0.9999999999998099 + (676.5203681218851 / (t_0 + 1.0))) + (-1259.1392167224028 / (t_0 + 2.0))) + (771.3234287776531 / (t_0 + 3.0))) + (-176.6150291621406 / (t_0 + 4.0))) + (12.507343278686905 / (t_0 + 5.0))) + (-0.13857109526572012 / (t_0 + 6.0))) + (9.984369578019572e-6 / t_1)) + (1.5056327351493116e-7 / (t_0 + 8.0))));
}

Java

public static double code(double z) {
	double t_0 = (1.0 - z) - 1.0;
	double t_1 = t_0 + 7.0;
	double t_2 = t_1 + 0.5;
	return (Math.PI / Math.sin((Math.PI * z))) * (((Math.sqrt((Math.PI * 2.0)) * Math.pow(t_2, (t_0 + 0.5))) * Math.exp(-t_2)) * ((((((((0.9999999999998099 + (676.5203681218851 / (t_0 + 1.0))) + (-1259.1392167224028 / (t_0 + 2.0))) + (771.3234287776531 / (t_0 + 3.0))) + (-176.6150291621406 / (t_0 + 4.0))) + (12.507343278686905 / (t_0 + 5.0))) + (-0.13857109526572012 / (t_0 + 6.0))) + (9.984369578019572e-6 / t_1)) + (1.5056327351493116e-7 / (t_0 + 8.0))));
}

Python

def code(z):
	t_0 = (1.0 - z) - 1.0
	t_1 = t_0 + 7.0
	t_2 = t_1 + 0.5
	return (math.pi / math.sin((math.pi * z))) * (((math.sqrt((math.pi * 2.0)) * math.pow(t_2, (t_0 + 0.5))) * math.exp(-t_2)) * ((((((((0.9999999999998099 + (676.5203681218851 / (t_0 + 1.0))) + (-1259.1392167224028 / (t_0 + 2.0))) + (771.3234287776531 / (t_0 + 3.0))) + (-176.6150291621406 / (t_0 + 4.0))) + (12.507343278686905 / (t_0 + 5.0))) + (-0.13857109526572012 / (t_0 + 6.0))) + (9.984369578019572e-6 / t_1)) + (1.5056327351493116e-7 / (t_0 + 8.0))))

Julia

function code(z)
	t_0 = Float64(Float64(1.0 - z) - 1.0)
	t_1 = Float64(t_0 + 7.0)
	t_2 = Float64(t_1 + 0.5)
	return Float64(Float64(pi / sin(Float64(pi * z))) * Float64(Float64(Float64(sqrt(Float64(pi * 2.0)) * (t_2 ^ Float64(t_0 + 0.5))) * exp(Float64(-t_2))) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(0.9999999999998099 + Float64(676.5203681218851 / Float64(t_0 + 1.0))) + Float64(-1259.1392167224028 / Float64(t_0 + 2.0))) + Float64(771.3234287776531 / Float64(t_0 + 3.0))) + Float64(-176.6150291621406 / Float64(t_0 + 4.0))) + Float64(12.507343278686905 / Float64(t_0 + 5.0))) + Float64(-0.13857109526572012 / Float64(t_0 + 6.0))) + Float64(9.984369578019572e-6 / t_1)) + Float64(1.5056327351493116e-7 / Float64(t_0 + 8.0)))))
end

MATLAB

function tmp = code(z)
	t_0 = (1.0 - z) - 1.0;
	t_1 = t_0 + 7.0;
	t_2 = t_1 + 0.5;
	tmp = (pi / sin((pi * z))) * (((sqrt((pi * 2.0)) * (t_2 ^ (t_0 + 0.5))) * exp(-t_2)) * ((((((((0.9999999999998099 + (676.5203681218851 / (t_0 + 1.0))) + (-1259.1392167224028 / (t_0 + 2.0))) + (771.3234287776531 / (t_0 + 3.0))) + (-176.6150291621406 / (t_0 + 4.0))) + (12.507343278686905 / (t_0 + 5.0))) + (-0.13857109526572012 / (t_0 + 6.0))) + (9.984369578019572e-6 / t_1)) + (1.5056327351493116e-7 / (t_0 + 8.0))));
end

Wolfram

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

Initial Program: 96.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := \left(1 - z\right) - 1\\ t_1 := t\_0 + 7\\ t_2 := t\_1 + 0.5\\ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {t\_2}^{\left(t\_0 + 0.5\right)}\right) \cdot e^{-t\_2}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{t\_0 + 1}\right) + \frac{-1259.1392167224028}{t\_0 + 2}\right) + \frac{771.3234287776531}{t\_0 + 3}\right) + \frac{-176.6150291621406}{t\_0 + 4}\right) + \frac{12.507343278686905}{t\_0 + 5}\right) + \frac{-0.13857109526572012}{t\_0 + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t\_1}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{t\_0 + 8}\right)\right) \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (- (- 1.0 z) 1.0)) (t_1 (+ t_0 7.0)) (t_2 (+ t_1 0.5)))
   (*
    (/ PI (sin (* PI z)))
    (*
     (* (* (sqrt (* PI 2.0)) (pow t_2 (+ t_0 0.5))) (exp (- t_2)))
     (+
      (+
       (+
        (+
         (+
          (+
           (+
            (+ 0.9999999999998099 (/ 676.5203681218851 (+ t_0 1.0)))
            (/ -1259.1392167224028 (+ t_0 2.0)))
           (/ 771.3234287776531 (+ t_0 3.0)))
          (/ -176.6150291621406 (+ t_0 4.0)))
         (/ 12.507343278686905 (+ t_0 5.0)))
        (/ -0.13857109526572012 (+ t_0 6.0)))
       (/ 9.984369578019572e-6 t_1))
      (/ 1.5056327351493116e-7 (+ t_0 8.0)))))))

C

double code(double z) {
	double t_0 = (1.0 - z) - 1.0;
	double t_1 = t_0 + 7.0;
	double t_2 = t_1 + 0.5;
	return (((double) M_PI) / sin((((double) M_PI) * z))) * (((sqrt((((double) M_PI) * 2.0)) * pow(t_2, (t_0 + 0.5))) * exp(-t_2)) * ((((((((0.9999999999998099 + (676.5203681218851 / (t_0 + 1.0))) + (-1259.1392167224028 / (t_0 + 2.0))) + (771.3234287776531 / (t_0 + 3.0))) + (-176.6150291621406 / (t_0 + 4.0))) + (12.507343278686905 / (t_0 + 5.0))) + (-0.13857109526572012 / (t_0 + 6.0))) + (9.984369578019572e-6 / t_1)) + (1.5056327351493116e-7 / (t_0 + 8.0))));
}

Java

public static double code(double z) {
	double t_0 = (1.0 - z) - 1.0;
	double t_1 = t_0 + 7.0;
	double t_2 = t_1 + 0.5;
	return (Math.PI / Math.sin((Math.PI * z))) * (((Math.sqrt((Math.PI * 2.0)) * Math.pow(t_2, (t_0 + 0.5))) * Math.exp(-t_2)) * ((((((((0.9999999999998099 + (676.5203681218851 / (t_0 + 1.0))) + (-1259.1392167224028 / (t_0 + 2.0))) + (771.3234287776531 / (t_0 + 3.0))) + (-176.6150291621406 / (t_0 + 4.0))) + (12.507343278686905 / (t_0 + 5.0))) + (-0.13857109526572012 / (t_0 + 6.0))) + (9.984369578019572e-6 / t_1)) + (1.5056327351493116e-7 / (t_0 + 8.0))));
}

Python

def code(z):
	t_0 = (1.0 - z) - 1.0
	t_1 = t_0 + 7.0
	t_2 = t_1 + 0.5
	return (math.pi / math.sin((math.pi * z))) * (((math.sqrt((math.pi * 2.0)) * math.pow(t_2, (t_0 + 0.5))) * math.exp(-t_2)) * ((((((((0.9999999999998099 + (676.5203681218851 / (t_0 + 1.0))) + (-1259.1392167224028 / (t_0 + 2.0))) + (771.3234287776531 / (t_0 + 3.0))) + (-176.6150291621406 / (t_0 + 4.0))) + (12.507343278686905 / (t_0 + 5.0))) + (-0.13857109526572012 / (t_0 + 6.0))) + (9.984369578019572e-6 / t_1)) + (1.5056327351493116e-7 / (t_0 + 8.0))))

Julia

function code(z)
	t_0 = Float64(Float64(1.0 - z) - 1.0)
	t_1 = Float64(t_0 + 7.0)
	t_2 = Float64(t_1 + 0.5)
	return Float64(Float64(pi / sin(Float64(pi * z))) * Float64(Float64(Float64(sqrt(Float64(pi * 2.0)) * (t_2 ^ Float64(t_0 + 0.5))) * exp(Float64(-t_2))) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(0.9999999999998099 + Float64(676.5203681218851 / Float64(t_0 + 1.0))) + Float64(-1259.1392167224028 / Float64(t_0 + 2.0))) + Float64(771.3234287776531 / Float64(t_0 + 3.0))) + Float64(-176.6150291621406 / Float64(t_0 + 4.0))) + Float64(12.507343278686905 / Float64(t_0 + 5.0))) + Float64(-0.13857109526572012 / Float64(t_0 + 6.0))) + Float64(9.984369578019572e-6 / t_1)) + Float64(1.5056327351493116e-7 / Float64(t_0 + 8.0)))))
end

MATLAB

function tmp = code(z)
	t_0 = (1.0 - z) - 1.0;
	t_1 = t_0 + 7.0;
	t_2 = t_1 + 0.5;
	tmp = (pi / sin((pi * z))) * (((sqrt((pi * 2.0)) * (t_2 ^ (t_0 + 0.5))) * exp(-t_2)) * ((((((((0.9999999999998099 + (676.5203681218851 / (t_0 + 1.0))) + (-1259.1392167224028 / (t_0 + 2.0))) + (771.3234287776531 / (t_0 + 3.0))) + (-176.6150291621406 / (t_0 + 4.0))) + (12.507343278686905 / (t_0 + 5.0))) + (-0.13857109526572012 / (t_0 + 6.0))) + (9.984369578019572e-6 / t_1)) + (1.5056327351493116e-7 / (t_0 + 8.0))));
end

Wolfram

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

Alternative 1: 99.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_0 := \sqrt{\pi + \pi}\\ t_1 := \frac{\pi}{\sin \left(\pi \cdot z\right)}\\ t_2 := \left(1 - z\right) - 0.5\\ \mathbf{if}\;z \leq -1000:\\ \;\;\;\;t\_1 \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(t\_0 \cdot \left({7.5}^{t\_2} \cdot e^{-7.5}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) - -7} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(1 - z\right) - -6} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - -5} + \left(\frac{12.507343278686905}{\left(1 - z\right) - -4} + \left(\left(\frac{676.5203681218851}{1 - z} - \left(\frac{1259.1392167224028}{\left(1 - z\right) - -1} - \left(\frac{771.3234287776531}{\left(1 - z\right) - -2} - \frac{-176.6150291621406}{-4 + z}\right)\right)\right) + 0.9999999999998099\right)\right)\right)\right)\right) \cdot \left(t\_0 \cdot \left({\left(\left(1 - \frac{-6.5}{1 - z}\right) \cdot \left(1 - z\right)\right)}^{t\_2} \cdot e^{z - 7.5}\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (sqrt (+ PI PI)))
        (t_1 (/ PI (sin (* PI z))))
        (t_2 (- (- 1.0 z) 0.5)))
   (if (<= z -1000.0)
     (*
      t_1
      (*
       (+
        263.3831869810514
        (* z (+ 436.8961725563396 (* 545.0353078428827 z))))
       (* t_0 (* (pow 7.5 t_2) (exp (- 7.5))))))
     (*
      t_1
      (*
       (+
        (/ 1.5056327351493116e-7 (- (- 1.0 z) -7.0))
        (+
         (/ 9.984369578019572e-6 (- (- 1.0 z) -6.0))
         (+
          (/ -0.13857109526572012 (- (- 1.0 z) -5.0))
          (+
           (/ 12.507343278686905 (- (- 1.0 z) -4.0))
           (+
            (-
             (/ 676.5203681218851 (- 1.0 z))
             (-
              (/ 1259.1392167224028 (- (- 1.0 z) -1.0))
              (-
               (/ 771.3234287776531 (- (- 1.0 z) -2.0))
               (/ -176.6150291621406 (+ -4.0 z)))))
            0.9999999999998099)))))
       (*
        t_0
        (*
         (pow (* (- 1.0 (/ -6.5 (- 1.0 z))) (- 1.0 z)) t_2)
         (exp (- z 7.5)))))))))

C

double code(double z) {
	double t_0 = sqrt((((double) M_PI) + ((double) M_PI)));
	double t_1 = ((double) M_PI) / sin((((double) M_PI) * z));
	double t_2 = (1.0 - z) - 0.5;
	double tmp;
	if (z <= -1000.0) {
		tmp = t_1 * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (t_0 * (pow(7.5, t_2) * exp(-7.5))));
	} else {
		tmp = t_1 * (((1.5056327351493116e-7 / ((1.0 - z) - -7.0)) + ((9.984369578019572e-6 / ((1.0 - z) - -6.0)) + ((-0.13857109526572012 / ((1.0 - z) - -5.0)) + ((12.507343278686905 / ((1.0 - z) - -4.0)) + (((676.5203681218851 / (1.0 - z)) - ((1259.1392167224028 / ((1.0 - z) - -1.0)) - ((771.3234287776531 / ((1.0 - z) - -2.0)) - (-176.6150291621406 / (-4.0 + z))))) + 0.9999999999998099))))) * (t_0 * (pow(((1.0 - (-6.5 / (1.0 - z))) * (1.0 - z)), t_2) * exp((z - 7.5)))));
	}
	return tmp;
}

Java

public static double code(double z) {
	double t_0 = Math.sqrt((Math.PI + Math.PI));
	double t_1 = Math.PI / Math.sin((Math.PI * z));
	double t_2 = (1.0 - z) - 0.5;
	double tmp;
	if (z <= -1000.0) {
		tmp = t_1 * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (t_0 * (Math.pow(7.5, t_2) * Math.exp(-7.5))));
	} else {
		tmp = t_1 * (((1.5056327351493116e-7 / ((1.0 - z) - -7.0)) + ((9.984369578019572e-6 / ((1.0 - z) - -6.0)) + ((-0.13857109526572012 / ((1.0 - z) - -5.0)) + ((12.507343278686905 / ((1.0 - z) - -4.0)) + (((676.5203681218851 / (1.0 - z)) - ((1259.1392167224028 / ((1.0 - z) - -1.0)) - ((771.3234287776531 / ((1.0 - z) - -2.0)) - (-176.6150291621406 / (-4.0 + z))))) + 0.9999999999998099))))) * (t_0 * (Math.pow(((1.0 - (-6.5 / (1.0 - z))) * (1.0 - z)), t_2) * Math.exp((z - 7.5)))));
	}
	return tmp;
}

Python

def code(z):
	t_0 = math.sqrt((math.pi + math.pi))
	t_1 = math.pi / math.sin((math.pi * z))
	t_2 = (1.0 - z) - 0.5
	tmp = 0
	if z <= -1000.0:
		tmp = t_1 * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (t_0 * (math.pow(7.5, t_2) * math.exp(-7.5))))
	else:
		tmp = t_1 * (((1.5056327351493116e-7 / ((1.0 - z) - -7.0)) + ((9.984369578019572e-6 / ((1.0 - z) - -6.0)) + ((-0.13857109526572012 / ((1.0 - z) - -5.0)) + ((12.507343278686905 / ((1.0 - z) - -4.0)) + (((676.5203681218851 / (1.0 - z)) - ((1259.1392167224028 / ((1.0 - z) - -1.0)) - ((771.3234287776531 / ((1.0 - z) - -2.0)) - (-176.6150291621406 / (-4.0 + z))))) + 0.9999999999998099))))) * (t_0 * (math.pow(((1.0 - (-6.5 / (1.0 - z))) * (1.0 - z)), t_2) * math.exp((z - 7.5)))))
	return tmp

Julia

function code(z)
	t_0 = sqrt(Float64(pi + pi))
	t_1 = Float64(pi / sin(Float64(pi * z)))
	t_2 = Float64(Float64(1.0 - z) - 0.5)
	tmp = 0.0
	if (z <= -1000.0)
		tmp = Float64(t_1 * Float64(Float64(263.3831869810514 + Float64(z * Float64(436.8961725563396 + Float64(545.0353078428827 * z)))) * Float64(t_0 * Float64((7.5 ^ t_2) * exp(Float64(-7.5))))));
	else
		tmp = Float64(t_1 * Float64(Float64(Float64(1.5056327351493116e-7 / Float64(Float64(1.0 - z) - -7.0)) + Float64(Float64(9.984369578019572e-6 / Float64(Float64(1.0 - z) - -6.0)) + Float64(Float64(-0.13857109526572012 / Float64(Float64(1.0 - z) - -5.0)) + Float64(Float64(12.507343278686905 / Float64(Float64(1.0 - z) - -4.0)) + Float64(Float64(Float64(676.5203681218851 / Float64(1.0 - z)) - Float64(Float64(1259.1392167224028 / Float64(Float64(1.0 - z) - -1.0)) - Float64(Float64(771.3234287776531 / Float64(Float64(1.0 - z) - -2.0)) - Float64(-176.6150291621406 / Float64(-4.0 + z))))) + 0.9999999999998099))))) * Float64(t_0 * Float64((Float64(Float64(1.0 - Float64(-6.5 / Float64(1.0 - z))) * Float64(1.0 - z)) ^ t_2) * exp(Float64(z - 7.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z)
	t_0 = sqrt((pi + pi));
	t_1 = pi / sin((pi * z));
	t_2 = (1.0 - z) - 0.5;
	tmp = 0.0;
	if (z <= -1000.0)
		tmp = t_1 * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (t_0 * ((7.5 ^ t_2) * exp(-7.5))));
	else
		tmp = t_1 * (((1.5056327351493116e-7 / ((1.0 - z) - -7.0)) + ((9.984369578019572e-6 / ((1.0 - z) - -6.0)) + ((-0.13857109526572012 / ((1.0 - z) - -5.0)) + ((12.507343278686905 / ((1.0 - z) - -4.0)) + (((676.5203681218851 / (1.0 - z)) - ((1259.1392167224028 / ((1.0 - z) - -1.0)) - ((771.3234287776531 / ((1.0 - z) - -2.0)) - (-176.6150291621406 / (-4.0 + z))))) + 0.9999999999998099))))) * (t_0 * ((((1.0 - (-6.5 / (1.0 - z))) * (1.0 - z)) ^ t_2) * exp((z - 7.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[z_] := Block[{t$95$0 = N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(Pi / N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 - z), $MachinePrecision] - 0.5), $MachinePrecision]}, If[LessEqual[z, -1000.0], N[(t$95$1 * N[(N[(263.3831869810514 + N[(z * N[(436.8961725563396 + N[(545.0353078428827 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 * N[(N[Power[7.5, t$95$2], $MachinePrecision] * N[Exp[(-7.5)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(N[(N[(1.5056327351493116e-7 / N[(N[(1.0 - z), $MachinePrecision] - -7.0), $MachinePrecision]), $MachinePrecision] + N[(N[(9.984369578019572e-6 / N[(N[(1.0 - z), $MachinePrecision] - -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(-0.13857109526572012 / N[(N[(1.0 - z), $MachinePrecision] - -5.0), $MachinePrecision]), $MachinePrecision] + N[(N[(12.507343278686905 / N[(N[(1.0 - z), $MachinePrecision] - -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(676.5203681218851 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - N[(N[(1259.1392167224028 / N[(N[(1.0 - z), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(771.3234287776531 / N[(N[(1.0 - z), $MachinePrecision] - -2.0), $MachinePrecision]), $MachinePrecision] - N[(-176.6150291621406 / N[(-4.0 + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 0.9999999999998099), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 * N[(N[Power[N[(N[(1.0 - N[(-6.5 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$2], $MachinePrecision] * N[Exp[N[(z - 7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1e3

   1. Initial program 96.6%

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

   3. Applied rewrites 98.5%

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

   5. Applied rewrites 98.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + \color{blue}{z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \color{blue}{\left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \color{blue}{\frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      4. lower-*.f64 96.7

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot \color{blue}{z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   8. Applied rewrites 96.7%

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   9. Taylor expanded in z around 0

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\color{blue}{\frac{15}{2}}}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 95.6%

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\color{blue}{7.5}}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   12. Taylor expanded in z around 0

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\frac{15}{2}}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\color{blue}{\frac{15}{2}}}\right)\right)\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 96.2%

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({7.5}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\color{blue}{7.5}}\right)\right)\right) \]

   if -1e3 < z

   1. Initial program 96.6%

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

   3. Applied rewrites 98.5%

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

   5. Applied rewrites 98.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7} + \left(\frac{\frac{2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \left(\frac{\frac{-3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5} + \left(\frac{\frac{2501468655737381}{200000000000000}}{\left(1 - z\right) - -4} + \left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \left(\frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1} - \left(\frac{\frac{7713234287776531}{10000000000000}}{\left(1 - z\right) - -2} - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right)\right)\right) + \frac{9999999999998099}{10000000000000000}\right)\right)\right)\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{\color{blue}{z - \frac{15}{2}}}\right)\right)\right) \]
   7. Step-by-step derivation

      1. lower--.f64 98.5

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

   8. Applied rewrites 98.5%

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) - -7} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(1 - z\right) - -6} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - -5} + \left(\frac{12.507343278686905}{\left(1 - z\right) - -4} + \left(\left(\frac{676.5203681218851}{1 - z} - \left(\frac{1259.1392167224028}{\left(1 - z\right) - -1} - \left(\frac{771.3234287776531}{\left(1 - z\right) - -2} - \frac{-176.6150291621406}{-4 + z}\right)\right)\right) + 0.9999999999998099\right)\right)\right)\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{\color{blue}{z - 7.5}}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7} + \left(\frac{\frac{2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \left(\frac{\frac{-3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5} + \left(\frac{\frac{2501468655737381}{200000000000000}}{\left(1 - z\right) - -4} + \left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \left(\frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1} - \left(\frac{\frac{7713234287776531}{10000000000000}}{\left(1 - z\right) - -2} - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right)\right)\right) + \frac{9999999999998099}{10000000000000000}\right)\right)\right)\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\color{blue}{\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{z - \frac{15}{2}}\right)\right)\right) \]

      2. lift--.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7} + \left(\frac{\frac{2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \left(\frac{\frac{-3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5} + \left(\frac{\frac{2501468655737381}{200000000000000}}{\left(1 - z\right) - -4} + \left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \left(\frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1} - \left(\frac{\frac{7713234287776531}{10000000000000}}{\left(1 - z\right) - -2} - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right)\right)\right) + \frac{9999999999998099}{10000000000000000}\right)\right)\right)\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\color{blue}{\left(\left(1 - z\right) - -6\right)} - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{z - \frac{15}{2}}\right)\right)\right) \]

      3. associate--l- N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7} + \left(\frac{\frac{2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \left(\frac{\frac{-3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5} + \left(\frac{\frac{2501468655737381}{200000000000000}}{\left(1 - z\right) - -4} + \left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \left(\frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1} - \left(\frac{\frac{7713234287776531}{10000000000000}}{\left(1 - z\right) - -2} - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right)\right)\right) + \frac{9999999999998099}{10000000000000000}\right)\right)\right)\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\color{blue}{\left(\left(1 - z\right) - \left(-6 + \frac{-1}{2}\right)\right)}}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{z - \frac{15}{2}}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7} + \left(\frac{\frac{2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \left(\frac{\frac{-3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5} + \left(\frac{\frac{2501468655737381}{200000000000000}}{\left(1 - z\right) - -4} + \left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \left(\frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1} - \left(\frac{\frac{7713234287776531}{10000000000000}}{\left(1 - z\right) - -2} - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right)\right)\right) + \frac{9999999999998099}{10000000000000000}\right)\right)\right)\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(1 - z\right) - \color{blue}{\frac{-13}{2}}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{z - \frac{15}{2}}\right)\right)\right) \]

      5. sub-to-mult N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7} + \left(\frac{\frac{2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \left(\frac{\frac{-3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5} + \left(\frac{\frac{2501468655737381}{200000000000000}}{\left(1 - z\right) - -4} + \left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \left(\frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1} - \left(\frac{\frac{7713234287776531}{10000000000000}}{\left(1 - z\right) - -2} - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right)\right)\right) + \frac{9999999999998099}{10000000000000000}\right)\right)\right)\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\color{blue}{\left(\left(1 - \frac{\frac{-13}{2}}{1 - z}\right) \cdot \left(1 - z\right)\right)}}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{z - \frac{15}{2}}\right)\right)\right) \]

      6. lower-unsound-*.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7} + \left(\frac{\frac{2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \left(\frac{\frac{-3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5} + \left(\frac{\frac{2501468655737381}{200000000000000}}{\left(1 - z\right) - -4} + \left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \left(\frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1} - \left(\frac{\frac{7713234287776531}{10000000000000}}{\left(1 - z\right) - -2} - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right)\right)\right) + \frac{9999999999998099}{10000000000000000}\right)\right)\right)\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\color{blue}{\left(\left(1 - \frac{\frac{-13}{2}}{1 - z}\right) \cdot \left(1 - z\right)\right)}}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{z - \frac{15}{2}}\right)\right)\right) \]

      7. lower-unsound--.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7} + \left(\frac{\frac{2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \left(\frac{\frac{-3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5} + \left(\frac{\frac{2501468655737381}{200000000000000}}{\left(1 - z\right) - -4} + \left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \left(\frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1} - \left(\frac{\frac{7713234287776531}{10000000000000}}{\left(1 - z\right) - -2} - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right)\right)\right) + \frac{9999999999998099}{10000000000000000}\right)\right)\right)\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\color{blue}{\left(1 - \frac{\frac{-13}{2}}{1 - z}\right)} \cdot \left(1 - z\right)\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{z - \frac{15}{2}}\right)\right)\right) \]

      8. lower-unsound-/.f64 98.5

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

   10. Applied rewrites 98.5%

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

Alternative 2: 99.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_0 := \sqrt{\pi + \pi}\\ t_1 := \frac{\pi}{\sin \left(\pi \cdot z\right)}\\ t_2 := \left(1 - z\right) - 0.5\\ t_3 := \left(1 - z\right) - -6\\ \mathbf{if}\;z \leq -1000:\\ \;\;\;\;t\_1 \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(t\_0 \cdot \left({7.5}^{t\_2} \cdot e^{-7.5}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) - -7} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{t\_3} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - -5} + \left(\frac{12.507343278686905}{\left(1 - z\right) - -4} + \left(\left(\frac{676.5203681218851}{1 - z} - \left(\frac{1259.1392167224028}{\left(1 - z\right) - -1} - \left(\frac{771.3234287776531}{\left(1 - z\right) - -2} - \frac{-176.6150291621406}{-4 + z}\right)\right)\right) + 0.9999999999998099\right)\right)\right)\right)\right) \cdot \left(t\_0 \cdot \left({\left(t\_3 - -0.5\right)}^{t\_2} \cdot e^{z - 7.5}\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (sqrt (+ PI PI)))
        (t_1 (/ PI (sin (* PI z))))
        (t_2 (- (- 1.0 z) 0.5))
        (t_3 (- (- 1.0 z) -6.0)))
   (if (<= z -1000.0)
     (*
      t_1
      (*
       (+
        263.3831869810514
        (* z (+ 436.8961725563396 (* 545.0353078428827 z))))
       (* t_0 (* (pow 7.5 t_2) (exp (- 7.5))))))
     (*
      t_1
      (*
       (+
        (/ 1.5056327351493116e-7 (- (- 1.0 z) -7.0))
        (+
         (/ 9.984369578019572e-6 t_3)
         (+
          (/ -0.13857109526572012 (- (- 1.0 z) -5.0))
          (+
           (/ 12.507343278686905 (- (- 1.0 z) -4.0))
           (+
            (-
             (/ 676.5203681218851 (- 1.0 z))
             (-
              (/ 1259.1392167224028 (- (- 1.0 z) -1.0))
              (-
               (/ 771.3234287776531 (- (- 1.0 z) -2.0))
               (/ -176.6150291621406 (+ -4.0 z)))))
            0.9999999999998099)))))
       (* t_0 (* (pow (- t_3 -0.5) t_2) (exp (- z 7.5)))))))))

C

double code(double z) {
	double t_0 = sqrt((((double) M_PI) + ((double) M_PI)));
	double t_1 = ((double) M_PI) / sin((((double) M_PI) * z));
	double t_2 = (1.0 - z) - 0.5;
	double t_3 = (1.0 - z) - -6.0;
	double tmp;
	if (z <= -1000.0) {
		tmp = t_1 * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (t_0 * (pow(7.5, t_2) * exp(-7.5))));
	} else {
		tmp = t_1 * (((1.5056327351493116e-7 / ((1.0 - z) - -7.0)) + ((9.984369578019572e-6 / t_3) + ((-0.13857109526572012 / ((1.0 - z) - -5.0)) + ((12.507343278686905 / ((1.0 - z) - -4.0)) + (((676.5203681218851 / (1.0 - z)) - ((1259.1392167224028 / ((1.0 - z) - -1.0)) - ((771.3234287776531 / ((1.0 - z) - -2.0)) - (-176.6150291621406 / (-4.0 + z))))) + 0.9999999999998099))))) * (t_0 * (pow((t_3 - -0.5), t_2) * exp((z - 7.5)))));
	}
	return tmp;
}

Java

public static double code(double z) {
	double t_0 = Math.sqrt((Math.PI + Math.PI));
	double t_1 = Math.PI / Math.sin((Math.PI * z));
	double t_2 = (1.0 - z) - 0.5;
	double t_3 = (1.0 - z) - -6.0;
	double tmp;
	if (z <= -1000.0) {
		tmp = t_1 * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (t_0 * (Math.pow(7.5, t_2) * Math.exp(-7.5))));
	} else {
		tmp = t_1 * (((1.5056327351493116e-7 / ((1.0 - z) - -7.0)) + ((9.984369578019572e-6 / t_3) + ((-0.13857109526572012 / ((1.0 - z) - -5.0)) + ((12.507343278686905 / ((1.0 - z) - -4.0)) + (((676.5203681218851 / (1.0 - z)) - ((1259.1392167224028 / ((1.0 - z) - -1.0)) - ((771.3234287776531 / ((1.0 - z) - -2.0)) - (-176.6150291621406 / (-4.0 + z))))) + 0.9999999999998099))))) * (t_0 * (Math.pow((t_3 - -0.5), t_2) * Math.exp((z - 7.5)))));
	}
	return tmp;
}

Python

def code(z):
	t_0 = math.sqrt((math.pi + math.pi))
	t_1 = math.pi / math.sin((math.pi * z))
	t_2 = (1.0 - z) - 0.5
	t_3 = (1.0 - z) - -6.0
	tmp = 0
	if z <= -1000.0:
		tmp = t_1 * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (t_0 * (math.pow(7.5, t_2) * math.exp(-7.5))))
	else:
		tmp = t_1 * (((1.5056327351493116e-7 / ((1.0 - z) - -7.0)) + ((9.984369578019572e-6 / t_3) + ((-0.13857109526572012 / ((1.0 - z) - -5.0)) + ((12.507343278686905 / ((1.0 - z) - -4.0)) + (((676.5203681218851 / (1.0 - z)) - ((1259.1392167224028 / ((1.0 - z) - -1.0)) - ((771.3234287776531 / ((1.0 - z) - -2.0)) - (-176.6150291621406 / (-4.0 + z))))) + 0.9999999999998099))))) * (t_0 * (math.pow((t_3 - -0.5), t_2) * math.exp((z - 7.5)))))
	return tmp

Julia

function code(z)
	t_0 = sqrt(Float64(pi + pi))
	t_1 = Float64(pi / sin(Float64(pi * z)))
	t_2 = Float64(Float64(1.0 - z) - 0.5)
	t_3 = Float64(Float64(1.0 - z) - -6.0)
	tmp = 0.0
	if (z <= -1000.0)
		tmp = Float64(t_1 * Float64(Float64(263.3831869810514 + Float64(z * Float64(436.8961725563396 + Float64(545.0353078428827 * z)))) * Float64(t_0 * Float64((7.5 ^ t_2) * exp(Float64(-7.5))))));
	else
		tmp = Float64(t_1 * Float64(Float64(Float64(1.5056327351493116e-7 / Float64(Float64(1.0 - z) - -7.0)) + Float64(Float64(9.984369578019572e-6 / t_3) + Float64(Float64(-0.13857109526572012 / Float64(Float64(1.0 - z) - -5.0)) + Float64(Float64(12.507343278686905 / Float64(Float64(1.0 - z) - -4.0)) + Float64(Float64(Float64(676.5203681218851 / Float64(1.0 - z)) - Float64(Float64(1259.1392167224028 / Float64(Float64(1.0 - z) - -1.0)) - Float64(Float64(771.3234287776531 / Float64(Float64(1.0 - z) - -2.0)) - Float64(-176.6150291621406 / Float64(-4.0 + z))))) + 0.9999999999998099))))) * Float64(t_0 * Float64((Float64(t_3 - -0.5) ^ t_2) * exp(Float64(z - 7.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z)
	t_0 = sqrt((pi + pi));
	t_1 = pi / sin((pi * z));
	t_2 = (1.0 - z) - 0.5;
	t_3 = (1.0 - z) - -6.0;
	tmp = 0.0;
	if (z <= -1000.0)
		tmp = t_1 * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (t_0 * ((7.5 ^ t_2) * exp(-7.5))));
	else
		tmp = t_1 * (((1.5056327351493116e-7 / ((1.0 - z) - -7.0)) + ((9.984369578019572e-6 / t_3) + ((-0.13857109526572012 / ((1.0 - z) - -5.0)) + ((12.507343278686905 / ((1.0 - z) - -4.0)) + (((676.5203681218851 / (1.0 - z)) - ((1259.1392167224028 / ((1.0 - z) - -1.0)) - ((771.3234287776531 / ((1.0 - z) - -2.0)) - (-176.6150291621406 / (-4.0 + z))))) + 0.9999999999998099))))) * (t_0 * (((t_3 - -0.5) ^ t_2) * exp((z - 7.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[z_] := Block[{t$95$0 = N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(Pi / N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 - z), $MachinePrecision] - 0.5), $MachinePrecision]}, Block[{t$95$3 = N[(N[(1.0 - z), $MachinePrecision] - -6.0), $MachinePrecision]}, If[LessEqual[z, -1000.0], N[(t$95$1 * N[(N[(263.3831869810514 + N[(z * N[(436.8961725563396 + N[(545.0353078428827 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 * N[(N[Power[7.5, t$95$2], $MachinePrecision] * N[Exp[(-7.5)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(N[(N[(1.5056327351493116e-7 / N[(N[(1.0 - z), $MachinePrecision] - -7.0), $MachinePrecision]), $MachinePrecision] + N[(N[(9.984369578019572e-6 / t$95$3), $MachinePrecision] + N[(N[(-0.13857109526572012 / N[(N[(1.0 - z), $MachinePrecision] - -5.0), $MachinePrecision]), $MachinePrecision] + N[(N[(12.507343278686905 / N[(N[(1.0 - z), $MachinePrecision] - -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(676.5203681218851 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - N[(N[(1259.1392167224028 / N[(N[(1.0 - z), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(771.3234287776531 / N[(N[(1.0 - z), $MachinePrecision] - -2.0), $MachinePrecision]), $MachinePrecision] - N[(-176.6150291621406 / N[(-4.0 + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 0.9999999999998099), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 * N[(N[Power[N[(t$95$3 - -0.5), $MachinePrecision], t$95$2], $MachinePrecision] * N[Exp[N[(z - 7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1e3

   1. Initial program 96.6%

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

   3. Applied rewrites 98.5%

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

   5. Applied rewrites 98.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + \color{blue}{z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \color{blue}{\left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \color{blue}{\frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      4. lower-*.f64 96.7

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot \color{blue}{z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   8. Applied rewrites 96.7%

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   9. Taylor expanded in z around 0

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\color{blue}{\frac{15}{2}}}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 95.6%

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\color{blue}{7.5}}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   12. Taylor expanded in z around 0

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\frac{15}{2}}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\color{blue}{\frac{15}{2}}}\right)\right)\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 96.2%

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({7.5}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\color{blue}{7.5}}\right)\right)\right) \]

   if -1e3 < z

   1. Initial program 96.6%

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

   3. Applied rewrites 98.5%

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

   5. Applied rewrites 98.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7} + \left(\frac{\frac{2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \left(\frac{\frac{-3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5} + \left(\frac{\frac{2501468655737381}{200000000000000}}{\left(1 - z\right) - -4} + \left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \left(\frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1} - \left(\frac{\frac{7713234287776531}{10000000000000}}{\left(1 - z\right) - -2} - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right)\right)\right) + \frac{9999999999998099}{10000000000000000}\right)\right)\right)\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{\color{blue}{z - \frac{15}{2}}}\right)\right)\right) \]
   7. Step-by-step derivation

      1. lower--.f64 98.5

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

   8. Applied rewrites 98.5%

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) - -7} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(1 - z\right) - -6} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - -5} + \left(\frac{12.507343278686905}{\left(1 - z\right) - -4} + \left(\left(\frac{676.5203681218851}{1 - z} - \left(\frac{1259.1392167224028}{\left(1 - z\right) - -1} - \left(\frac{771.3234287776531}{\left(1 - z\right) - -2} - \frac{-176.6150291621406}{-4 + z}\right)\right)\right) + 0.9999999999998099\right)\right)\right)\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{\color{blue}{z - 7.5}}\right)\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 99.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_0 := \frac{\pi}{\sin \left(\pi \cdot z\right)}\\ \mathbf{if}\;z \leq -1000:\\ \;\;\;\;t\_0 \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({7.5}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-7.5}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) - -7} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(1 - z\right) - -6} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - -5} + \left(\frac{12.507343278686905}{\left(1 - z\right) - -4} + \left(\left(\frac{676.5203681218851}{1 - z} - \left(\frac{1259.1392167224028}{\left(1 - z\right) - -1} - \left(\frac{771.3234287776531}{\left(1 - z\right) - -2} - \frac{-176.6150291621406}{-4 + z}\right)\right)\right) + 0.9999999999998099\right)\right)\right)\right)\right) \cdot \left(e^{\log \left(7.5 - z\right) \cdot \left(0.5 - z\right)} \cdot \left(e^{z - 7.5} \cdot \sqrt{2 \cdot \pi}\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (/ PI (sin (* PI z)))))
   (if (<= z -1000.0)
     (*
      t_0
      (*
       (+
        263.3831869810514
        (* z (+ 436.8961725563396 (* 545.0353078428827 z))))
       (* (sqrt (+ PI PI)) (* (pow 7.5 (- (- 1.0 z) 0.5)) (exp (- 7.5))))))
     (*
      t_0
      (*
       (+
        (/ 1.5056327351493116e-7 (- (- 1.0 z) -7.0))
        (+
         (/ 9.984369578019572e-6 (- (- 1.0 z) -6.0))
         (+
          (/ -0.13857109526572012 (- (- 1.0 z) -5.0))
          (+
           (/ 12.507343278686905 (- (- 1.0 z) -4.0))
           (+
            (-
             (/ 676.5203681218851 (- 1.0 z))
             (-
              (/ 1259.1392167224028 (- (- 1.0 z) -1.0))
              (-
               (/ 771.3234287776531 (- (- 1.0 z) -2.0))
               (/ -176.6150291621406 (+ -4.0 z)))))
            0.9999999999998099)))))
       (*
        (exp (* (log (- 7.5 z)) (- 0.5 z)))
        (* (exp (- z 7.5)) (sqrt (* 2.0 PI)))))))))

C

double code(double z) {
	double t_0 = ((double) M_PI) / sin((((double) M_PI) * z));
	double tmp;
	if (z <= -1000.0) {
		tmp = t_0 * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (sqrt((((double) M_PI) + ((double) M_PI))) * (pow(7.5, ((1.0 - z) - 0.5)) * exp(-7.5))));
	} else {
		tmp = t_0 * (((1.5056327351493116e-7 / ((1.0 - z) - -7.0)) + ((9.984369578019572e-6 / ((1.0 - z) - -6.0)) + ((-0.13857109526572012 / ((1.0 - z) - -5.0)) + ((12.507343278686905 / ((1.0 - z) - -4.0)) + (((676.5203681218851 / (1.0 - z)) - ((1259.1392167224028 / ((1.0 - z) - -1.0)) - ((771.3234287776531 / ((1.0 - z) - -2.0)) - (-176.6150291621406 / (-4.0 + z))))) + 0.9999999999998099))))) * (exp((log((7.5 - z)) * (0.5 - z))) * (exp((z - 7.5)) * sqrt((2.0 * ((double) M_PI))))));
	}
	return tmp;
}

Java

public static double code(double z) {
	double t_0 = Math.PI / Math.sin((Math.PI * z));
	double tmp;
	if (z <= -1000.0) {
		tmp = t_0 * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (Math.sqrt((Math.PI + Math.PI)) * (Math.pow(7.5, ((1.0 - z) - 0.5)) * Math.exp(-7.5))));
	} else {
		tmp = t_0 * (((1.5056327351493116e-7 / ((1.0 - z) - -7.0)) + ((9.984369578019572e-6 / ((1.0 - z) - -6.0)) + ((-0.13857109526572012 / ((1.0 - z) - -5.0)) + ((12.507343278686905 / ((1.0 - z) - -4.0)) + (((676.5203681218851 / (1.0 - z)) - ((1259.1392167224028 / ((1.0 - z) - -1.0)) - ((771.3234287776531 / ((1.0 - z) - -2.0)) - (-176.6150291621406 / (-4.0 + z))))) + 0.9999999999998099))))) * (Math.exp((Math.log((7.5 - z)) * (0.5 - z))) * (Math.exp((z - 7.5)) * Math.sqrt((2.0 * Math.PI)))));
	}
	return tmp;
}

Python

def code(z):
	t_0 = math.pi / math.sin((math.pi * z))
	tmp = 0
	if z <= -1000.0:
		tmp = t_0 * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (math.sqrt((math.pi + math.pi)) * (math.pow(7.5, ((1.0 - z) - 0.5)) * math.exp(-7.5))))
	else:
		tmp = t_0 * (((1.5056327351493116e-7 / ((1.0 - z) - -7.0)) + ((9.984369578019572e-6 / ((1.0 - z) - -6.0)) + ((-0.13857109526572012 / ((1.0 - z) - -5.0)) + ((12.507343278686905 / ((1.0 - z) - -4.0)) + (((676.5203681218851 / (1.0 - z)) - ((1259.1392167224028 / ((1.0 - z) - -1.0)) - ((771.3234287776531 / ((1.0 - z) - -2.0)) - (-176.6150291621406 / (-4.0 + z))))) + 0.9999999999998099))))) * (math.exp((math.log((7.5 - z)) * (0.5 - z))) * (math.exp((z - 7.5)) * math.sqrt((2.0 * math.pi)))))
	return tmp

Julia

function code(z)
	t_0 = Float64(pi / sin(Float64(pi * z)))
	tmp = 0.0
	if (z <= -1000.0)
		tmp = Float64(t_0 * Float64(Float64(263.3831869810514 + Float64(z * Float64(436.8961725563396 + Float64(545.0353078428827 * z)))) * Float64(sqrt(Float64(pi + pi)) * Float64((7.5 ^ Float64(Float64(1.0 - z) - 0.5)) * exp(Float64(-7.5))))));
	else
		tmp = Float64(t_0 * Float64(Float64(Float64(1.5056327351493116e-7 / Float64(Float64(1.0 - z) - -7.0)) + Float64(Float64(9.984369578019572e-6 / Float64(Float64(1.0 - z) - -6.0)) + Float64(Float64(-0.13857109526572012 / Float64(Float64(1.0 - z) - -5.0)) + Float64(Float64(12.507343278686905 / Float64(Float64(1.0 - z) - -4.0)) + Float64(Float64(Float64(676.5203681218851 / Float64(1.0 - z)) - Float64(Float64(1259.1392167224028 / Float64(Float64(1.0 - z) - -1.0)) - Float64(Float64(771.3234287776531 / Float64(Float64(1.0 - z) - -2.0)) - Float64(-176.6150291621406 / Float64(-4.0 + z))))) + 0.9999999999998099))))) * Float64(exp(Float64(log(Float64(7.5 - z)) * Float64(0.5 - z))) * Float64(exp(Float64(z - 7.5)) * sqrt(Float64(2.0 * pi))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z)
	t_0 = pi / sin((pi * z));
	tmp = 0.0;
	if (z <= -1000.0)
		tmp = t_0 * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (sqrt((pi + pi)) * ((7.5 ^ ((1.0 - z) - 0.5)) * exp(-7.5))));
	else
		tmp = t_0 * (((1.5056327351493116e-7 / ((1.0 - z) - -7.0)) + ((9.984369578019572e-6 / ((1.0 - z) - -6.0)) + ((-0.13857109526572012 / ((1.0 - z) - -5.0)) + ((12.507343278686905 / ((1.0 - z) - -4.0)) + (((676.5203681218851 / (1.0 - z)) - ((1259.1392167224028 / ((1.0 - z) - -1.0)) - ((771.3234287776531 / ((1.0 - z) - -2.0)) - (-176.6150291621406 / (-4.0 + z))))) + 0.9999999999998099))))) * (exp((log((7.5 - z)) * (0.5 - z))) * (exp((z - 7.5)) * sqrt((2.0 * pi)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[z_] := Block[{t$95$0 = N[(Pi / N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1000.0], N[(t$95$0 * N[(N[(263.3831869810514 + N[(z * N[(436.8961725563396 + N[(545.0353078428827 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision] * N[(N[Power[7.5, N[(N[(1.0 - z), $MachinePrecision] - 0.5), $MachinePrecision]], $MachinePrecision] * N[Exp[(-7.5)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(N[(N[(1.5056327351493116e-7 / N[(N[(1.0 - z), $MachinePrecision] - -7.0), $MachinePrecision]), $MachinePrecision] + N[(N[(9.984369578019572e-6 / N[(N[(1.0 - z), $MachinePrecision] - -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(-0.13857109526572012 / N[(N[(1.0 - z), $MachinePrecision] - -5.0), $MachinePrecision]), $MachinePrecision] + N[(N[(12.507343278686905 / N[(N[(1.0 - z), $MachinePrecision] - -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(676.5203681218851 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - N[(N[(1259.1392167224028 / N[(N[(1.0 - z), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(771.3234287776531 / N[(N[(1.0 - z), $MachinePrecision] - -2.0), $MachinePrecision]), $MachinePrecision] - N[(-176.6150291621406 / N[(-4.0 + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 0.9999999999998099), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Exp[N[(N[Log[N[(7.5 - z), $MachinePrecision]], $MachinePrecision] * N[(0.5 - z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(N[Exp[N[(z - 7.5), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(2.0 * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1e3

   1. Initial program 96.6%

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

   3. Applied rewrites 98.5%

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

   5. Applied rewrites 98.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + \color{blue}{z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \color{blue}{\left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \color{blue}{\frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      4. lower-*.f64 96.7

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot \color{blue}{z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   8. Applied rewrites 96.7%

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   9. Taylor expanded in z around 0

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\color{blue}{\frac{15}{2}}}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 95.6%

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\color{blue}{7.5}}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   12. Taylor expanded in z around 0

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\frac{15}{2}}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\color{blue}{\frac{15}{2}}}\right)\right)\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 96.2%

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({7.5}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\color{blue}{7.5}}\right)\right)\right) \]

   if -1e3 < z

   1. Initial program 96.6%

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

   3. Applied rewrites 98.5%

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

   5. Applied rewrites 98.5%

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

   6. Taylor expanded in z around inf

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7} + \left(\frac{\frac{2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \left(\frac{\frac{-3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5} + \left(\frac{\frac{2501468655737381}{200000000000000}}{\left(1 - z\right) - -4} + \left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \left(\frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1} - \left(\frac{\frac{7713234287776531}{10000000000000}}{\left(1 - z\right) - -2} - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right)\right)\right) + \frac{9999999999998099}{10000000000000000}\right)\right)\right)\right)\right) \cdot \color{blue}{\left(e^{\log \left(\frac{15}{2} - z\right) \cdot \left(\frac{1}{2} - z\right)} \cdot \left(e^{z - \frac{15}{2}} \cdot \sqrt{2 \cdot \mathsf{PI}\left(\right)}\right)\right)}\right) \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7} + \left(\frac{\frac{2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \left(\frac{\frac{-3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5} + \left(\frac{\frac{2501468655737381}{200000000000000}}{\left(1 - z\right) - -4} + \left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \left(\frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1} - \left(\frac{\frac{7713234287776531}{10000000000000}}{\left(1 - z\right) - -2} - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right)\right)\right) + \frac{9999999999998099}{10000000000000000}\right)\right)\right)\right)\right) \cdot \left(e^{\log \left(\frac{15}{2} - z\right) \cdot \left(\frac{1}{2} - z\right)} \cdot \color{blue}{\left(e^{z - \frac{15}{2}} \cdot \sqrt{2 \cdot \mathsf{PI}\left(\right)}\right)}\right)\right) \]

      2. lower-exp.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7} + \left(\frac{\frac{2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \left(\frac{\frac{-3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5} + \left(\frac{\frac{2501468655737381}{200000000000000}}{\left(1 - z\right) - -4} + \left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \left(\frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1} - \left(\frac{\frac{7713234287776531}{10000000000000}}{\left(1 - z\right) - -2} - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right)\right)\right) + \frac{9999999999998099}{10000000000000000}\right)\right)\right)\right)\right) \cdot \left(e^{\log \left(\frac{15}{2} - z\right) \cdot \left(\frac{1}{2} - z\right)} \cdot \left(\color{blue}{e^{z - \frac{15}{2}}} \cdot \sqrt{2 \cdot \mathsf{PI}\left(\right)}\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7} + \left(\frac{\frac{2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \left(\frac{\frac{-3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5} + \left(\frac{\frac{2501468655737381}{200000000000000}}{\left(1 - z\right) - -4} + \left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \left(\frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1} - \left(\frac{\frac{7713234287776531}{10000000000000}}{\left(1 - z\right) - -2} - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right)\right)\right) + \frac{9999999999998099}{10000000000000000}\right)\right)\right)\right)\right) \cdot \left(e^{\log \left(\frac{15}{2} - z\right) \cdot \left(\frac{1}{2} - z\right)} \cdot \left(e^{\color{blue}{z - \frac{15}{2}}} \cdot \sqrt{2 \cdot \mathsf{PI}\left(\right)}\right)\right)\right) \]

      4. lower-log.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7} + \left(\frac{\frac{2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \left(\frac{\frac{-3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5} + \left(\frac{\frac{2501468655737381}{200000000000000}}{\left(1 - z\right) - -4} + \left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \left(\frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1} - \left(\frac{\frac{7713234287776531}{10000000000000}}{\left(1 - z\right) - -2} - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right)\right)\right) + \frac{9999999999998099}{10000000000000000}\right)\right)\right)\right)\right) \cdot \left(e^{\log \left(\frac{15}{2} - z\right) \cdot \left(\frac{1}{2} - z\right)} \cdot \left(e^{\color{blue}{z} - \frac{15}{2}} \cdot \sqrt{2 \cdot \mathsf{PI}\left(\right)}\right)\right)\right) \]

      5. lower--.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7} + \left(\frac{\frac{2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \left(\frac{\frac{-3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5} + \left(\frac{\frac{2501468655737381}{200000000000000}}{\left(1 - z\right) - -4} + \left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \left(\frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1} - \left(\frac{\frac{7713234287776531}{10000000000000}}{\left(1 - z\right) - -2} - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right)\right)\right) + \frac{9999999999998099}{10000000000000000}\right)\right)\right)\right)\right) \cdot \left(e^{\log \left(\frac{15}{2} - z\right) \cdot \left(\frac{1}{2} - z\right)} \cdot \left(e^{z - \frac{15}{2}} \cdot \sqrt{2 \cdot \mathsf{PI}\left(\right)}\right)\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7} + \left(\frac{\frac{2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \left(\frac{\frac{-3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5} + \left(\frac{\frac{2501468655737381}{200000000000000}}{\left(1 - z\right) - -4} + \left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \left(\frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1} - \left(\frac{\frac{7713234287776531}{10000000000000}}{\left(1 - z\right) - -2} - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right)\right)\right) + \frac{9999999999998099}{10000000000000000}\right)\right)\right)\right)\right) \cdot \left(e^{\log \left(\frac{15}{2} - z\right) \cdot \left(\frac{1}{2} - z\right)} \cdot \left(e^{z - \color{blue}{\frac{15}{2}}} \cdot \sqrt{2 \cdot \mathsf{PI}\left(\right)}\right)\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7} + \left(\frac{\frac{2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \left(\frac{\frac{-3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5} + \left(\frac{\frac{2501468655737381}{200000000000000}}{\left(1 - z\right) - -4} + \left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \left(\frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1} - \left(\frac{\frac{7713234287776531}{10000000000000}}{\left(1 - z\right) - -2} - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right)\right)\right) + \frac{9999999999998099}{10000000000000000}\right)\right)\right)\right)\right) \cdot \left(e^{\log \left(\frac{15}{2} - z\right) \cdot \left(\frac{1}{2} - z\right)} \cdot \left(e^{z - \frac{15}{2}} \cdot \color{blue}{\sqrt{2 \cdot \mathsf{PI}\left(\right)}}\right)\right)\right) \]

      8. lower-exp.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7} + \left(\frac{\frac{2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \left(\frac{\frac{-3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5} + \left(\frac{\frac{2501468655737381}{200000000000000}}{\left(1 - z\right) - -4} + \left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \left(\frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1} - \left(\frac{\frac{7713234287776531}{10000000000000}}{\left(1 - z\right) - -2} - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right)\right)\right) + \frac{9999999999998099}{10000000000000000}\right)\right)\right)\right)\right) \cdot \left(e^{\log \left(\frac{15}{2} - z\right) \cdot \left(\frac{1}{2} - z\right)} \cdot \left(e^{z - \frac{15}{2}} \cdot \sqrt{\color{blue}{2 \cdot \mathsf{PI}\left(\right)}}\right)\right)\right) \]

      9. lower--.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7} + \left(\frac{\frac{2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \left(\frac{\frac{-3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5} + \left(\frac{\frac{2501468655737381}{200000000000000}}{\left(1 - z\right) - -4} + \left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \left(\frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1} - \left(\frac{\frac{7713234287776531}{10000000000000}}{\left(1 - z\right) - -2} - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right)\right)\right) + \frac{9999999999998099}{10000000000000000}\right)\right)\right)\right)\right) \cdot \left(e^{\log \left(\frac{15}{2} - z\right) \cdot \left(\frac{1}{2} - z\right)} \cdot \left(e^{z - \frac{15}{2}} \cdot \sqrt{\color{blue}{2} \cdot \mathsf{PI}\left(\right)}\right)\right)\right) \]

      10. lower-sqrt.f64 N/A

          \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7} + \left(\frac{\frac{2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \left(\frac{\frac{-3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5} + \left(\frac{\frac{2501468655737381}{200000000000000}}{\left(1 - z\right) - -4} + \left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \left(\frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1} - \left(\frac{\frac{7713234287776531}{10000000000000}}{\left(1 - z\right) - -2} - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right)\right)\right) + \frac{9999999999998099}{10000000000000000}\right)\right)\right)\right)\right) \cdot \left(e^{\log \left(\frac{15}{2} - z\right) \cdot \left(\frac{1}{2} - z\right)} \cdot \left(e^{z - \frac{15}{2}} \cdot \sqrt{2 \cdot \mathsf{PI}\left(\right)}\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7} + \left(\frac{\frac{2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \left(\frac{\frac{-3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5} + \left(\frac{\frac{2501468655737381}{200000000000000}}{\left(1 - z\right) - -4} + \left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \left(\frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1} - \left(\frac{\frac{7713234287776531}{10000000000000}}{\left(1 - z\right) - -2} - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right)\right)\right) + \frac{9999999999998099}{10000000000000000}\right)\right)\right)\right)\right) \cdot \left(e^{\log \left(\frac{15}{2} - z\right) \cdot \left(\frac{1}{2} - z\right)} \cdot \left(e^{z - \frac{15}{2}} \cdot \sqrt{2 \cdot \mathsf{PI}\left(\right)}\right)\right)\right) \]

      12. lower-PI.f64 98.5

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

   8. Applied rewrites 98.5%

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) - -7} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(1 - z\right) - -6} + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - -5} + \left(\frac{12.507343278686905}{\left(1 - z\right) - -4} + \left(\left(\frac{676.5203681218851}{1 - z} - \left(\frac{1259.1392167224028}{\left(1 - z\right) - -1} - \left(\frac{771.3234287776531}{\left(1 - z\right) - -2} - \frac{-176.6150291621406}{-4 + z}\right)\right)\right) + 0.9999999999998099\right)\right)\right)\right)\right) \cdot \color{blue}{\left(e^{\log \left(7.5 - z\right) \cdot \left(0.5 - z\right)} \cdot \left(e^{z - 7.5} \cdot \sqrt{2 \cdot \pi}\right)\right)}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 99.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} t_0 := \left(1 - z\right) - 0.5\\ \mathbf{if}\;z \leq -1000:\\ \;\;\;\;\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({7.5}^{t\_0} \cdot e^{-7.5}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \frac{\left(\left(\left(\left(\left(\left(\left(\frac{676.5203681218851}{1 - z} - -0.9999999999998099\right) - \frac{1259.1392167224028}{\left(1 - z\right) - -1}\right) - \frac{-771.3234287776531}{\left(1 - z\right) - -2}\right) - \frac{-176.6150291621406}{-4 + z}\right) - \frac{-12.507343278686905}{\left(1 - z\right) - -4}\right) - \frac{0.13857109526572012}{\left(1 - z\right) - -5}\right) - \left(\frac{-9.984369578019572 \cdot 10^{-6}}{\left(1 - z\right) - -6} + \frac{-1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) - -7}\right)\right) \cdot \left(\left({\left(\left(1 - z\right) - -6.5\right)}^{t\_0} \cdot 2.5066282746310007\right) \cdot e^{z - 7.5}\right)}{\sin \left(z \cdot \pi\right)}\\ \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (- (- 1.0 z) 0.5)))
   (if (<= z -1000.0)
     (*
      (/ PI (sin (* PI z)))
      (*
       (+
        263.3831869810514
        (* z (+ 436.8961725563396 (* 545.0353078428827 z))))
       (* (sqrt (+ PI PI)) (* (pow 7.5 t_0) (exp (- 7.5))))))
     (*
      PI
      (/
       (*
        (-
         (-
          (-
           (-
            (-
             (-
              (- (/ 676.5203681218851 (- 1.0 z)) -0.9999999999998099)
              (/ 1259.1392167224028 (- (- 1.0 z) -1.0)))
             (/ -771.3234287776531 (- (- 1.0 z) -2.0)))
            (/ -176.6150291621406 (+ -4.0 z)))
           (/ -12.507343278686905 (- (- 1.0 z) -4.0)))
          (/ 0.13857109526572012 (- (- 1.0 z) -5.0)))
         (+
          (/ -9.984369578019572e-6 (- (- 1.0 z) -6.0))
          (/ -1.5056327351493116e-7 (- (- 1.0 z) -7.0))))
        (*
         (* (pow (- (- 1.0 z) -6.5) t_0) 2.5066282746310007)
         (exp (- z 7.5))))
       (sin (* z PI)))))))

C

double code(double z) {
	double t_0 = (1.0 - z) - 0.5;
	double tmp;
	if (z <= -1000.0) {
		tmp = (((double) M_PI) / sin((((double) M_PI) * z))) * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (sqrt((((double) M_PI) + ((double) M_PI))) * (pow(7.5, t_0) * exp(-7.5))));
	} else {
		tmp = ((double) M_PI) * ((((((((((676.5203681218851 / (1.0 - z)) - -0.9999999999998099) - (1259.1392167224028 / ((1.0 - z) - -1.0))) - (-771.3234287776531 / ((1.0 - z) - -2.0))) - (-176.6150291621406 / (-4.0 + z))) - (-12.507343278686905 / ((1.0 - z) - -4.0))) - (0.13857109526572012 / ((1.0 - z) - -5.0))) - ((-9.984369578019572e-6 / ((1.0 - z) - -6.0)) + (-1.5056327351493116e-7 / ((1.0 - z) - -7.0)))) * ((pow(((1.0 - z) - -6.5), t_0) * 2.5066282746310007) * exp((z - 7.5)))) / sin((z * ((double) M_PI))));
	}
	return tmp;
}

Java

public static double code(double z) {
	double t_0 = (1.0 - z) - 0.5;
	double tmp;
	if (z <= -1000.0) {
		tmp = (Math.PI / Math.sin((Math.PI * z))) * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (Math.sqrt((Math.PI + Math.PI)) * (Math.pow(7.5, t_0) * Math.exp(-7.5))));
	} else {
		tmp = Math.PI * ((((((((((676.5203681218851 / (1.0 - z)) - -0.9999999999998099) - (1259.1392167224028 / ((1.0 - z) - -1.0))) - (-771.3234287776531 / ((1.0 - z) - -2.0))) - (-176.6150291621406 / (-4.0 + z))) - (-12.507343278686905 / ((1.0 - z) - -4.0))) - (0.13857109526572012 / ((1.0 - z) - -5.0))) - ((-9.984369578019572e-6 / ((1.0 - z) - -6.0)) + (-1.5056327351493116e-7 / ((1.0 - z) - -7.0)))) * ((Math.pow(((1.0 - z) - -6.5), t_0) * 2.5066282746310007) * Math.exp((z - 7.5)))) / Math.sin((z * Math.PI)));
	}
	return tmp;
}

Python

def code(z):
	t_0 = (1.0 - z) - 0.5
	tmp = 0
	if z <= -1000.0:
		tmp = (math.pi / math.sin((math.pi * z))) * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (math.sqrt((math.pi + math.pi)) * (math.pow(7.5, t_0) * math.exp(-7.5))))
	else:
		tmp = math.pi * ((((((((((676.5203681218851 / (1.0 - z)) - -0.9999999999998099) - (1259.1392167224028 / ((1.0 - z) - -1.0))) - (-771.3234287776531 / ((1.0 - z) - -2.0))) - (-176.6150291621406 / (-4.0 + z))) - (-12.507343278686905 / ((1.0 - z) - -4.0))) - (0.13857109526572012 / ((1.0 - z) - -5.0))) - ((-9.984369578019572e-6 / ((1.0 - z) - -6.0)) + (-1.5056327351493116e-7 / ((1.0 - z) - -7.0)))) * ((math.pow(((1.0 - z) - -6.5), t_0) * 2.5066282746310007) * math.exp((z - 7.5)))) / math.sin((z * math.pi)))
	return tmp

Julia

function code(z)
	t_0 = Float64(Float64(1.0 - z) - 0.5)
	tmp = 0.0
	if (z <= -1000.0)
		tmp = Float64(Float64(pi / sin(Float64(pi * z))) * Float64(Float64(263.3831869810514 + Float64(z * Float64(436.8961725563396 + Float64(545.0353078428827 * z)))) * Float64(sqrt(Float64(pi + pi)) * Float64((7.5 ^ t_0) * exp(Float64(-7.5))))));
	else
		tmp = Float64(pi * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(676.5203681218851 / Float64(1.0 - z)) - -0.9999999999998099) - Float64(1259.1392167224028 / Float64(Float64(1.0 - z) - -1.0))) - Float64(-771.3234287776531 / Float64(Float64(1.0 - z) - -2.0))) - Float64(-176.6150291621406 / Float64(-4.0 + z))) - Float64(-12.507343278686905 / Float64(Float64(1.0 - z) - -4.0))) - Float64(0.13857109526572012 / Float64(Float64(1.0 - z) - -5.0))) - Float64(Float64(-9.984369578019572e-6 / Float64(Float64(1.0 - z) - -6.0)) + Float64(-1.5056327351493116e-7 / Float64(Float64(1.0 - z) - -7.0)))) * Float64(Float64((Float64(Float64(1.0 - z) - -6.5) ^ t_0) * 2.5066282746310007) * exp(Float64(z - 7.5)))) / sin(Float64(z * pi))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z)
	t_0 = (1.0 - z) - 0.5;
	tmp = 0.0;
	if (z <= -1000.0)
		tmp = (pi / sin((pi * z))) * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (sqrt((pi + pi)) * ((7.5 ^ t_0) * exp(-7.5))));
	else
		tmp = pi * ((((((((((676.5203681218851 / (1.0 - z)) - -0.9999999999998099) - (1259.1392167224028 / ((1.0 - z) - -1.0))) - (-771.3234287776531 / ((1.0 - z) - -2.0))) - (-176.6150291621406 / (-4.0 + z))) - (-12.507343278686905 / ((1.0 - z) - -4.0))) - (0.13857109526572012 / ((1.0 - z) - -5.0))) - ((-9.984369578019572e-6 / ((1.0 - z) - -6.0)) + (-1.5056327351493116e-7 / ((1.0 - z) - -7.0)))) * (((((1.0 - z) - -6.5) ^ t_0) * 2.5066282746310007) * exp((z - 7.5)))) / sin((z * pi)));
	end
	tmp_2 = tmp;
end

Wolfram

code[z_] := Block[{t$95$0 = N[(N[(1.0 - z), $MachinePrecision] - 0.5), $MachinePrecision]}, If[LessEqual[z, -1000.0], N[(N[(Pi / N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(263.3831869810514 + N[(z * N[(436.8961725563396 + N[(545.0353078428827 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision] * N[(N[Power[7.5, t$95$0], $MachinePrecision] * N[Exp[(-7.5)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(Pi * N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(676.5203681218851 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - -0.9999999999998099), $MachinePrecision] - N[(1259.1392167224028 / N[(N[(1.0 - z), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-771.3234287776531 / N[(N[(1.0 - z), $MachinePrecision] - -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-176.6150291621406 / N[(-4.0 + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-12.507343278686905 / N[(N[(1.0 - z), $MachinePrecision] - -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.13857109526572012 / N[(N[(1.0 - z), $MachinePrecision] - -5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(-9.984369578019572e-6 / N[(N[(1.0 - z), $MachinePrecision] - -6.0), $MachinePrecision]), $MachinePrecision] + N[(-1.5056327351493116e-7 / N[(N[(1.0 - z), $MachinePrecision] - -7.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[Power[N[(N[(1.0 - z), $MachinePrecision] - -6.5), $MachinePrecision], t$95$0], $MachinePrecision] * 2.5066282746310007), $MachinePrecision] * N[Exp[N[(z - 7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Sin[N[(z * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1e3

   1. Initial program 96.6%

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

   3. Applied rewrites 98.5%

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

   5. Applied rewrites 98.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + \color{blue}{z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \color{blue}{\left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \color{blue}{\frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      4. lower-*.f64 96.7

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot \color{blue}{z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   8. Applied rewrites 96.7%

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   9. Taylor expanded in z around 0

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\color{blue}{\frac{15}{2}}}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 95.6%

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\color{blue}{7.5}}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   12. Taylor expanded in z around 0

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\frac{15}{2}}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\color{blue}{\frac{15}{2}}}\right)\right)\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 96.2%

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({7.5}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\color{blue}{7.5}}\right)\right)\right) \]

   if -1e3 < z

   1. Initial program 96.6%

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

   3. Applied rewrites 96.5%

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

      1. lift--.f64 N/A

         \[\leadsto \pi \cdot \frac{\color{blue}{\left(\left(\left(\left(\left(\left(\left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \frac{-9999999999998099}{10000000000000000}\right) - \frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1}\right) - \frac{\frac{-7713234287776531}{10000000000000}}{\left(1 - z\right) - -2}\right) - \frac{\frac{883075145810703}{5000000000000}}{\left(1 - z\right) - -3}\right) - \frac{\frac{-2501468655737381}{200000000000000}}{\left(1 - z\right) - -4}\right) - \frac{\frac{3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5}\right) - \frac{\frac{-2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6}\right) - \frac{\frac{-3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7}\right)} \cdot \left(e^{\left(0 + z\right) + \frac{-15}{2}} \cdot \left({\left(\left(1 - z\right) - \frac{-13}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot \sqrt{\pi + \pi}\right)\right)}{\sin \left(z \cdot \pi\right)} \]

      2. lift--.f64 N/A

         \[\leadsto \pi \cdot \frac{\left(\color{blue}{\left(\left(\left(\left(\left(\left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \frac{-9999999999998099}{10000000000000000}\right) - \frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1}\right) - \frac{\frac{-7713234287776531}{10000000000000}}{\left(1 - z\right) - -2}\right) - \frac{\frac{883075145810703}{5000000000000}}{\left(1 - z\right) - -3}\right) - \frac{\frac{-2501468655737381}{200000000000000}}{\left(1 - z\right) - -4}\right) - \frac{\frac{3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5}\right) - \frac{\frac{-2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6}\right)} - \frac{\frac{-3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7}\right) \cdot \left(e^{\left(0 + z\right) + \frac{-15}{2}} \cdot \left({\left(\left(1 - z\right) - \frac{-13}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot \sqrt{\pi + \pi}\right)\right)}{\sin \left(z \cdot \pi\right)} \]

      3. associate--l- N/A

         \[\leadsto \pi \cdot \frac{\color{blue}{\left(\left(\left(\left(\left(\left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \frac{-9999999999998099}{10000000000000000}\right) - \frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1}\right) - \frac{\frac{-7713234287776531}{10000000000000}}{\left(1 - z\right) - -2}\right) - \frac{\frac{883075145810703}{5000000000000}}{\left(1 - z\right) - -3}\right) - \frac{\frac{-2501468655737381}{200000000000000}}{\left(1 - z\right) - -4}\right) - \frac{\frac{3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5}\right) - \left(\frac{\frac{-2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \frac{\frac{-3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7}\right)\right)} \cdot \left(e^{\left(0 + z\right) + \frac{-15}{2}} \cdot \left({\left(\left(1 - z\right) - \frac{-13}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot \sqrt{\pi + \pi}\right)\right)}{\sin \left(z \cdot \pi\right)} \]

      4. lower--.f64 N/A

         \[\leadsto \pi \cdot \frac{\color{blue}{\left(\left(\left(\left(\left(\left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \frac{-9999999999998099}{10000000000000000}\right) - \frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1}\right) - \frac{\frac{-7713234287776531}{10000000000000}}{\left(1 - z\right) - -2}\right) - \frac{\frac{883075145810703}{5000000000000}}{\left(1 - z\right) - -3}\right) - \frac{\frac{-2501468655737381}{200000000000000}}{\left(1 - z\right) - -4}\right) - \frac{\frac{3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5}\right) - \left(\frac{\frac{-2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \frac{\frac{-3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7}\right)\right)} \cdot \left(e^{\left(0 + z\right) + \frac{-15}{2}} \cdot \left({\left(\left(1 - z\right) - \frac{-13}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot \sqrt{\pi + \pi}\right)\right)}{\sin \left(z \cdot \pi\right)} \]

   5. Applied rewrites 97.7%

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

   7. Applied rewrites 97.7%

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

   8. Evaluated real constant 98.4%

      \[\leadsto \pi \cdot \frac{\left(\left(\left(\left(\left(\left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \frac{-9999999999998099}{10000000000000000}\right) - \frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1}\right) - \frac{\frac{-7713234287776531}{10000000000000}}{\left(1 - z\right) - -2}\right) - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right) - \frac{\frac{-2501468655737381}{200000000000000}}{\left(1 - z\right) - -4}\right) - \frac{\frac{3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5}\right) - \left(\frac{\frac{-2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \frac{\frac{-3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7}\right)\right) \cdot \left(\left({\left(\left(1 - z\right) - \frac{-13}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot \color{blue}{\frac{2822212540896131}{1125899906842624}}\right) \cdot e^{z - \frac{15}{2}}\right)}{\sin \left(z \cdot \pi\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 98.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := \left(1 - z\right) - 1\\ t_1 := t\_0 + 7\\ t_2 := t\_1 + 0.5\\ t_3 := \frac{\pi}{\sin \left(\pi \cdot z\right)}\\ t_4 := \left(1 - z\right) - 0.5\\ \mathbf{if}\;t\_3 \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {t\_2}^{\left(t\_0 + 0.5\right)}\right) \cdot e^{-t\_2}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{t\_0 + 1}\right) + \frac{-1259.1392167224028}{t\_0 + 2}\right) + \frac{771.3234287776531}{t\_0 + 3}\right) + \frac{-176.6150291621406}{t\_0 + 4}\right) + \frac{12.507343278686905}{t\_0 + 5}\right) + \frac{-0.13857109526572012}{t\_0 + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t\_1}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{t\_0 + 8}\right)\right) \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\pi \cdot \frac{\left(\left(\left(\left(\left(\left(\left(\frac{676.5203681218851}{1 - z} - -0.9999999999998099\right) - \frac{1259.1392167224028}{\left(1 - z\right) - -1}\right) - \frac{-771.3234287776531}{\left(1 - z\right) - -2}\right) - \frac{-176.6150291621406}{-4 + z}\right) - \frac{-12.507343278686905}{\left(1 - z\right) - -4}\right) - \frac{0.13857109526572012}{\left(1 - z\right) - -5}\right) - -1.4451589203350195 \cdot 10^{-6}\right) \cdot \left(e^{\left(0 + z\right) + -7.5} \cdot \left({\left(\left(1 - z\right) - -6.5\right)}^{t\_4} \cdot 2.5066282746310007\right)\right)}{\sin \left(z \cdot \pi\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_3 \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({7.5}^{t\_4} \cdot e^{-7.5}\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (- (- 1.0 z) 1.0))
        (t_1 (+ t_0 7.0))
        (t_2 (+ t_1 0.5))
        (t_3 (/ PI (sin (* PI z))))
        (t_4 (- (- 1.0 z) 0.5)))
   (if (<=
        (*
         t_3
         (*
          (* (* (sqrt (* PI 2.0)) (pow t_2 (+ t_0 0.5))) (exp (- t_2)))
          (+
           (+
            (+
             (+
              (+
               (+
                (+
                 (+ 0.9999999999998099 (/ 676.5203681218851 (+ t_0 1.0)))
                 (/ -1259.1392167224028 (+ t_0 2.0)))
                (/ 771.3234287776531 (+ t_0 3.0)))
               (/ -176.6150291621406 (+ t_0 4.0)))
              (/ 12.507343278686905 (+ t_0 5.0)))
             (/ -0.13857109526572012 (+ t_0 6.0)))
            (/ 9.984369578019572e-6 t_1))
           (/ 1.5056327351493116e-7 (+ t_0 8.0)))))
        2e+306)
     (*
      PI
      (/
       (*
        (-
         (-
          (-
           (-
            (-
             (-
              (- (/ 676.5203681218851 (- 1.0 z)) -0.9999999999998099)
              (/ 1259.1392167224028 (- (- 1.0 z) -1.0)))
             (/ -771.3234287776531 (- (- 1.0 z) -2.0)))
            (/ -176.6150291621406 (+ -4.0 z)))
           (/ -12.507343278686905 (- (- 1.0 z) -4.0)))
          (/ 0.13857109526572012 (- (- 1.0 z) -5.0)))
         -1.4451589203350195e-6)
        (*
         (exp (+ (+ 0.0 z) -7.5))
         (* (pow (- (- 1.0 z) -6.5) t_4) 2.5066282746310007)))
       (sin (* z PI))))
     (*
      t_3
      (*
       (+
        263.3831869810514
        (* z (+ 436.8961725563396 (* 545.0353078428827 z))))
       (* (sqrt (+ PI PI)) (* (pow 7.5 t_4) (exp (- 7.5)))))))))

C

double code(double z) {
	double t_0 = (1.0 - z) - 1.0;
	double t_1 = t_0 + 7.0;
	double t_2 = t_1 + 0.5;
	double t_3 = ((double) M_PI) / sin((((double) M_PI) * z));
	double t_4 = (1.0 - z) - 0.5;
	double tmp;
	if ((t_3 * (((sqrt((((double) M_PI) * 2.0)) * pow(t_2, (t_0 + 0.5))) * exp(-t_2)) * ((((((((0.9999999999998099 + (676.5203681218851 / (t_0 + 1.0))) + (-1259.1392167224028 / (t_0 + 2.0))) + (771.3234287776531 / (t_0 + 3.0))) + (-176.6150291621406 / (t_0 + 4.0))) + (12.507343278686905 / (t_0 + 5.0))) + (-0.13857109526572012 / (t_0 + 6.0))) + (9.984369578019572e-6 / t_1)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+306) {
		tmp = ((double) M_PI) * ((((((((((676.5203681218851 / (1.0 - z)) - -0.9999999999998099) - (1259.1392167224028 / ((1.0 - z) - -1.0))) - (-771.3234287776531 / ((1.0 - z) - -2.0))) - (-176.6150291621406 / (-4.0 + z))) - (-12.507343278686905 / ((1.0 - z) - -4.0))) - (0.13857109526572012 / ((1.0 - z) - -5.0))) - -1.4451589203350195e-6) * (exp(((0.0 + z) + -7.5)) * (pow(((1.0 - z) - -6.5), t_4) * 2.5066282746310007))) / sin((z * ((double) M_PI))));
	} else {
		tmp = t_3 * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (sqrt((((double) M_PI) + ((double) M_PI))) * (pow(7.5, t_4) * exp(-7.5))));
	}
	return tmp;
}

Java

public static double code(double z) {
	double t_0 = (1.0 - z) - 1.0;
	double t_1 = t_0 + 7.0;
	double t_2 = t_1 + 0.5;
	double t_3 = Math.PI / Math.sin((Math.PI * z));
	double t_4 = (1.0 - z) - 0.5;
	double tmp;
	if ((t_3 * (((Math.sqrt((Math.PI * 2.0)) * Math.pow(t_2, (t_0 + 0.5))) * Math.exp(-t_2)) * ((((((((0.9999999999998099 + (676.5203681218851 / (t_0 + 1.0))) + (-1259.1392167224028 / (t_0 + 2.0))) + (771.3234287776531 / (t_0 + 3.0))) + (-176.6150291621406 / (t_0 + 4.0))) + (12.507343278686905 / (t_0 + 5.0))) + (-0.13857109526572012 / (t_0 + 6.0))) + (9.984369578019572e-6 / t_1)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+306) {
		tmp = Math.PI * ((((((((((676.5203681218851 / (1.0 - z)) - -0.9999999999998099) - (1259.1392167224028 / ((1.0 - z) - -1.0))) - (-771.3234287776531 / ((1.0 - z) - -2.0))) - (-176.6150291621406 / (-4.0 + z))) - (-12.507343278686905 / ((1.0 - z) - -4.0))) - (0.13857109526572012 / ((1.0 - z) - -5.0))) - -1.4451589203350195e-6) * (Math.exp(((0.0 + z) + -7.5)) * (Math.pow(((1.0 - z) - -6.5), t_4) * 2.5066282746310007))) / Math.sin((z * Math.PI)));
	} else {
		tmp = t_3 * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (Math.sqrt((Math.PI + Math.PI)) * (Math.pow(7.5, t_4) * Math.exp(-7.5))));
	}
	return tmp;
}

Python

def code(z):
	t_0 = (1.0 - z) - 1.0
	t_1 = t_0 + 7.0
	t_2 = t_1 + 0.5
	t_3 = math.pi / math.sin((math.pi * z))
	t_4 = (1.0 - z) - 0.5
	tmp = 0
	if (t_3 * (((math.sqrt((math.pi * 2.0)) * math.pow(t_2, (t_0 + 0.5))) * math.exp(-t_2)) * ((((((((0.9999999999998099 + (676.5203681218851 / (t_0 + 1.0))) + (-1259.1392167224028 / (t_0 + 2.0))) + (771.3234287776531 / (t_0 + 3.0))) + (-176.6150291621406 / (t_0 + 4.0))) + (12.507343278686905 / (t_0 + 5.0))) + (-0.13857109526572012 / (t_0 + 6.0))) + (9.984369578019572e-6 / t_1)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+306:
		tmp = math.pi * ((((((((((676.5203681218851 / (1.0 - z)) - -0.9999999999998099) - (1259.1392167224028 / ((1.0 - z) - -1.0))) - (-771.3234287776531 / ((1.0 - z) - -2.0))) - (-176.6150291621406 / (-4.0 + z))) - (-12.507343278686905 / ((1.0 - z) - -4.0))) - (0.13857109526572012 / ((1.0 - z) - -5.0))) - -1.4451589203350195e-6) * (math.exp(((0.0 + z) + -7.5)) * (math.pow(((1.0 - z) - -6.5), t_4) * 2.5066282746310007))) / math.sin((z * math.pi)))
	else:
		tmp = t_3 * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (math.sqrt((math.pi + math.pi)) * (math.pow(7.5, t_4) * math.exp(-7.5))))
	return tmp

Julia

function code(z)
	t_0 = Float64(Float64(1.0 - z) - 1.0)
	t_1 = Float64(t_0 + 7.0)
	t_2 = Float64(t_1 + 0.5)
	t_3 = Float64(pi / sin(Float64(pi * z)))
	t_4 = Float64(Float64(1.0 - z) - 0.5)
	tmp = 0.0
	if (Float64(t_3 * Float64(Float64(Float64(sqrt(Float64(pi * 2.0)) * (t_2 ^ Float64(t_0 + 0.5))) * exp(Float64(-t_2))) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(0.9999999999998099 + Float64(676.5203681218851 / Float64(t_0 + 1.0))) + Float64(-1259.1392167224028 / Float64(t_0 + 2.0))) + Float64(771.3234287776531 / Float64(t_0 + 3.0))) + Float64(-176.6150291621406 / Float64(t_0 + 4.0))) + Float64(12.507343278686905 / Float64(t_0 + 5.0))) + Float64(-0.13857109526572012 / Float64(t_0 + 6.0))) + Float64(9.984369578019572e-6 / t_1)) + Float64(1.5056327351493116e-7 / Float64(t_0 + 8.0))))) <= 2e+306)
		tmp = Float64(pi * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(676.5203681218851 / Float64(1.0 - z)) - -0.9999999999998099) - Float64(1259.1392167224028 / Float64(Float64(1.0 - z) - -1.0))) - Float64(-771.3234287776531 / Float64(Float64(1.0 - z) - -2.0))) - Float64(-176.6150291621406 / Float64(-4.0 + z))) - Float64(-12.507343278686905 / Float64(Float64(1.0 - z) - -4.0))) - Float64(0.13857109526572012 / Float64(Float64(1.0 - z) - -5.0))) - -1.4451589203350195e-6) * Float64(exp(Float64(Float64(0.0 + z) + -7.5)) * Float64((Float64(Float64(1.0 - z) - -6.5) ^ t_4) * 2.5066282746310007))) / sin(Float64(z * pi))));
	else
		tmp = Float64(t_3 * Float64(Float64(263.3831869810514 + Float64(z * Float64(436.8961725563396 + Float64(545.0353078428827 * z)))) * Float64(sqrt(Float64(pi + pi)) * Float64((7.5 ^ t_4) * exp(Float64(-7.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z)
	t_0 = (1.0 - z) - 1.0;
	t_1 = t_0 + 7.0;
	t_2 = t_1 + 0.5;
	t_3 = pi / sin((pi * z));
	t_4 = (1.0 - z) - 0.5;
	tmp = 0.0;
	if ((t_3 * (((sqrt((pi * 2.0)) * (t_2 ^ (t_0 + 0.5))) * exp(-t_2)) * ((((((((0.9999999999998099 + (676.5203681218851 / (t_0 + 1.0))) + (-1259.1392167224028 / (t_0 + 2.0))) + (771.3234287776531 / (t_0 + 3.0))) + (-176.6150291621406 / (t_0 + 4.0))) + (12.507343278686905 / (t_0 + 5.0))) + (-0.13857109526572012 / (t_0 + 6.0))) + (9.984369578019572e-6 / t_1)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+306)
		tmp = pi * ((((((((((676.5203681218851 / (1.0 - z)) - -0.9999999999998099) - (1259.1392167224028 / ((1.0 - z) - -1.0))) - (-771.3234287776531 / ((1.0 - z) - -2.0))) - (-176.6150291621406 / (-4.0 + z))) - (-12.507343278686905 / ((1.0 - z) - -4.0))) - (0.13857109526572012 / ((1.0 - z) - -5.0))) - -1.4451589203350195e-6) * (exp(((0.0 + z) + -7.5)) * ((((1.0 - z) - -6.5) ^ t_4) * 2.5066282746310007))) / sin((z * pi)));
	else
		tmp = t_3 * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (sqrt((pi + pi)) * ((7.5 ^ t_4) * exp(-7.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[z_] := Block[{t$95$0 = N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + 7.0), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + 0.5), $MachinePrecision]}, Block[{t$95$3 = N[(Pi / N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(1.0 - z), $MachinePrecision] - 0.5), $MachinePrecision]}, If[LessEqual[N[(t$95$3 * N[(N[(N[(N[Sqrt[N[(Pi * 2.0), $MachinePrecision]], $MachinePrecision] * N[Power[t$95$2, N[(t$95$0 + 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Exp[(-t$95$2)], $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(0.9999999999998099 + N[(676.5203681218851 / N[(t$95$0 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1259.1392167224028 / N[(t$95$0 + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(771.3234287776531 / N[(t$95$0 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-176.6150291621406 / N[(t$95$0 + 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(12.507343278686905 / N[(t$95$0 + 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.13857109526572012 / N[(t$95$0 + 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(9.984369578019572e-6 / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(t$95$0 + 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e+306], N[(Pi * N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(676.5203681218851 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - -0.9999999999998099), $MachinePrecision] - N[(1259.1392167224028 / N[(N[(1.0 - z), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-771.3234287776531 / N[(N[(1.0 - z), $MachinePrecision] - -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-176.6150291621406 / N[(-4.0 + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-12.507343278686905 / N[(N[(1.0 - z), $MachinePrecision] - -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.13857109526572012 / N[(N[(1.0 - z), $MachinePrecision] - -5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.4451589203350195e-6), $MachinePrecision] * N[(N[Exp[N[(N[(0.0 + z), $MachinePrecision] + -7.5), $MachinePrecision]], $MachinePrecision] * N[(N[Power[N[(N[(1.0 - z), $MachinePrecision] - -6.5), $MachinePrecision], t$95$4], $MachinePrecision] * 2.5066282746310007), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Sin[N[(z * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$3 * N[(N[(263.3831869810514 + N[(z * N[(436.8961725563396 + N[(545.0353078428827 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision] * N[(N[Power[7.5, t$95$4], $MachinePrecision] * N[Exp[(-7.5)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 (PI.f64) (sin.f64 (*.f64 (PI.f64) z))) (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 7 binary64)) #s(literal 1/2 binary64)) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 1/2 binary64)))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 7 binary64)) #s(literal 1/2 binary64))))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 #s(literal 9999999999998099/10000000000000000 binary64) (/.f64 #s(literal 6765203681218851/10000000000000 binary64) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 1 binary64)))) (/.f64 #s(literal -3147848041806007/2500000000000 binary64) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 7713234287776531/10000000000000 binary64) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 3 binary64)))) (/.f64 #s(literal -883075145810703/5000000000000 binary64) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 4 binary64)))) (/.f64 #s(literal 2501468655737381/200000000000000 binary64) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal -3464277381643003/25000000000000000 binary64) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 6 binary64)))) (/.f64 #s(literal 2496092394504893/250000000000000000000 binary64) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 7 binary64)))) (/.f64 #s(literal 3764081837873279/25000000000000000000000 binary64) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 8 binary64)))))) < 2.00000000000000003e306

   1. Initial program 96.6%

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

   3. Applied rewrites 96.5%

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

      1. lift--.f64 N/A

         \[\leadsto \pi \cdot \frac{\color{blue}{\left(\left(\left(\left(\left(\left(\left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \frac{-9999999999998099}{10000000000000000}\right) - \frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1}\right) - \frac{\frac{-7713234287776531}{10000000000000}}{\left(1 - z\right) - -2}\right) - \frac{\frac{883075145810703}{5000000000000}}{\left(1 - z\right) - -3}\right) - \frac{\frac{-2501468655737381}{200000000000000}}{\left(1 - z\right) - -4}\right) - \frac{\frac{3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5}\right) - \frac{\frac{-2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6}\right) - \frac{\frac{-3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7}\right)} \cdot \left(e^{\left(0 + z\right) + \frac{-15}{2}} \cdot \left({\left(\left(1 - z\right) - \frac{-13}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot \sqrt{\pi + \pi}\right)\right)}{\sin \left(z \cdot \pi\right)} \]

      2. lift--.f64 N/A

         \[\leadsto \pi \cdot \frac{\left(\color{blue}{\left(\left(\left(\left(\left(\left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \frac{-9999999999998099}{10000000000000000}\right) - \frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1}\right) - \frac{\frac{-7713234287776531}{10000000000000}}{\left(1 - z\right) - -2}\right) - \frac{\frac{883075145810703}{5000000000000}}{\left(1 - z\right) - -3}\right) - \frac{\frac{-2501468655737381}{200000000000000}}{\left(1 - z\right) - -4}\right) - \frac{\frac{3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5}\right) - \frac{\frac{-2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6}\right)} - \frac{\frac{-3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7}\right) \cdot \left(e^{\left(0 + z\right) + \frac{-15}{2}} \cdot \left({\left(\left(1 - z\right) - \frac{-13}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot \sqrt{\pi + \pi}\right)\right)}{\sin \left(z \cdot \pi\right)} \]

      3. associate--l- N/A

         \[\leadsto \pi \cdot \frac{\color{blue}{\left(\left(\left(\left(\left(\left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \frac{-9999999999998099}{10000000000000000}\right) - \frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1}\right) - \frac{\frac{-7713234287776531}{10000000000000}}{\left(1 - z\right) - -2}\right) - \frac{\frac{883075145810703}{5000000000000}}{\left(1 - z\right) - -3}\right) - \frac{\frac{-2501468655737381}{200000000000000}}{\left(1 - z\right) - -4}\right) - \frac{\frac{3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5}\right) - \left(\frac{\frac{-2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \frac{\frac{-3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7}\right)\right)} \cdot \left(e^{\left(0 + z\right) + \frac{-15}{2}} \cdot \left({\left(\left(1 - z\right) - \frac{-13}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot \sqrt{\pi + \pi}\right)\right)}{\sin \left(z \cdot \pi\right)} \]

      4. lower--.f64 N/A

         \[\leadsto \pi \cdot \frac{\color{blue}{\left(\left(\left(\left(\left(\left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \frac{-9999999999998099}{10000000000000000}\right) - \frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1}\right) - \frac{\frac{-7713234287776531}{10000000000000}}{\left(1 - z\right) - -2}\right) - \frac{\frac{883075145810703}{5000000000000}}{\left(1 - z\right) - -3}\right) - \frac{\frac{-2501468655737381}{200000000000000}}{\left(1 - z\right) - -4}\right) - \frac{\frac{3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5}\right) - \left(\frac{\frac{-2496092394504893}{250000000000000000000}}{\left(1 - z\right) - -6} + \frac{\frac{-3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7}\right)\right)} \cdot \left(e^{\left(0 + z\right) + \frac{-15}{2}} \cdot \left({\left(\left(1 - z\right) - \frac{-13}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot \sqrt{\pi + \pi}\right)\right)}{\sin \left(z \cdot \pi\right)} \]

   5. Applied rewrites 97.7%

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

   6. Taylor expanded in z around 0

      \[\leadsto \pi \cdot \frac{\left(\left(\left(\left(\left(\left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \frac{-9999999999998099}{10000000000000000}\right) - \frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1}\right) - \frac{\frac{-7713234287776531}{10000000000000}}{\left(1 - z\right) - -2}\right) - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right) - \frac{\frac{-2501468655737381}{200000000000000}}{\left(1 - z\right) - -4}\right) - \frac{\frac{3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5}\right) - \color{blue}{\frac{-2023222488469027353}{1400000000000000000000000}}\right) \cdot \left(e^{\left(0 + z\right) + \frac{-15}{2}} \cdot \left({\left(\left(1 - z\right) - \frac{-13}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot \sqrt{\pi + \pi}\right)\right)}{\sin \left(z \cdot \pi\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 97.2%

      \[\leadsto \pi \cdot \frac{\left(\left(\left(\left(\left(\left(\left(\frac{676.5203681218851}{1 - z} - -0.9999999999998099\right) - \frac{1259.1392167224028}{\left(1 - z\right) - -1}\right) - \frac{-771.3234287776531}{\left(1 - z\right) - -2}\right) - \frac{-176.6150291621406}{-4 + z}\right) - \frac{-12.507343278686905}{\left(1 - z\right) - -4}\right) - \frac{0.13857109526572012}{\left(1 - z\right) - -5}\right) - \color{blue}{-1.4451589203350195 \cdot 10^{-6}}\right) \cdot \left(e^{\left(0 + z\right) + -7.5} \cdot \left({\left(\left(1 - z\right) - -6.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot \sqrt{\pi + \pi}\right)\right)}{\sin \left(z \cdot \pi\right)} \]

   9. Evaluated real constant 98.0%

      \[\leadsto \pi \cdot \frac{\left(\left(\left(\left(\left(\left(\left(\frac{\frac{6765203681218851}{10000000000000}}{1 - z} - \frac{-9999999999998099}{10000000000000000}\right) - \frac{\frac{3147848041806007}{2500000000000}}{\left(1 - z\right) - -1}\right) - \frac{\frac{-7713234287776531}{10000000000000}}{\left(1 - z\right) - -2}\right) - \frac{\frac{-883075145810703}{5000000000000}}{-4 + z}\right) - \frac{\frac{-2501468655737381}{200000000000000}}{\left(1 - z\right) - -4}\right) - \frac{\frac{3464277381643003}{25000000000000000}}{\left(1 - z\right) - -5}\right) - \frac{-2023222488469027353}{1400000000000000000000000}\right) \cdot \left(e^{\left(0 + z\right) + \frac{-15}{2}} \cdot \left({\left(\left(1 - z\right) - \frac{-13}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot \color{blue}{\frac{2822212540896131}{1125899906842624}}\right)\right)}{\sin \left(z \cdot \pi\right)} \]

   if 2.00000000000000003e306 < (*.f64 (/.f64 (PI.f64) (sin.f64 (*.f64 (PI.f64) z))) (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 7 binary64)) #s(literal 1/2 binary64)) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 1/2 binary64)))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 7 binary64)) #s(literal 1/2 binary64))))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 #s(literal 9999999999998099/10000000000000000 binary64) (/.f64 #s(literal 6765203681218851/10000000000000 binary64) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 1 binary64)))) (/.f64 #s(literal -3147848041806007/2500000000000 binary64) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 7713234287776531/10000000000000 binary64) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 3 binary64)))) (/.f64 #s(literal -883075145810703/5000000000000 binary64) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 4 binary64)))) (/.f64 #s(literal 2501468655737381/200000000000000 binary64) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal -3464277381643003/25000000000000000 binary64) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 6 binary64)))) (/.f64 #s(literal 2496092394504893/250000000000000000000 binary64) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 7 binary64)))) (/.f64 #s(literal 3764081837873279/25000000000000000000000 binary64) (+.f64 (-.f64 (-.f64 #s(literal 1 binary64) z) #s(literal 1 binary64)) #s(literal 8 binary64))))))

   1. Initial program 96.6%

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

   3. Applied rewrites 98.5%

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

   5. Applied rewrites 98.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + \color{blue}{z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \color{blue}{\left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \color{blue}{\frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      4. lower-*.f64 96.7

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot \color{blue}{z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   8. Applied rewrites 96.7%

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   9. Taylor expanded in z around 0

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\color{blue}{\frac{15}{2}}}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 95.6%

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\color{blue}{7.5}}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   12. Taylor expanded in z around 0

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\frac{15}{2}}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\color{blue}{\frac{15}{2}}}\right)\right)\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 96.2%

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({7.5}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\color{blue}{7.5}}\right)\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 98.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} t_0 := \left(\left(1 - z\right) - -6\right) - -0.5\\ t_1 := \frac{\pi}{\sin \left(\pi \cdot z\right)}\\ t_2 := \left(1 - z\right) - 0.5\\ t_3 := 263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\\ \mathbf{if}\;z \leq -1000:\\ \;\;\;\;t\_1 \cdot \left(t\_3 \cdot \left(\sqrt{\pi + \pi} \cdot \left({7.5}^{t\_2} \cdot e^{-7.5}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \left(t\_3 \cdot \left(2.5066282746310007 \cdot \left({t\_0}^{t\_2} \cdot e^{-t\_0}\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (- (- (- 1.0 z) -6.0) -0.5))
        (t_1 (/ PI (sin (* PI z))))
        (t_2 (- (- 1.0 z) 0.5))
        (t_3
         (+
          263.3831869810514
          (* z (+ 436.8961725563396 (* 545.0353078428827 z))))))
   (if (<= z -1000.0)
     (* t_1 (* t_3 (* (sqrt (+ PI PI)) (* (pow 7.5 t_2) (exp (- 7.5))))))
     (* t_1 (* t_3 (* 2.5066282746310007 (* (pow t_0 t_2) (exp (- t_0)))))))))

C

double code(double z) {
	double t_0 = ((1.0 - z) - -6.0) - -0.5;
	double t_1 = ((double) M_PI) / sin((((double) M_PI) * z));
	double t_2 = (1.0 - z) - 0.5;
	double t_3 = 263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)));
	double tmp;
	if (z <= -1000.0) {
		tmp = t_1 * (t_3 * (sqrt((((double) M_PI) + ((double) M_PI))) * (pow(7.5, t_2) * exp(-7.5))));
	} else {
		tmp = t_1 * (t_3 * (2.5066282746310007 * (pow(t_0, t_2) * exp(-t_0))));
	}
	return tmp;
}

Java

public static double code(double z) {
	double t_0 = ((1.0 - z) - -6.0) - -0.5;
	double t_1 = Math.PI / Math.sin((Math.PI * z));
	double t_2 = (1.0 - z) - 0.5;
	double t_3 = 263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)));
	double tmp;
	if (z <= -1000.0) {
		tmp = t_1 * (t_3 * (Math.sqrt((Math.PI + Math.PI)) * (Math.pow(7.5, t_2) * Math.exp(-7.5))));
	} else {
		tmp = t_1 * (t_3 * (2.5066282746310007 * (Math.pow(t_0, t_2) * Math.exp(-t_0))));
	}
	return tmp;
}

Python

def code(z):
	t_0 = ((1.0 - z) - -6.0) - -0.5
	t_1 = math.pi / math.sin((math.pi * z))
	t_2 = (1.0 - z) - 0.5
	t_3 = 263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))
	tmp = 0
	if z <= -1000.0:
		tmp = t_1 * (t_3 * (math.sqrt((math.pi + math.pi)) * (math.pow(7.5, t_2) * math.exp(-7.5))))
	else:
		tmp = t_1 * (t_3 * (2.5066282746310007 * (math.pow(t_0, t_2) * math.exp(-t_0))))
	return tmp

Julia

function code(z)
	t_0 = Float64(Float64(Float64(1.0 - z) - -6.0) - -0.5)
	t_1 = Float64(pi / sin(Float64(pi * z)))
	t_2 = Float64(Float64(1.0 - z) - 0.5)
	t_3 = Float64(263.3831869810514 + Float64(z * Float64(436.8961725563396 + Float64(545.0353078428827 * z))))
	tmp = 0.0
	if (z <= -1000.0)
		tmp = Float64(t_1 * Float64(t_3 * Float64(sqrt(Float64(pi + pi)) * Float64((7.5 ^ t_2) * exp(Float64(-7.5))))));
	else
		tmp = Float64(t_1 * Float64(t_3 * Float64(2.5066282746310007 * Float64((t_0 ^ t_2) * exp(Float64(-t_0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z)
	t_0 = ((1.0 - z) - -6.0) - -0.5;
	t_1 = pi / sin((pi * z));
	t_2 = (1.0 - z) - 0.5;
	t_3 = 263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)));
	tmp = 0.0;
	if (z <= -1000.0)
		tmp = t_1 * (t_3 * (sqrt((pi + pi)) * ((7.5 ^ t_2) * exp(-7.5))));
	else
		tmp = t_1 * (t_3 * (2.5066282746310007 * ((t_0 ^ t_2) * exp(-t_0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[z_] := Block[{t$95$0 = N[(N[(N[(1.0 - z), $MachinePrecision] - -6.0), $MachinePrecision] - -0.5), $MachinePrecision]}, Block[{t$95$1 = N[(Pi / N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 - z), $MachinePrecision] - 0.5), $MachinePrecision]}, Block[{t$95$3 = N[(263.3831869810514 + N[(z * N[(436.8961725563396 + N[(545.0353078428827 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1000.0], N[(t$95$1 * N[(t$95$3 * N[(N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision] * N[(N[Power[7.5, t$95$2], $MachinePrecision] * N[Exp[(-7.5)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(t$95$3 * N[(2.5066282746310007 * N[(N[Power[t$95$0, t$95$2], $MachinePrecision] * N[Exp[(-t$95$0)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1e3

   1. Initial program 96.6%

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

   3. Applied rewrites 98.5%

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

   5. Applied rewrites 98.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + \color{blue}{z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \color{blue}{\left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \color{blue}{\frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      4. lower-*.f64 96.7

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot \color{blue}{z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   8. Applied rewrites 96.7%

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   9. Taylor expanded in z around 0

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\color{blue}{\frac{15}{2}}}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 95.6%

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\color{blue}{7.5}}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   12. Taylor expanded in z around 0

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\frac{15}{2}}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\color{blue}{\frac{15}{2}}}\right)\right)\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 96.2%

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({7.5}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\color{blue}{7.5}}\right)\right)\right) \]

   if -1e3 < z

   1. Initial program 96.6%

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

   3. Applied rewrites 98.5%

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

   5. Applied rewrites 98.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + \color{blue}{z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \color{blue}{\left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \color{blue}{\frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      4. lower-*.f64 96.7

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot \color{blue}{z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   8. Applied rewrites 96.7%

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   9. Evaluated real constant 97.5%

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\color{blue}{\frac{2822212540896131}{1125899906842624}} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 97.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} t_0 := \sqrt{\pi + \pi}\\ t_1 := \frac{\pi}{\sin \left(\pi \cdot z\right)}\\ t_2 := 263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\\ \mathbf{if}\;z \leq -1000:\\ \;\;\;\;t\_1 \cdot \left(t\_2 \cdot \left(t\_0 \cdot \left({7.5}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-7.5}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \left(t\_2 \cdot \left(t\_0 \cdot \left(e^{\log \left(7.5 - z\right) \cdot \left(0.5 - z\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (sqrt (+ PI PI)))
        (t_1 (/ PI (sin (* PI z))))
        (t_2
         (+
          263.3831869810514
          (* z (+ 436.8961725563396 (* 545.0353078428827 z))))))
   (if (<= z -1000.0)
     (* t_1 (* t_2 (* t_0 (* (pow 7.5 (- (- 1.0 z) 0.5)) (exp (- 7.5))))))
     (*
      t_1
      (*
       t_2
       (*
        t_0
        (*
         (exp (* (log (- 7.5 z)) (- 0.5 z)))
         (exp (- (- (- (- 1.0 z) -6.0) -0.5))))))))))

C

double code(double z) {
	double t_0 = sqrt((((double) M_PI) + ((double) M_PI)));
	double t_1 = ((double) M_PI) / sin((((double) M_PI) * z));
	double t_2 = 263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)));
	double tmp;
	if (z <= -1000.0) {
		tmp = t_1 * (t_2 * (t_0 * (pow(7.5, ((1.0 - z) - 0.5)) * exp(-7.5))));
	} else {
		tmp = t_1 * (t_2 * (t_0 * (exp((log((7.5 - z)) * (0.5 - z))) * exp(-(((1.0 - z) - -6.0) - -0.5)))));
	}
	return tmp;
}

Java

public static double code(double z) {
	double t_0 = Math.sqrt((Math.PI + Math.PI));
	double t_1 = Math.PI / Math.sin((Math.PI * z));
	double t_2 = 263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)));
	double tmp;
	if (z <= -1000.0) {
		tmp = t_1 * (t_2 * (t_0 * (Math.pow(7.5, ((1.0 - z) - 0.5)) * Math.exp(-7.5))));
	} else {
		tmp = t_1 * (t_2 * (t_0 * (Math.exp((Math.log((7.5 - z)) * (0.5 - z))) * Math.exp(-(((1.0 - z) - -6.0) - -0.5)))));
	}
	return tmp;
}

Python

def code(z):
	t_0 = math.sqrt((math.pi + math.pi))
	t_1 = math.pi / math.sin((math.pi * z))
	t_2 = 263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))
	tmp = 0
	if z <= -1000.0:
		tmp = t_1 * (t_2 * (t_0 * (math.pow(7.5, ((1.0 - z) - 0.5)) * math.exp(-7.5))))
	else:
		tmp = t_1 * (t_2 * (t_0 * (math.exp((math.log((7.5 - z)) * (0.5 - z))) * math.exp(-(((1.0 - z) - -6.0) - -0.5)))))
	return tmp

Julia

function code(z)
	t_0 = sqrt(Float64(pi + pi))
	t_1 = Float64(pi / sin(Float64(pi * z)))
	t_2 = Float64(263.3831869810514 + Float64(z * Float64(436.8961725563396 + Float64(545.0353078428827 * z))))
	tmp = 0.0
	if (z <= -1000.0)
		tmp = Float64(t_1 * Float64(t_2 * Float64(t_0 * Float64((7.5 ^ Float64(Float64(1.0 - z) - 0.5)) * exp(Float64(-7.5))))));
	else
		tmp = Float64(t_1 * Float64(t_2 * Float64(t_0 * Float64(exp(Float64(log(Float64(7.5 - z)) * Float64(0.5 - z))) * exp(Float64(-Float64(Float64(Float64(1.0 - z) - -6.0) - -0.5)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z)
	t_0 = sqrt((pi + pi));
	t_1 = pi / sin((pi * z));
	t_2 = 263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)));
	tmp = 0.0;
	if (z <= -1000.0)
		tmp = t_1 * (t_2 * (t_0 * ((7.5 ^ ((1.0 - z) - 0.5)) * exp(-7.5))));
	else
		tmp = t_1 * (t_2 * (t_0 * (exp((log((7.5 - z)) * (0.5 - z))) * exp(-(((1.0 - z) - -6.0) - -0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[z_] := Block[{t$95$0 = N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(Pi / N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(263.3831869810514 + N[(z * N[(436.8961725563396 + N[(545.0353078428827 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1000.0], N[(t$95$1 * N[(t$95$2 * N[(t$95$0 * N[(N[Power[7.5, N[(N[(1.0 - z), $MachinePrecision] - 0.5), $MachinePrecision]], $MachinePrecision] * N[Exp[(-7.5)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(t$95$2 * N[(t$95$0 * N[(N[Exp[N[(N[Log[N[(7.5 - z), $MachinePrecision]], $MachinePrecision] * N[(0.5 - z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Exp[(-N[(N[(N[(1.0 - z), $MachinePrecision] - -6.0), $MachinePrecision] - -0.5), $MachinePrecision])], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1e3

   1. Initial program 96.6%

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

   3. Applied rewrites 98.5%

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

   5. Applied rewrites 98.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + \color{blue}{z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \color{blue}{\left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \color{blue}{\frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      4. lower-*.f64 96.7

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot \color{blue}{z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   8. Applied rewrites 96.7%

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   9. Taylor expanded in z around 0

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\color{blue}{\frac{15}{2}}}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 95.6%

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\color{blue}{7.5}}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   12. Taylor expanded in z around 0

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\frac{15}{2}}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\color{blue}{\frac{15}{2}}}\right)\right)\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 96.2%

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({7.5}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\color{blue}{7.5}}\right)\right)\right) \]

   if -1e3 < z

   1. Initial program 96.6%

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

   3. Applied rewrites 98.5%

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

   5. Applied rewrites 98.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + \color{blue}{z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \color{blue}{\left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \color{blue}{\frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      4. lower-*.f64 96.7

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot \color{blue}{z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   8. Applied rewrites 96.7%

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   9. Taylor expanded in z around inf

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left(\color{blue}{e^{\log \left(\frac{15}{2} - z\right) \cdot \left(\frac{1}{2} - z\right)}} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
   10. Step-by-step derivation

       1. lower-exp.f64 N/A

          \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left(e^{\log \left(\frac{15}{2} - z\right) \cdot \left(\frac{1}{2} - z\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

       2. lower-*.f64 N/A

          \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left(e^{\log \left(\frac{15}{2} - z\right) \cdot \left(\frac{1}{2} - z\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

       3. lower-log.f64 N/A

          \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left(e^{\log \left(\frac{15}{2} - z\right) \cdot \left(\frac{1}{2} - z\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

       4. lower--.f64 N/A

          \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left(e^{\log \left(\frac{15}{2} - z\right) \cdot \left(\frac{1}{2} - z\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

       5. lower--.f64 96.7

          \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left(e^{\log \left(7.5 - z\right) \cdot \left(0.5 - z\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   11. Applied rewrites 96.7%

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left(\color{blue}{e^{\log \left(7.5 - z\right) \cdot \left(0.5 - z\right)}} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 97.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} t_0 := \frac{\pi}{\sin \left(\pi \cdot z\right)}\\ t_1 := \left(1 - z\right) - 0.5\\ t_2 := \sqrt{\pi + \pi}\\ t_3 := \left(1 - z\right) - -6.5\\ \mathbf{if}\;z \leq -1000:\\ \;\;\;\;t\_0 \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(t\_2 \cdot \left({7.5}^{t\_1} \cdot e^{-7.5}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \left(\left(\left({t\_3}^{t\_1} \cdot t\_2\right) \cdot e^{-t\_3}\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(545.0353078428827, z, 436.8961725563396\right), z, 263.3831869810514\right)\right)\\ \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (/ PI (sin (* PI z))))
        (t_1 (- (- 1.0 z) 0.5))
        (t_2 (sqrt (+ PI PI)))
        (t_3 (- (- 1.0 z) -6.5)))
   (if (<= z -1000.0)
     (*
      t_0
      (*
       (+
        263.3831869810514
        (* z (+ 436.8961725563396 (* 545.0353078428827 z))))
       (* t_2 (* (pow 7.5 t_1) (exp (- 7.5))))))
     (*
      t_0
      (*
       (* (* (pow t_3 t_1) t_2) (exp (- t_3)))
       (fma
        (fma 545.0353078428827 z 436.8961725563396)
        z
        263.3831869810514))))))

C

double code(double z) {
	double t_0 = ((double) M_PI) / sin((((double) M_PI) * z));
	double t_1 = (1.0 - z) - 0.5;
	double t_2 = sqrt((((double) M_PI) + ((double) M_PI)));
	double t_3 = (1.0 - z) - -6.5;
	double tmp;
	if (z <= -1000.0) {
		tmp = t_0 * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (t_2 * (pow(7.5, t_1) * exp(-7.5))));
	} else {
		tmp = t_0 * (((pow(t_3, t_1) * t_2) * exp(-t_3)) * fma(fma(545.0353078428827, z, 436.8961725563396), z, 263.3831869810514));
	}
	return tmp;
}

Julia

function code(z)
	t_0 = Float64(pi / sin(Float64(pi * z)))
	t_1 = Float64(Float64(1.0 - z) - 0.5)
	t_2 = sqrt(Float64(pi + pi))
	t_3 = Float64(Float64(1.0 - z) - -6.5)
	tmp = 0.0
	if (z <= -1000.0)
		tmp = Float64(t_0 * Float64(Float64(263.3831869810514 + Float64(z * Float64(436.8961725563396 + Float64(545.0353078428827 * z)))) * Float64(t_2 * Float64((7.5 ^ t_1) * exp(Float64(-7.5))))));
	else
		tmp = Float64(t_0 * Float64(Float64(Float64((t_3 ^ t_1) * t_2) * exp(Float64(-t_3))) * fma(fma(545.0353078428827, z, 436.8961725563396), z, 263.3831869810514)));
	end
	return tmp
end

Wolfram

code[z_] := Block[{t$95$0 = N[(Pi / N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(1.0 - z), $MachinePrecision] - 0.5), $MachinePrecision]}, Block[{t$95$2 = N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(N[(1.0 - z), $MachinePrecision] - -6.5), $MachinePrecision]}, If[LessEqual[z, -1000.0], N[(t$95$0 * N[(N[(263.3831869810514 + N[(z * N[(436.8961725563396 + N[(545.0353078428827 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(t$95$2 * N[(N[Power[7.5, t$95$1], $MachinePrecision] * N[Exp[(-7.5)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(N[(N[(N[Power[t$95$3, t$95$1], $MachinePrecision] * t$95$2), $MachinePrecision] * N[Exp[(-t$95$3)], $MachinePrecision]), $MachinePrecision] * N[(N[(545.0353078428827 * z + 436.8961725563396), $MachinePrecision] * z + 263.3831869810514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1e3

   1. Initial program 96.6%

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

   3. Applied rewrites 98.5%

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

   5. Applied rewrites 98.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + \color{blue}{z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \color{blue}{\left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \color{blue}{\frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      4. lower-*.f64 96.7

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot \color{blue}{z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   8. Applied rewrites 96.7%

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   9. Taylor expanded in z around 0

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\color{blue}{\frac{15}{2}}}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 95.6%

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\color{blue}{7.5}}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   12. Taylor expanded in z around 0

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\frac{15}{2}}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\color{blue}{\frac{15}{2}}}\right)\right)\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 96.2%

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({7.5}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\color{blue}{7.5}}\right)\right)\right) \]

   if -1e3 < z

   1. Initial program 96.6%

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

   3. Applied rewrites 98.5%

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

   5. Applied rewrites 98.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + \color{blue}{z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \color{blue}{\left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \color{blue}{\frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

      4. lower-*.f64 96.7

         \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot \color{blue}{z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   8. Applied rewrites 96.7%

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

   10. Applied rewrites 96.7%

       \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \color{blue}{\left(\left(\left({\left(\left(1 - z\right) - -6.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot \sqrt{\pi + \pi}\right) \cdot e^{-\left(\left(1 - z\right) - -6.5\right)}\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(545.0353078428827, z, 436.8961725563396\right), z, 263.3831869810514\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 96.4% accurate, 2.3× speedup

Math

\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({7.5}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-7.5}\right)\right)\right) \]

FPCore

(FPCore (z)
 :precision binary64
 (*
  (/ PI (sin (* PI z)))
  (*
   (+ 263.3831869810514 (* z (+ 436.8961725563396 (* 545.0353078428827 z))))
   (* (sqrt (+ PI PI)) (* (pow 7.5 (- (- 1.0 z) 0.5)) (exp (- 7.5)))))))

C

double code(double z) {
	return (((double) M_PI) / sin((((double) M_PI) * z))) * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (sqrt((((double) M_PI) + ((double) M_PI))) * (pow(7.5, ((1.0 - z) - 0.5)) * exp(-7.5))));
}

Java

public static double code(double z) {
	return (Math.PI / Math.sin((Math.PI * z))) * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (Math.sqrt((Math.PI + Math.PI)) * (Math.pow(7.5, ((1.0 - z) - 0.5)) * Math.exp(-7.5))));
}

Python

def code(z):
	return (math.pi / math.sin((math.pi * z))) * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (math.sqrt((math.pi + math.pi)) * (math.pow(7.5, ((1.0 - z) - 0.5)) * math.exp(-7.5))))

Julia

function code(z)
	return Float64(Float64(pi / sin(Float64(pi * z))) * Float64(Float64(263.3831869810514 + Float64(z * Float64(436.8961725563396 + Float64(545.0353078428827 * z)))) * Float64(sqrt(Float64(pi + pi)) * Float64((7.5 ^ Float64(Float64(1.0 - z) - 0.5)) * exp(Float64(-7.5))))))
end

MATLAB

function tmp = code(z)
	tmp = (pi / sin((pi * z))) * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (sqrt((pi + pi)) * ((7.5 ^ ((1.0 - z) - 0.5)) * exp(-7.5))));
end

Wolfram

code[z_] := N[(N[(Pi / N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(263.3831869810514 + N[(z * N[(436.8961725563396 + N[(545.0353078428827 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision] * N[(N[Power[7.5, N[(N[(1.0 - z), $MachinePrecision] - 0.5), $MachinePrecision]], $MachinePrecision] * N[Exp[(-7.5)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.6%

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

3. Applied rewrites 98.5%

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

5. Applied rewrites 98.5%

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

6. Taylor expanded in z around 0

   \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
7. Step-by-step derivation

   1. lower-+.f64 N/A

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + \color{blue}{z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

   2. lower-*.f64 N/A

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \color{blue}{\left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

   3. lower-+.f64 N/A

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \color{blue}{\frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

   4. lower-*.f64 96.7

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot \color{blue}{z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

8. Applied rewrites 96.7%

   \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

9. Taylor expanded in z around 0

   \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\color{blue}{\frac{15}{2}}}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
10. Step-by-step derivation

11. Applied rewrites 95.6%

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\color{blue}{7.5}}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

12. Taylor expanded in z around 0

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\frac{15}{2}}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\color{blue}{\frac{15}{2}}}\right)\right)\right) \]
13. Step-by-step derivation

14. Applied rewrites 96.2%

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({7.5}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\color{blue}{7.5}}\right)\right)\right) \]
15. Add Preprocessing

Alternative 10: 96.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} t_0 := \left(\left(1 - z\right) - -6\right) - -0.5\\ \frac{\pi}{z \cdot \pi} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({t\_0}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-t\_0}\right)\right)\right) \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (- (- (- 1.0 z) -6.0) -0.5)))
   (*
    (/ PI (* z PI))
    (*
     (+ 263.3831869810514 (* z (+ 436.8961725563396 (* 545.0353078428827 z))))
     (* (sqrt (+ PI PI)) (* (pow t_0 (- (- 1.0 z) 0.5)) (exp (- t_0))))))))

C

double code(double z) {
	double t_0 = ((1.0 - z) - -6.0) - -0.5;
	return (((double) M_PI) / (z * ((double) M_PI))) * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (sqrt((((double) M_PI) + ((double) M_PI))) * (pow(t_0, ((1.0 - z) - 0.5)) * exp(-t_0))));
}

Java

public static double code(double z) {
	double t_0 = ((1.0 - z) - -6.0) - -0.5;
	return (Math.PI / (z * Math.PI)) * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (Math.sqrt((Math.PI + Math.PI)) * (Math.pow(t_0, ((1.0 - z) - 0.5)) * Math.exp(-t_0))));
}

Python

def code(z):
	t_0 = ((1.0 - z) - -6.0) - -0.5
	return (math.pi / (z * math.pi)) * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (math.sqrt((math.pi + math.pi)) * (math.pow(t_0, ((1.0 - z) - 0.5)) * math.exp(-t_0))))

Julia

function code(z)
	t_0 = Float64(Float64(Float64(1.0 - z) - -6.0) - -0.5)
	return Float64(Float64(pi / Float64(z * pi)) * Float64(Float64(263.3831869810514 + Float64(z * Float64(436.8961725563396 + Float64(545.0353078428827 * z)))) * Float64(sqrt(Float64(pi + pi)) * Float64((t_0 ^ Float64(Float64(1.0 - z) - 0.5)) * exp(Float64(-t_0))))))
end

MATLAB

function tmp = code(z)
	t_0 = ((1.0 - z) - -6.0) - -0.5;
	tmp = (pi / (z * pi)) * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (sqrt((pi + pi)) * ((t_0 ^ ((1.0 - z) - 0.5)) * exp(-t_0))));
end

Wolfram

code[z_] := Block[{t$95$0 = N[(N[(N[(1.0 - z), $MachinePrecision] - -6.0), $MachinePrecision] - -0.5), $MachinePrecision]}, N[(N[(Pi / N[(z * Pi), $MachinePrecision]), $MachinePrecision] * N[(N[(263.3831869810514 + N[(z * N[(436.8961725563396 + N[(545.0353078428827 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision] * N[(N[Power[t$95$0, N[(N[(1.0 - z), $MachinePrecision] - 0.5), $MachinePrecision]], $MachinePrecision] * N[Exp[(-t$95$0)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 96.6%

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

3. Applied rewrites 98.5%

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

5. Applied rewrites 98.5%

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

6. Taylor expanded in z around 0

   \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
7. Step-by-step derivation

   1. lower-+.f64 N/A

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + \color{blue}{z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

   2. lower-*.f64 N/A

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \color{blue}{\left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

   3. lower-+.f64 N/A

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \color{blue}{\frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

   4. lower-*.f64 96.7

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot \color{blue}{z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

8. Applied rewrites 96.7%

   \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

9. Taylor expanded in z around 0

   \[\leadsto \frac{\pi}{\color{blue}{z \cdot \mathsf{PI}\left(\right)}} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
10. Step-by-step derivation

    1. lower-*.f64 N/A

       \[\leadsto \frac{\pi}{z \cdot \color{blue}{\mathsf{PI}\left(\right)}} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

    2. lower-PI.f64 96.3

       \[\leadsto \frac{\pi}{z \cdot \pi} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

11. Applied rewrites 96.3%

    \[\leadsto \frac{\pi}{\color{blue}{z \cdot \pi}} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]
12. Add Preprocessing

Alternative 11: 96.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} t_0 := \left(\left(1 - z\right) - -6\right) - -0.5\\ \frac{1}{z} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({t\_0}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-t\_0}\right)\right)\right) \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (- (- (- 1.0 z) -6.0) -0.5)))
   (*
    (/ 1.0 z)
    (*
     (+ 263.3831869810514 (* z (+ 436.8961725563396 (* 545.0353078428827 z))))
     (* (sqrt (+ PI PI)) (* (pow t_0 (- (- 1.0 z) 0.5)) (exp (- t_0))))))))

C

double code(double z) {
	double t_0 = ((1.0 - z) - -6.0) - -0.5;
	return (1.0 / z) * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (sqrt((((double) M_PI) + ((double) M_PI))) * (pow(t_0, ((1.0 - z) - 0.5)) * exp(-t_0))));
}

Java

public static double code(double z) {
	double t_0 = ((1.0 - z) - -6.0) - -0.5;
	return (1.0 / z) * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (Math.sqrt((Math.PI + Math.PI)) * (Math.pow(t_0, ((1.0 - z) - 0.5)) * Math.exp(-t_0))));
}

Python

def code(z):
	t_0 = ((1.0 - z) - -6.0) - -0.5
	return (1.0 / z) * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (math.sqrt((math.pi + math.pi)) * (math.pow(t_0, ((1.0 - z) - 0.5)) * math.exp(-t_0))))

Julia

function code(z)
	t_0 = Float64(Float64(Float64(1.0 - z) - -6.0) - -0.5)
	return Float64(Float64(1.0 / z) * Float64(Float64(263.3831869810514 + Float64(z * Float64(436.8961725563396 + Float64(545.0353078428827 * z)))) * Float64(sqrt(Float64(pi + pi)) * Float64((t_0 ^ Float64(Float64(1.0 - z) - 0.5)) * exp(Float64(-t_0))))))
end

MATLAB

function tmp = code(z)
	t_0 = ((1.0 - z) - -6.0) - -0.5;
	tmp = (1.0 / z) * ((263.3831869810514 + (z * (436.8961725563396 + (545.0353078428827 * z)))) * (sqrt((pi + pi)) * ((t_0 ^ ((1.0 - z) - 0.5)) * exp(-t_0))));
end

Wolfram

code[z_] := Block[{t$95$0 = N[(N[(N[(1.0 - z), $MachinePrecision] - -6.0), $MachinePrecision] - -0.5), $MachinePrecision]}, N[(N[(1.0 / z), $MachinePrecision] * N[(N[(263.3831869810514 + N[(z * N[(436.8961725563396 + N[(545.0353078428827 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision] * N[(N[Power[t$95$0, N[(N[(1.0 - z), $MachinePrecision] - 0.5), $MachinePrecision]], $MachinePrecision] * N[Exp[(-t$95$0)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 96.6%

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

3. Applied rewrites 98.5%

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

5. Applied rewrites 98.5%

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

6. Taylor expanded in z around 0

   \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
7. Step-by-step derivation

   1. lower-+.f64 N/A

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + \color{blue}{z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

   2. lower-*.f64 N/A

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \color{blue}{\left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)}\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

   3. lower-+.f64 N/A

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \color{blue}{\frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]

   4. lower-*.f64 96.7

      \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot \color{blue}{z}\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

8. Applied rewrites 96.7%

   \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right)} \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

9. Taylor expanded in z around 0

   \[\leadsto \color{blue}{\frac{1}{z}} \cdot \left(\left(\frac{1106209385320415913103082059}{4200000000000000000000000} + z \cdot \left(\frac{102757979785251069442117317613}{235200000000000000000000000} + \frac{64608921419941589693928044520019}{118540800000000000000000000000} \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - \frac{-1}{2}\right)}\right)\right)\right) \]
10. Step-by-step derivation

    1. lower-/.f64 96.3

       \[\leadsto \frac{1}{\color{blue}{z}} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]

11. Applied rewrites 96.3%

    \[\leadsto \color{blue}{\frac{1}{z}} \cdot \left(\left(263.3831869810514 + z \cdot \left(436.8961725563396 + 545.0353078428827 \cdot z\right)\right) \cdot \left(\sqrt{\pi + \pi} \cdot \left({\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}^{\left(\left(1 - z\right) - 0.5\right)} \cdot e^{-\left(\left(\left(1 - z\right) - -6\right) - -0.5\right)}\right)\right)\right) \]
12. Add Preprocessing

Alternative 12: 96.3% accurate, 11.0× speedup

Math

\[263.3831869810514 \cdot \frac{e^{-7.5} \cdot 6.864684246478268}{z} \]

FPCore

(FPCore (z)
 :precision binary64
 (* 263.3831869810514 (/ (* (exp -7.5) 6.864684246478268) z)))

C

double code(double z) {
	return 263.3831869810514 * ((exp(-7.5) * 6.864684246478268) / z);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(z)
use fmin_fmax_functions
    real(8), intent (in) :: z
    code = 263.3831869810514d0 * ((exp((-7.5d0)) * 6.864684246478268d0) / z)
end function

Java

public static double code(double z) {
	return 263.3831869810514 * ((Math.exp(-7.5) * 6.864684246478268) / z);
}

Python

def code(z):
	return 263.3831869810514 * ((math.exp(-7.5) * 6.864684246478268) / z)

Julia

function code(z)
	return Float64(263.3831869810514 * Float64(Float64(exp(-7.5) * 6.864684246478268) / z))
end

MATLAB

function tmp = code(z)
	tmp = 263.3831869810514 * ((exp(-7.5) * 6.864684246478268) / z);
end

Wolfram

code[z_] := N[(263.3831869810514 * N[(N[(N[Exp[-7.5], $MachinePrecision] * 6.864684246478268), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.6%

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

2. Taylor expanded in z around 0

   \[\leadsto \color{blue}{\frac{1106209385320415913103082059}{4200000000000000000000000} \cdot \frac{e^{\frac{-15}{2}} \cdot \left(\sqrt{2 \cdot \mathsf{PI}\left(\right)} \cdot {\frac{15}{2}}^{\frac{1}{2}}\right)}{z}} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \frac{1106209385320415913103082059}{4200000000000000000000000} \cdot \color{blue}{\frac{e^{\frac{-15}{2}} \cdot \left(\sqrt{2 \cdot \mathsf{PI}\left(\right)} \cdot {\frac{15}{2}}^{\frac{1}{2}}\right)}{z}} \]

   2. lower-/.f64 N/A

      \[\leadsto \frac{1106209385320415913103082059}{4200000000000000000000000} \cdot \frac{e^{\frac{-15}{2}} \cdot \left(\sqrt{2 \cdot \mathsf{PI}\left(\right)} \cdot {\frac{15}{2}}^{\frac{1}{2}}\right)}{\color{blue}{z}} \]

4. Applied rewrites 95.7%

   \[\leadsto \color{blue}{263.3831869810514 \cdot \frac{e^{-7.5} \cdot \left(\sqrt{2 \cdot \pi} \cdot {7.5}^{0.5}\right)}{z}} \]

5. Evaluated real constant 96.4%

   \[\leadsto \frac{1106209385320415913103082059}{4200000000000000000000000} \cdot \frac{e^{\frac{-15}{2}} \cdot \frac{3864473676806955}{562949953421312}}{z} \]
6. Add Preprocessing

Alternative 13: 96.3% accurate, 30.7× speedup

Math

\[1.0000000000000002 \cdot \frac{1}{z} \]

FPCore

(FPCore (z) :precision binary64 (* 1.0000000000000002 (/ 1.0 z)))

C

double code(double z) {
	return 1.0000000000000002 * (1.0 / z);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(z)
use fmin_fmax_functions
    real(8), intent (in) :: z
    code = 1.0000000000000002d0 * (1.0d0 / z)
end function

Java

public static double code(double z) {
	return 1.0000000000000002 * (1.0 / z);
}

Python

def code(z):
	return 1.0000000000000002 * (1.0 / z)

Julia

function code(z)
	return Float64(1.0000000000000002 * Float64(1.0 / z))
end

MATLAB

function tmp = code(z)
	tmp = 1.0000000000000002 * (1.0 / z);
end

Wolfram

code[z_] := N[(1.0000000000000002 * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.6%

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

2. Taylor expanded in z around 0

   \[\leadsto \color{blue}{\frac{1106209385320415913103082059}{4200000000000000000000000} \cdot \frac{e^{\frac{-15}{2}} \cdot \left(\sqrt{2 \cdot \mathsf{PI}\left(\right)} \cdot {\frac{15}{2}}^{\frac{1}{2}}\right)}{z}} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \frac{1106209385320415913103082059}{4200000000000000000000000} \cdot \color{blue}{\frac{e^{\frac{-15}{2}} \cdot \left(\sqrt{2 \cdot \mathsf{PI}\left(\right)} \cdot {\frac{15}{2}}^{\frac{1}{2}}\right)}{z}} \]

   2. lower-/.f64 N/A

      \[\leadsto \frac{1106209385320415913103082059}{4200000000000000000000000} \cdot \frac{e^{\frac{-15}{2}} \cdot \left(\sqrt{2 \cdot \mathsf{PI}\left(\right)} \cdot {\frac{15}{2}}^{\frac{1}{2}}\right)}{\color{blue}{z}} \]

4. Applied rewrites 95.7%

   \[\leadsto \color{blue}{263.3831869810514 \cdot \frac{e^{-7.5} \cdot \left(\sqrt{2 \cdot \pi} \cdot {7.5}^{0.5}\right)}{z}} \]

5. Evaluated real constant 95.7%

   \[\leadsto \frac{1106209385320415913103082059}{4200000000000000000000000} \cdot \frac{\frac{2188677109237409}{576460752303423488}}{z} \]
6. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \frac{1106209385320415913103082059}{4200000000000000000000000} \cdot \color{blue}{\frac{\frac{2188677109237409}{576460752303423488}}{z}} \]

   2. lift-/.f64 N/A

      \[\leadsto \frac{1106209385320415913103082059}{4200000000000000000000000} \cdot \frac{\frac{2188677109237409}{576460752303423488}}{\color{blue}{z}} \]

   3. associate-*r/ N/A

      \[\leadsto \frac{\frac{1106209385320415913103082059}{4200000000000000000000000} \cdot \frac{2188677109237409}{576460752303423488}}{\color{blue}{z}} \]

   4. lower-/.f64 N/A

      \[\leadsto \frac{\frac{1106209385320415913103082059}{4200000000000000000000000} \cdot \frac{2188677109237409}{576460752303423488}}{\color{blue}{z}} \]

   5. metadata-eval 96.3

      \[\leadsto \frac{1.0000000000000002}{z} \]

7. Applied rewrites 96.3%

   \[\leadsto \color{blue}{\frac{1.0000000000000002}{z}} \]
8. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \frac{\frac{345876451382054143332511925913682434220733}{345876451382054092800000000000000000000000}}{\color{blue}{z}} \]

   2. mult-flip N/A

      \[\leadsto \frac{345876451382054143332511925913682434220733}{345876451382054092800000000000000000000000} \cdot \color{blue}{\frac{1}{z}} \]

   3. lower-*.f64 N/A

      \[\leadsto \frac{345876451382054143332511925913682434220733}{345876451382054092800000000000000000000000} \cdot \color{blue}{\frac{1}{z}} \]

   4. lower-/.f64 96.3

      \[\leadsto 1.0000000000000002 \cdot \frac{1}{\color{blue}{z}} \]

9. Applied rewrites 96.3%

   \[\leadsto 1.0000000000000002 \cdot \color{blue}{\frac{1}{z}} \]
10. Add Preprocessing

Alternative 14: 96.2% accurate, 51.4× speedup

Math

\[\frac{1.0000000000000002}{z} \]

FPCore

(FPCore (z) :precision binary64 (/ 1.0000000000000002 z))

C

double code(double z) {
	return 1.0000000000000002 / z;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(z)
use fmin_fmax_functions
    real(8), intent (in) :: z
    code = 1.0000000000000002d0 / z
end function

Java

public static double code(double z) {
	return 1.0000000000000002 / z;
}

Python

def code(z):
	return 1.0000000000000002 / z

Julia

function code(z)
	return Float64(1.0000000000000002 / z)
end

MATLAB

function tmp = code(z)
	tmp = 1.0000000000000002 / z;
end

Wolfram

code[z_] := N[(1.0000000000000002 / z), $MachinePrecision]

Derivation

1. Initial program 96.6%

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

2. Taylor expanded in z around 0

   \[\leadsto \color{blue}{\frac{1106209385320415913103082059}{4200000000000000000000000} \cdot \frac{e^{\frac{-15}{2}} \cdot \left(\sqrt{2 \cdot \mathsf{PI}\left(\right)} \cdot {\frac{15}{2}}^{\frac{1}{2}}\right)}{z}} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \frac{1106209385320415913103082059}{4200000000000000000000000} \cdot \color{blue}{\frac{e^{\frac{-15}{2}} \cdot \left(\sqrt{2 \cdot \mathsf{PI}\left(\right)} \cdot {\frac{15}{2}}^{\frac{1}{2}}\right)}{z}} \]

   2. lower-/.f64 N/A

      \[\leadsto \frac{1106209385320415913103082059}{4200000000000000000000000} \cdot \frac{e^{\frac{-15}{2}} \cdot \left(\sqrt{2 \cdot \mathsf{PI}\left(\right)} \cdot {\frac{15}{2}}^{\frac{1}{2}}\right)}{\color{blue}{z}} \]

4. Applied rewrites 95.7%

   \[\leadsto \color{blue}{263.3831869810514 \cdot \frac{e^{-7.5} \cdot \left(\sqrt{2 \cdot \pi} \cdot {7.5}^{0.5}\right)}{z}} \]

5. Evaluated real constant 95.7%

   \[\leadsto \frac{1106209385320415913103082059}{4200000000000000000000000} \cdot \frac{\frac{2188677109237409}{576460752303423488}}{z} \]
6. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \frac{1106209385320415913103082059}{4200000000000000000000000} \cdot \color{blue}{\frac{\frac{2188677109237409}{576460752303423488}}{z}} \]

   2. lift-/.f64 N/A

      \[\leadsto \frac{1106209385320415913103082059}{4200000000000000000000000} \cdot \frac{\frac{2188677109237409}{576460752303423488}}{\color{blue}{z}} \]

   3. associate-*r/ N/A

      \[\leadsto \frac{\frac{1106209385320415913103082059}{4200000000000000000000000} \cdot \frac{2188677109237409}{576460752303423488}}{\color{blue}{z}} \]

   4. lower-/.f64 N/A

      \[\leadsto \frac{\frac{1106209385320415913103082059}{4200000000000000000000000} \cdot \frac{2188677109237409}{576460752303423488}}{\color{blue}{z}} \]

   5. metadata-eval 96.3

      \[\leadsto \frac{1.0000000000000002}{z} \]

7. Applied rewrites 96.3%

   \[\leadsto \color{blue}{\frac{1.0000000000000002}{z}} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025170 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  :precision binary64
  :pre (<= z 0.5)
  (* (/ PI (sin (* PI z))) (* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- (- 1.0 z) 1.0) 7.0) 0.5) (+ (- (- 1.0 z) 1.0) 0.5))) (exp (- (+ (+ (- (- 1.0 z) 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- (- 1.0 z) 1.0) 1.0))) (/ -1259.1392167224028 (+ (- (- 1.0 z) 1.0) 2.0))) (/ 771.3234287776531 (+ (- (- 1.0 z) 1.0) 3.0))) (/ -176.6150291621406 (+ (- (- 1.0 z) 1.0) 4.0))) (/ 12.507343278686905 (+ (- (- 1.0 z) 1.0) 5.0))) (/ -0.13857109526572012 (+ (- (- 1.0 z) 1.0) 6.0))) (/ 9.984369578019572e-6 (+ (- (- 1.0 z) 1.0) 7.0))) (/ 1.5056327351493116e-7 (+ (- (- 1.0 z) 1.0) 8.0))))))