Jmat.Real.gamma, branch z less than 0.5

Percentage Accurate: 96.4% → 99.3%

Time: 18.7s

Alternatives: 20

Speedup: 1.7×

• could not determine a ground truth

  1. z = -15810516257497.309

Specification

\[z \leq 0.5\]

Math

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

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: 96.4% accurate, 1.0× speedup

Math

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

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, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(\pi \cdot z\right)\\ t_1 := \sqrt{\pi + \pi}\\ t_2 := \frac{\pi \cdot \left(\left(t\_1 \cdot {\left(\left(1 - z\right) - -6.5\right)}^{\left(\left(1 - z\right) - 0.5\right)}\right) \cdot e^{\left(0 + z\right) + -7.5}\right)}{t\_0}\\ \mathbf{if}\;z \leq -2000:\\ \;\;\;\;\left(t\_1 \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(263.3831869810514 \cdot e^{-7.5}\right) \cdot \frac{\pi}{t\_0}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_2, \left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{-1 - \left(1 - z\right)}\right) - \left(\frac{771.3234287776531}{-2 - \left(1 - z\right)} - \frac{-176.6150291621406}{\left(1 - z\right) - -3}\right)\right) - \left(\frac{12.507343278686905}{-4 - \left(1 - z\right)} - \frac{-0.13857109526572012}{\left(1 - z\right) - -5}\right), t\_2 \cdot \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(1 - z\right) - -6} - \frac{1.5056327351493116 \cdot 10^{-7}}{-7 - \left(1 - z\right)}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (sin (* PI z)))
        (t_1 (sqrt (+ PI PI)))
        (t_2
         (/
          (*
           PI
           (*
            (* t_1 (pow (- (- 1.0 z) -6.5) (- (- 1.0 z) 0.5)))
            (exp (+ (+ 0.0 z) -7.5))))
          t_0)))
   (if (<= z -2000.0)
     (*
      (* t_1 (pow (- (- z 7.5)) (- 0.5 z)))
      (* (* 263.3831869810514 (exp -7.5)) (/ PI t_0)))
     (fma
      t_2
      (-
       (-
        (-
         (- (/ -676.5203681218851 (- z 1.0)) -0.9999999999998099)
         (/ -1259.1392167224028 (- -1.0 (- 1.0 z))))
        (-
         (/ 771.3234287776531 (- -2.0 (- 1.0 z)))
         (/ -176.6150291621406 (- (- 1.0 z) -3.0))))
       (-
        (/ 12.507343278686905 (- -4.0 (- 1.0 z)))
        (/ -0.13857109526572012 (- (- 1.0 z) -5.0))))
      (*
       t_2
       (-
        (/ 9.984369578019572e-6 (- (- 1.0 z) -6.0))
        (/ 1.5056327351493116e-7 (- -7.0 (- 1.0 z)))))))))

C

double code(double z) {
	double t_0 = sin((((double) M_PI) * z));
	double t_1 = sqrt((((double) M_PI) + ((double) M_PI)));
	double t_2 = (((double) M_PI) * ((t_1 * pow(((1.0 - z) - -6.5), ((1.0 - z) - 0.5))) * exp(((0.0 + z) + -7.5)))) / t_0;
	double tmp;
	if (z <= -2000.0) {
		tmp = (t_1 * pow(-(z - 7.5), (0.5 - z))) * ((263.3831869810514 * exp(-7.5)) * (((double) M_PI) / t_0));
	} else {
		tmp = fma(t_2, (((((-676.5203681218851 / (z - 1.0)) - -0.9999999999998099) - (-1259.1392167224028 / (-1.0 - (1.0 - z)))) - ((771.3234287776531 / (-2.0 - (1.0 - z))) - (-176.6150291621406 / ((1.0 - z) - -3.0)))) - ((12.507343278686905 / (-4.0 - (1.0 - z))) - (-0.13857109526572012 / ((1.0 - z) - -5.0)))), (t_2 * ((9.984369578019572e-6 / ((1.0 - z) - -6.0)) - (1.5056327351493116e-7 / (-7.0 - (1.0 - z))))));
	}
	return tmp;
}

Julia

function code(z)
	t_0 = sin(Float64(pi * z))
	t_1 = sqrt(Float64(pi + pi))
	t_2 = Float64(Float64(pi * Float64(Float64(t_1 * (Float64(Float64(1.0 - z) - -6.5) ^ Float64(Float64(1.0 - z) - 0.5))) * exp(Float64(Float64(0.0 + z) + -7.5)))) / t_0)
	tmp = 0.0
	if (z <= -2000.0)
		tmp = Float64(Float64(t_1 * (Float64(-Float64(z - 7.5)) ^ Float64(0.5 - z))) * Float64(Float64(263.3831869810514 * exp(-7.5)) * Float64(pi / t_0)));
	else
		tmp = fma(t_2, Float64(Float64(Float64(Float64(Float64(-676.5203681218851 / Float64(z - 1.0)) - -0.9999999999998099) - Float64(-1259.1392167224028 / Float64(-1.0 - Float64(1.0 - z)))) - Float64(Float64(771.3234287776531 / Float64(-2.0 - Float64(1.0 - z))) - Float64(-176.6150291621406 / Float64(Float64(1.0 - z) - -3.0)))) - Float64(Float64(12.507343278686905 / Float64(-4.0 - Float64(1.0 - z))) - Float64(-0.13857109526572012 / Float64(Float64(1.0 - z) - -5.0)))), Float64(t_2 * Float64(Float64(9.984369578019572e-6 / Float64(Float64(1.0 - z) - -6.0)) - Float64(1.5056327351493116e-7 / Float64(-7.0 - Float64(1.0 - z))))));
	end
	return tmp
end

Wolfram

code[z_] := Block[{t$95$0 = N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(Pi * N[(N[(t$95$1 * N[Power[N[(N[(1.0 - z), $MachinePrecision] - -6.5), $MachinePrecision], N[(N[(1.0 - z), $MachinePrecision] - 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Exp[N[(N[(0.0 + z), $MachinePrecision] + -7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[z, -2000.0], N[(N[(t$95$1 * N[Power[(-N[(z - 7.5), $MachinePrecision]), N[(0.5 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(263.3831869810514 * N[Exp[-7.5], $MachinePrecision]), $MachinePrecision] * N[(Pi / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 * N[(N[(N[(N[(N[(-676.5203681218851 / N[(z - 1.0), $MachinePrecision]), $MachinePrecision] - -0.9999999999998099), $MachinePrecision] - N[(-1259.1392167224028 / N[(-1.0 - N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(771.3234287776531 / N[(-2.0 - N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-176.6150291621406 / N[(N[(1.0 - z), $MachinePrecision] - -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(12.507343278686905 / N[(-4.0 - N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-0.13857109526572012 / N[(N[(1.0 - z), $MachinePrecision] - -5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(N[(9.984369578019572e-6 / N[(N[(1.0 - z), $MachinePrecision] - -6.0), $MachinePrecision]), $MachinePrecision] - N[(1.5056327351493116e-7 / N[(-7.0 - N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if z < -2e3

   1. Initial program 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 96.2%

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

   if -2e3 < z

   1. Initial program 96.4%

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

   3. Applied rewrites 98.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\pi \cdot \left(\left(\sqrt{\pi + \pi} \cdot {\left(\left(1 - z\right) - -6.5\right)}^{\left(\left(1 - z\right) - 0.5\right)}\right) \cdot e^{\left(0 + z\right) + -7.5}\right)}{\sin \left(\pi \cdot z\right)}, \left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{-1 - \left(1 - z\right)}\right) - \left(\frac{771.3234287776531}{-2 - \left(1 - z\right)} - \frac{-176.6150291621406}{\left(1 - z\right) - -3}\right)\right) - \left(\frac{12.507343278686905}{-4 - \left(1 - z\right)} - \frac{-0.13857109526572012}{\left(1 - z\right) - -5}\right), \frac{\pi \cdot \left(\left(\sqrt{\pi + \pi} \cdot {\left(\left(1 - z\right) - -6.5\right)}^{\left(\left(1 - z\right) - 0.5\right)}\right) \cdot e^{\left(0 + z\right) + -7.5}\right)}{\sin \left(\pi \cdot z\right)} \cdot \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(1 - z\right) - -6} - \frac{1.5056327351493116 \cdot 10^{-7}}{-7 - \left(1 - z\right)}\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 99.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\pi}{\sin \left(\pi \cdot z\right)}\\ t_1 := -\left(z - 7.5\right)\\ t_2 := \left(1 - z\right) - 1\\ t_3 := t\_2 + 7\\ t_4 := t\_3 + 0.5\\ t_5 := \sqrt{\pi + \pi}\\ \mathbf{if}\;t\_0 \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {t\_4}^{\left(t\_2 + 0.5\right)}\right) \cdot e^{-t\_4}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{t\_2 + 1}\right) + \frac{-1259.1392167224028}{t\_2 + 2}\right) + \frac{771.3234287776531}{t\_2 + 3}\right) + \frac{-176.6150291621406}{t\_2 + 4}\right) + \frac{12.507343278686905}{t\_2 + 5}\right) + \frac{-0.13857109526572012}{t\_2 + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t\_3}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{t\_2 + 8}\right)\right) \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\left(t\_5 \cdot {t\_1}^{\left(1 - \left(0.5 + z\right)\right)}\right) \cdot \left(\left(\left(\left(\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t\_5 \cdot {t\_1}^{\left(0.5 - z\right)}\right) \cdot \left(\left(263.3831869810514 \cdot e^{-7.5}\right) \cdot t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (/ PI (sin (* PI z))))
        (t_1 (- (- z 7.5)))
        (t_2 (- (- 1.0 z) 1.0))
        (t_3 (+ t_2 7.0))
        (t_4 (+ t_3 0.5))
        (t_5 (sqrt (+ PI PI))))
   (if (<=
        (*
         t_0
         (*
          (* (* (sqrt (* PI 2.0)) (pow t_4 (+ t_2 0.5))) (exp (- t_4)))
          (+
           (+
            (+
             (+
              (+
               (+
                (+
                 (+ 0.9999999999998099 (/ 676.5203681218851 (+ t_2 1.0)))
                 (/ -1259.1392167224028 (+ t_2 2.0)))
                (/ 771.3234287776531 (+ t_2 3.0)))
               (/ -176.6150291621406 (+ t_2 4.0)))
              (/ 12.507343278686905 (+ t_2 5.0)))
             (/ -0.13857109526572012 (+ t_2 6.0)))
            (/ 9.984369578019572e-6 t_3))
           (/ 1.5056327351493116e-7 (+ t_2 8.0)))))
        2e+304)
     (*
      (* t_5 (pow t_1 (- 1.0 (+ 0.5 z))))
      (*
       (*
        (-
         (-
          (-
           (/ -771.3234287776531 (- z 3.0))
           (-
            (-
             (/ -1259.1392167224028 (- z 2.0))
             (/ -676.5203681218851 (- z 1.0)))
            0.9999999999998099))
          (/ 176.6150291621406 (- 4.0 z)))
         (-
          (-
           (/ 12.507343278686905 (- z 5.0))
           (/ -0.13857109526572012 (- 6.0 z)))
          (-
           (/ 9.984369578019572e-6 (- 7.0 z))
           (/ -1.5056327351493116e-7 (- 8.0 z)))))
        (exp (- z 7.5)))
       t_0))
     (*
      (* t_5 (pow t_1 (- 0.5 z)))
      (* (* 263.3831869810514 (exp -7.5)) t_0)))))

C

double code(double z) {
	double t_0 = ((double) M_PI) / sin((((double) M_PI) * z));
	double t_1 = -(z - 7.5);
	double t_2 = (1.0 - z) - 1.0;
	double t_3 = t_2 + 7.0;
	double t_4 = t_3 + 0.5;
	double t_5 = sqrt((((double) M_PI) + ((double) M_PI)));
	double tmp;
	if ((t_0 * (((sqrt((((double) M_PI) * 2.0)) * pow(t_4, (t_2 + 0.5))) * exp(-t_4)) * ((((((((0.9999999999998099 + (676.5203681218851 / (t_2 + 1.0))) + (-1259.1392167224028 / (t_2 + 2.0))) + (771.3234287776531 / (t_2 + 3.0))) + (-176.6150291621406 / (t_2 + 4.0))) + (12.507343278686905 / (t_2 + 5.0))) + (-0.13857109526572012 / (t_2 + 6.0))) + (9.984369578019572e-6 / t_3)) + (1.5056327351493116e-7 / (t_2 + 8.0))))) <= 2e+304) {
		tmp = (t_5 * pow(t_1, (1.0 - (0.5 + z)))) * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - ((9.984369578019572e-6 / (7.0 - z)) - (-1.5056327351493116e-7 / (8.0 - z))))) * exp((z - 7.5))) * t_0);
	} else {
		tmp = (t_5 * pow(t_1, (0.5 - z))) * ((263.3831869810514 * exp(-7.5)) * t_0);
	}
	return tmp;
}

Java

public static double code(double z) {
	double t_0 = Math.PI / Math.sin((Math.PI * z));
	double t_1 = -(z - 7.5);
	double t_2 = (1.0 - z) - 1.0;
	double t_3 = t_2 + 7.0;
	double t_4 = t_3 + 0.5;
	double t_5 = Math.sqrt((Math.PI + Math.PI));
	double tmp;
	if ((t_0 * (((Math.sqrt((Math.PI * 2.0)) * Math.pow(t_4, (t_2 + 0.5))) * Math.exp(-t_4)) * ((((((((0.9999999999998099 + (676.5203681218851 / (t_2 + 1.0))) + (-1259.1392167224028 / (t_2 + 2.0))) + (771.3234287776531 / (t_2 + 3.0))) + (-176.6150291621406 / (t_2 + 4.0))) + (12.507343278686905 / (t_2 + 5.0))) + (-0.13857109526572012 / (t_2 + 6.0))) + (9.984369578019572e-6 / t_3)) + (1.5056327351493116e-7 / (t_2 + 8.0))))) <= 2e+304) {
		tmp = (t_5 * Math.pow(t_1, (1.0 - (0.5 + z)))) * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - ((9.984369578019572e-6 / (7.0 - z)) - (-1.5056327351493116e-7 / (8.0 - z))))) * Math.exp((z - 7.5))) * t_0);
	} else {
		tmp = (t_5 * Math.pow(t_1, (0.5 - z))) * ((263.3831869810514 * Math.exp(-7.5)) * t_0);
	}
	return tmp;
}

Python

def code(z):
	t_0 = math.pi / math.sin((math.pi * z))
	t_1 = -(z - 7.5)
	t_2 = (1.0 - z) - 1.0
	t_3 = t_2 + 7.0
	t_4 = t_3 + 0.5
	t_5 = math.sqrt((math.pi + math.pi))
	tmp = 0
	if (t_0 * (((math.sqrt((math.pi * 2.0)) * math.pow(t_4, (t_2 + 0.5))) * math.exp(-t_4)) * ((((((((0.9999999999998099 + (676.5203681218851 / (t_2 + 1.0))) + (-1259.1392167224028 / (t_2 + 2.0))) + (771.3234287776531 / (t_2 + 3.0))) + (-176.6150291621406 / (t_2 + 4.0))) + (12.507343278686905 / (t_2 + 5.0))) + (-0.13857109526572012 / (t_2 + 6.0))) + (9.984369578019572e-6 / t_3)) + (1.5056327351493116e-7 / (t_2 + 8.0))))) <= 2e+304:
		tmp = (t_5 * math.pow(t_1, (1.0 - (0.5 + z)))) * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - ((9.984369578019572e-6 / (7.0 - z)) - (-1.5056327351493116e-7 / (8.0 - z))))) * math.exp((z - 7.5))) * t_0)
	else:
		tmp = (t_5 * math.pow(t_1, (0.5 - z))) * ((263.3831869810514 * math.exp(-7.5)) * t_0)
	return tmp

Julia

function code(z)
	t_0 = Float64(pi / sin(Float64(pi * z)))
	t_1 = Float64(-Float64(z - 7.5))
	t_2 = Float64(Float64(1.0 - z) - 1.0)
	t_3 = Float64(t_2 + 7.0)
	t_4 = Float64(t_3 + 0.5)
	t_5 = sqrt(Float64(pi + pi))
	tmp = 0.0
	if (Float64(t_0 * Float64(Float64(Float64(sqrt(Float64(pi * 2.0)) * (t_4 ^ Float64(t_2 + 0.5))) * exp(Float64(-t_4))) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(0.9999999999998099 + Float64(676.5203681218851 / Float64(t_2 + 1.0))) + Float64(-1259.1392167224028 / Float64(t_2 + 2.0))) + Float64(771.3234287776531 / Float64(t_2 + 3.0))) + Float64(-176.6150291621406 / Float64(t_2 + 4.0))) + Float64(12.507343278686905 / Float64(t_2 + 5.0))) + Float64(-0.13857109526572012 / Float64(t_2 + 6.0))) + Float64(9.984369578019572e-6 / t_3)) + Float64(1.5056327351493116e-7 / Float64(t_2 + 8.0))))) <= 2e+304)
		tmp = Float64(Float64(t_5 * (t_1 ^ Float64(1.0 - Float64(0.5 + z)))) * Float64(Float64(Float64(Float64(Float64(Float64(-771.3234287776531 / Float64(z - 3.0)) - Float64(Float64(Float64(-1259.1392167224028 / Float64(z - 2.0)) - Float64(-676.5203681218851 / Float64(z - 1.0))) - 0.9999999999998099)) - Float64(176.6150291621406 / Float64(4.0 - z))) - Float64(Float64(Float64(12.507343278686905 / Float64(z - 5.0)) - Float64(-0.13857109526572012 / Float64(6.0 - z))) - Float64(Float64(9.984369578019572e-6 / Float64(7.0 - z)) - Float64(-1.5056327351493116e-7 / Float64(8.0 - z))))) * exp(Float64(z - 7.5))) * t_0));
	else
		tmp = Float64(Float64(t_5 * (t_1 ^ Float64(0.5 - z))) * Float64(Float64(263.3831869810514 * exp(-7.5)) * t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z)
	t_0 = pi / sin((pi * z));
	t_1 = -(z - 7.5);
	t_2 = (1.0 - z) - 1.0;
	t_3 = t_2 + 7.0;
	t_4 = t_3 + 0.5;
	t_5 = sqrt((pi + pi));
	tmp = 0.0;
	if ((t_0 * (((sqrt((pi * 2.0)) * (t_4 ^ (t_2 + 0.5))) * exp(-t_4)) * ((((((((0.9999999999998099 + (676.5203681218851 / (t_2 + 1.0))) + (-1259.1392167224028 / (t_2 + 2.0))) + (771.3234287776531 / (t_2 + 3.0))) + (-176.6150291621406 / (t_2 + 4.0))) + (12.507343278686905 / (t_2 + 5.0))) + (-0.13857109526572012 / (t_2 + 6.0))) + (9.984369578019572e-6 / t_3)) + (1.5056327351493116e-7 / (t_2 + 8.0))))) <= 2e+304)
		tmp = (t_5 * (t_1 ^ (1.0 - (0.5 + z)))) * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - ((9.984369578019572e-6 / (7.0 - z)) - (-1.5056327351493116e-7 / (8.0 - z))))) * exp((z - 7.5))) * t_0);
	else
		tmp = (t_5 * (t_1 ^ (0.5 - z))) * ((263.3831869810514 * exp(-7.5)) * t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[z_] := Block[{t$95$0 = N[(Pi / N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = (-N[(z - 7.5), $MachinePrecision])}, Block[{t$95$2 = N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + 7.0), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + 0.5), $MachinePrecision]}, Block[{t$95$5 = N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(t$95$0 * N[(N[(N[(N[Sqrt[N[(Pi * 2.0), $MachinePrecision]], $MachinePrecision] * N[Power[t$95$4, N[(t$95$2 + 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Exp[(-t$95$4)], $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(0.9999999999998099 + N[(676.5203681218851 / N[(t$95$2 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1259.1392167224028 / N[(t$95$2 + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(771.3234287776531 / N[(t$95$2 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-176.6150291621406 / N[(t$95$2 + 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(12.507343278686905 / N[(t$95$2 + 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.13857109526572012 / N[(t$95$2 + 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(9.984369578019572e-6 / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(t$95$2 + 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e+304], N[(N[(t$95$5 * N[Power[t$95$1, N[(1.0 - N[(0.5 + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(N[(N[(-771.3234287776531 / N[(z - 3.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(-1259.1392167224028 / N[(z - 2.0), $MachinePrecision]), $MachinePrecision] - N[(-676.5203681218851 / N[(z - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 0.9999999999998099), $MachinePrecision]), $MachinePrecision] - N[(176.6150291621406 / N[(4.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(12.507343278686905 / N[(z - 5.0), $MachinePrecision]), $MachinePrecision] - N[(-0.13857109526572012 / N[(6.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(9.984369578019572e-6 / N[(7.0 - z), $MachinePrecision]), $MachinePrecision] - N[(-1.5056327351493116e-7 / N[(8.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Exp[N[(z - 7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$5 * N[Power[t$95$1, N[(0.5 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(263.3831869810514 * N[Exp[-7.5], $MachinePrecision]), $MachinePrecision] * t$95$0), $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)))))) < 1.9999999999999999e304

   1. Initial program 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   7. Applied rewrites 98.3%

      \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\color{blue}{\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right)} - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   9. Applied rewrites 98.3%

      \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\color{blue}{\left(1 - \left(0.5 + z\right)\right)}}\right) \cdot \left(\left(\left(\left(\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   if 1.9999999999999999e304 < (*.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 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 96.2%

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

Alternative 3: 99.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - z\right) - 1\\ t_1 := t\_0 + 7\\ t_2 := t\_1 + 0.5\\ t_3 := \frac{\pi}{\sin \left(\pi \cdot z\right)}\\ t_4 := \sqrt{\pi + \pi}\\ \mathbf{if}\;t\_3 \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {t\_2}^{\left(t\_0 + 0.5\right)}\right) \cdot e^{-t\_2}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{t\_0 + 1}\right) + \frac{-1259.1392167224028}{t\_0 + 2}\right) + \frac{771.3234287776531}{t\_0 + 3}\right) + \frac{-176.6150291621406}{t\_0 + 4}\right) + \frac{12.507343278686905}{t\_0 + 5}\right) + \frac{-0.13857109526572012}{t\_0 + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t\_1}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{t\_0 + 8}\right)\right) \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\left({\left(7.5 - z\right)}^{\left(0.5 - z\right)} \cdot t\_4\right) \cdot \left(\left(\left(\left(\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot t\_3\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t\_4 \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(263.3831869810514 \cdot e^{-7.5}\right) \cdot t\_3\right)\\ \end{array} \end{array} \]

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 (sqrt (+ PI PI))))
   (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+304)
     (*
      (* (pow (- 7.5 z) (- 0.5 z)) t_4)
      (*
       (*
        (-
         (-
          (-
           (/ -771.3234287776531 (- z 3.0))
           (-
            (-
             (/ -1259.1392167224028 (- z 2.0))
             (/ -676.5203681218851 (- z 1.0)))
            0.9999999999998099))
          (/ 176.6150291621406 (- 4.0 z)))
         (-
          (-
           (/ 12.507343278686905 (- z 5.0))
           (/ -0.13857109526572012 (- 6.0 z)))
          (-
           (/ 9.984369578019572e-6 (- 7.0 z))
           (/ -1.5056327351493116e-7 (- 8.0 z)))))
        (exp (- z 7.5)))
       t_3))
     (*
      (* t_4 (pow (- (- z 7.5)) (- 0.5 z)))
      (* (* 263.3831869810514 (exp -7.5)) t_3)))))

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 = sqrt((((double) M_PI) + ((double) M_PI)));
	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+304) {
		tmp = (pow((7.5 - z), (0.5 - z)) * t_4) * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - ((9.984369578019572e-6 / (7.0 - z)) - (-1.5056327351493116e-7 / (8.0 - z))))) * exp((z - 7.5))) * t_3);
	} else {
		tmp = (t_4 * pow(-(z - 7.5), (0.5 - z))) * ((263.3831869810514 * exp(-7.5)) * t_3);
	}
	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 = Math.sqrt((Math.PI + Math.PI));
	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+304) {
		tmp = (Math.pow((7.5 - z), (0.5 - z)) * t_4) * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - ((9.984369578019572e-6 / (7.0 - z)) - (-1.5056327351493116e-7 / (8.0 - z))))) * Math.exp((z - 7.5))) * t_3);
	} else {
		tmp = (t_4 * Math.pow(-(z - 7.5), (0.5 - z))) * ((263.3831869810514 * Math.exp(-7.5)) * t_3);
	}
	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 = math.sqrt((math.pi + math.pi))
	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+304:
		tmp = (math.pow((7.5 - z), (0.5 - z)) * t_4) * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - ((9.984369578019572e-6 / (7.0 - z)) - (-1.5056327351493116e-7 / (8.0 - z))))) * math.exp((z - 7.5))) * t_3)
	else:
		tmp = (t_4 * math.pow(-(z - 7.5), (0.5 - z))) * ((263.3831869810514 * math.exp(-7.5)) * t_3)
	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 = sqrt(Float64(pi + pi))
	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+304)
		tmp = Float64(Float64((Float64(7.5 - z) ^ Float64(0.5 - z)) * t_4) * Float64(Float64(Float64(Float64(Float64(Float64(-771.3234287776531 / Float64(z - 3.0)) - Float64(Float64(Float64(-1259.1392167224028 / Float64(z - 2.0)) - Float64(-676.5203681218851 / Float64(z - 1.0))) - 0.9999999999998099)) - Float64(176.6150291621406 / Float64(4.0 - z))) - Float64(Float64(Float64(12.507343278686905 / Float64(z - 5.0)) - Float64(-0.13857109526572012 / Float64(6.0 - z))) - Float64(Float64(9.984369578019572e-6 / Float64(7.0 - z)) - Float64(-1.5056327351493116e-7 / Float64(8.0 - z))))) * exp(Float64(z - 7.5))) * t_3));
	else
		tmp = Float64(Float64(t_4 * (Float64(-Float64(z - 7.5)) ^ Float64(0.5 - z))) * Float64(Float64(263.3831869810514 * exp(-7.5)) * t_3));
	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 = sqrt((pi + pi));
	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+304)
		tmp = (((7.5 - z) ^ (0.5 - z)) * t_4) * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - ((9.984369578019572e-6 / (7.0 - z)) - (-1.5056327351493116e-7 / (8.0 - z))))) * exp((z - 7.5))) * t_3);
	else
		tmp = (t_4 * (-(z - 7.5) ^ (0.5 - z))) * ((263.3831869810514 * exp(-7.5)) * t_3);
	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[Sqrt[N[(Pi + Pi), $MachinePrecision]], $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+304], N[(N[(N[Power[N[(7.5 - z), $MachinePrecision], N[(0.5 - z), $MachinePrecision]], $MachinePrecision] * t$95$4), $MachinePrecision] * N[(N[(N[(N[(N[(N[(-771.3234287776531 / N[(z - 3.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(-1259.1392167224028 / N[(z - 2.0), $MachinePrecision]), $MachinePrecision] - N[(-676.5203681218851 / N[(z - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 0.9999999999998099), $MachinePrecision]), $MachinePrecision] - N[(176.6150291621406 / N[(4.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(12.507343278686905 / N[(z - 5.0), $MachinePrecision]), $MachinePrecision] - N[(-0.13857109526572012 / N[(6.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(9.984369578019572e-6 / N[(7.0 - z), $MachinePrecision]), $MachinePrecision] - N[(-1.5056327351493116e-7 / N[(8.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Exp[N[(z - 7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$4 * N[Power[(-N[(z - 7.5), $MachinePrecision]), N[(0.5 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(263.3831869810514 * N[Exp[-7.5], $MachinePrecision]), $MachinePrecision] * t$95$3), $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)))))) < 1.9999999999999999e304

   1. Initial program 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   7. Applied rewrites 98.3%

      \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\color{blue}{\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right)} - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   9. Applied rewrites 98.3%

      \[\leadsto \color{blue}{\left({\left(7.5 - z\right)}^{\left(0.5 - z\right)} \cdot \sqrt{\pi + \pi}\right)} \cdot \left(\left(\left(\left(\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   if 1.9999999999999999e304 < (*.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 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 96.2%

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

Alternative 4: 99.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - z\right) - 1\\ t_1 := t\_0 + 7\\ t_2 := t\_1 + 0.5\\ t_3 := \sqrt{\pi + \pi}\\ t_4 := \frac{\pi}{\sin \left(\pi \cdot z\right)}\\ \mathbf{if}\;t\_4 \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {t\_2}^{\left(t\_0 + 0.5\right)}\right) \cdot e^{-t\_2}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{t\_0 + 1}\right) + \frac{-1259.1392167224028}{t\_0 + 2}\right) + \frac{771.3234287776531}{t\_0 + 3}\right) + \frac{-176.6150291621406}{t\_0 + 4}\right) + \frac{12.507343278686905}{t\_0 + 5}\right) + \frac{-0.13857109526572012}{t\_0 + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t\_1}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{t\_0 + 8}\right)\right) \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\left(t\_4 \cdot \left(t\_3 \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right)\right) \cdot \left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \left(\frac{771.3234287776531}{z - 3} - \frac{-176.6150291621406}{4 - z}\right)\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t\_3 \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(263.3831869810514 \cdot e^{-7.5}\right) \cdot t\_4\right)\\ \end{array} \end{array} \]

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 (sqrt (+ PI PI)))
        (t_4 (/ PI (sin (* PI z)))))
   (if (<=
        (*
         t_4
         (*
          (* (* (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+304)
     (*
      (* t_4 (* t_3 (pow (- 7.5 z) (- 0.5 z))))
      (*
       (-
        (-
         (-
          (- (/ -676.5203681218851 (- z 1.0)) -0.9999999999998099)
          (/ -1259.1392167224028 (- z 2.0)))
         (- (/ 771.3234287776531 (- z 3.0)) (/ -176.6150291621406 (- 4.0 z))))
        (-
         (-
          (/ 12.507343278686905 (- z 5.0))
          (/ -0.13857109526572012 (- 6.0 z)))
         (-
          (/ 9.984369578019572e-6 (- 7.0 z))
          (/ -1.5056327351493116e-7 (- 8.0 z)))))
       (exp (- z 7.5))))
     (*
      (* t_3 (pow (- (- z 7.5)) (- 0.5 z)))
      (* (* 263.3831869810514 (exp -7.5)) t_4)))))

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 = sqrt((((double) M_PI) + ((double) M_PI)));
	double t_4 = ((double) M_PI) / sin((((double) M_PI) * z));
	double tmp;
	if ((t_4 * (((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+304) {
		tmp = (t_4 * (t_3 * pow((7.5 - z), (0.5 - z)))) * ((((((-676.5203681218851 / (z - 1.0)) - -0.9999999999998099) - (-1259.1392167224028 / (z - 2.0))) - ((771.3234287776531 / (z - 3.0)) - (-176.6150291621406 / (4.0 - z)))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - ((9.984369578019572e-6 / (7.0 - z)) - (-1.5056327351493116e-7 / (8.0 - z))))) * exp((z - 7.5)));
	} else {
		tmp = (t_3 * pow(-(z - 7.5), (0.5 - z))) * ((263.3831869810514 * exp(-7.5)) * t_4);
	}
	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.sqrt((Math.PI + Math.PI));
	double t_4 = Math.PI / Math.sin((Math.PI * z));
	double tmp;
	if ((t_4 * (((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+304) {
		tmp = (t_4 * (t_3 * Math.pow((7.5 - z), (0.5 - z)))) * ((((((-676.5203681218851 / (z - 1.0)) - -0.9999999999998099) - (-1259.1392167224028 / (z - 2.0))) - ((771.3234287776531 / (z - 3.0)) - (-176.6150291621406 / (4.0 - z)))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - ((9.984369578019572e-6 / (7.0 - z)) - (-1.5056327351493116e-7 / (8.0 - z))))) * Math.exp((z - 7.5)));
	} else {
		tmp = (t_3 * Math.pow(-(z - 7.5), (0.5 - z))) * ((263.3831869810514 * Math.exp(-7.5)) * t_4);
	}
	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.sqrt((math.pi + math.pi))
	t_4 = math.pi / math.sin((math.pi * z))
	tmp = 0
	if (t_4 * (((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+304:
		tmp = (t_4 * (t_3 * math.pow((7.5 - z), (0.5 - z)))) * ((((((-676.5203681218851 / (z - 1.0)) - -0.9999999999998099) - (-1259.1392167224028 / (z - 2.0))) - ((771.3234287776531 / (z - 3.0)) - (-176.6150291621406 / (4.0 - z)))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - ((9.984369578019572e-6 / (7.0 - z)) - (-1.5056327351493116e-7 / (8.0 - z))))) * math.exp((z - 7.5)))
	else:
		tmp = (t_3 * math.pow(-(z - 7.5), (0.5 - z))) * ((263.3831869810514 * math.exp(-7.5)) * t_4)
	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 = sqrt(Float64(pi + pi))
	t_4 = Float64(pi / sin(Float64(pi * z)))
	tmp = 0.0
	if (Float64(t_4 * 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+304)
		tmp = Float64(Float64(t_4 * Float64(t_3 * (Float64(7.5 - z) ^ Float64(0.5 - z)))) * Float64(Float64(Float64(Float64(Float64(Float64(-676.5203681218851 / Float64(z - 1.0)) - -0.9999999999998099) - Float64(-1259.1392167224028 / Float64(z - 2.0))) - Float64(Float64(771.3234287776531 / Float64(z - 3.0)) - Float64(-176.6150291621406 / Float64(4.0 - z)))) - Float64(Float64(Float64(12.507343278686905 / Float64(z - 5.0)) - Float64(-0.13857109526572012 / Float64(6.0 - z))) - Float64(Float64(9.984369578019572e-6 / Float64(7.0 - z)) - Float64(-1.5056327351493116e-7 / Float64(8.0 - z))))) * exp(Float64(z - 7.5))));
	else
		tmp = Float64(Float64(t_3 * (Float64(-Float64(z - 7.5)) ^ Float64(0.5 - z))) * Float64(Float64(263.3831869810514 * exp(-7.5)) * t_4));
	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 = sqrt((pi + pi));
	t_4 = pi / sin((pi * z));
	tmp = 0.0;
	if ((t_4 * (((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+304)
		tmp = (t_4 * (t_3 * ((7.5 - z) ^ (0.5 - z)))) * ((((((-676.5203681218851 / (z - 1.0)) - -0.9999999999998099) - (-1259.1392167224028 / (z - 2.0))) - ((771.3234287776531 / (z - 3.0)) - (-176.6150291621406 / (4.0 - z)))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - ((9.984369578019572e-6 / (7.0 - z)) - (-1.5056327351493116e-7 / (8.0 - z))))) * exp((z - 7.5)));
	else
		tmp = (t_3 * (-(z - 7.5) ^ (0.5 - z))) * ((263.3831869810514 * exp(-7.5)) * t_4);
	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[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[(Pi / N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$4 * 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+304], N[(N[(t$95$4 * N[(t$95$3 * N[Power[N[(7.5 - z), $MachinePrecision], N[(0.5 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(N[(N[(-676.5203681218851 / N[(z - 1.0), $MachinePrecision]), $MachinePrecision] - -0.9999999999998099), $MachinePrecision] - N[(-1259.1392167224028 / N[(z - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(771.3234287776531 / N[(z - 3.0), $MachinePrecision]), $MachinePrecision] - N[(-176.6150291621406 / N[(4.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(12.507343278686905 / N[(z - 5.0), $MachinePrecision]), $MachinePrecision] - N[(-0.13857109526572012 / N[(6.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(9.984369578019572e-6 / N[(7.0 - z), $MachinePrecision]), $MachinePrecision] - N[(-1.5056327351493116e-7 / N[(8.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Exp[N[(z - 7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$3 * N[Power[(-N[(z - 7.5), $MachinePrecision]), N[(0.5 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(263.3831869810514 * N[Exp[-7.5], $MachinePrecision]), $MachinePrecision] * t$95$4), $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)))))) < 1.9999999999999999e304

   1. Initial program 96.4%

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

   3. Applied rewrites 98.2%

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

   5. Applied rewrites 98.2%

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

   7. Applied rewrites 98.1%

      \[\leadsto \color{blue}{\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\sqrt{\pi + \pi} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right)\right) \cdot \left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \left(\frac{771.3234287776531}{z - 3} - \frac{-176.6150291621406}{4 - z}\right)\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right)} \]

   if 1.9999999999999999e304 < (*.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 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 96.2%

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

Alternative 5: 99.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - z\right) - 1\\ t_1 := t\_0 + 7\\ t_2 := t\_1 + 0.5\\ t_3 := \sqrt{\pi + \pi}\\ t_4 := \sin \left(\pi \cdot z\right)\\ t_5 := \frac{\pi}{t\_4}\\ \mathbf{if}\;t\_5 \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {t\_2}^{\left(t\_0 + 0.5\right)}\right) \cdot e^{-t\_2}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{t\_0 + 1}\right) + \frac{-1259.1392167224028}{t\_0 + 2}\right) + \frac{771.3234287776531}{t\_0 + 3}\right) + \frac{-176.6150291621406}{t\_0 + 4}\right) + \frac{12.507343278686905}{t\_0 + 5}\right) + \frac{-0.13857109526572012}{t\_0 + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t\_1}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{t\_0 + 8}\right)\right) \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\left(\left(t\_3 \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \left(\frac{771.3234287776531}{z - 3} - \frac{-176.6150291621406}{4 - z}\right)\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right)\right) \cdot \frac{e^{z - 7.5} \cdot \pi}{t\_4}\\ \mathbf{else}:\\ \;\;\;\;\left(t\_3 \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(263.3831869810514 \cdot e^{-7.5}\right) \cdot t\_5\right)\\ \end{array} \end{array} \]

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 (sqrt (+ PI PI)))
        (t_4 (sin (* PI z)))
        (t_5 (/ PI t_4)))
   (if (<=
        (*
         t_5
         (*
          (* (* (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+304)
     (*
      (*
       (* t_3 (pow (- 7.5 z) (- 0.5 z)))
       (-
        (-
         (-
          (- (/ -676.5203681218851 (- z 1.0)) -0.9999999999998099)
          (/ -1259.1392167224028 (- z 2.0)))
         (- (/ 771.3234287776531 (- z 3.0)) (/ -176.6150291621406 (- 4.0 z))))
        (-
         (-
          (/ 12.507343278686905 (- z 5.0))
          (/ -0.13857109526572012 (- 6.0 z)))
         (-
          (/ 9.984369578019572e-6 (- 7.0 z))
          (/ -1.5056327351493116e-7 (- 8.0 z))))))
      (/ (* (exp (- z 7.5)) PI) t_4))
     (*
      (* t_3 (pow (- (- z 7.5)) (- 0.5 z)))
      (* (* 263.3831869810514 (exp -7.5)) t_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 = sqrt((((double) M_PI) + ((double) M_PI)));
	double t_4 = sin((((double) M_PI) * z));
	double t_5 = ((double) M_PI) / t_4;
	double tmp;
	if ((t_5 * (((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+304) {
		tmp = ((t_3 * pow((7.5 - z), (0.5 - z))) * (((((-676.5203681218851 / (z - 1.0)) - -0.9999999999998099) - (-1259.1392167224028 / (z - 2.0))) - ((771.3234287776531 / (z - 3.0)) - (-176.6150291621406 / (4.0 - z)))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - ((9.984369578019572e-6 / (7.0 - z)) - (-1.5056327351493116e-7 / (8.0 - z)))))) * ((exp((z - 7.5)) * ((double) M_PI)) / t_4);
	} else {
		tmp = (t_3 * pow(-(z - 7.5), (0.5 - z))) * ((263.3831869810514 * exp(-7.5)) * t_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.sqrt((Math.PI + Math.PI));
	double t_4 = Math.sin((Math.PI * z));
	double t_5 = Math.PI / t_4;
	double tmp;
	if ((t_5 * (((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+304) {
		tmp = ((t_3 * Math.pow((7.5 - z), (0.5 - z))) * (((((-676.5203681218851 / (z - 1.0)) - -0.9999999999998099) - (-1259.1392167224028 / (z - 2.0))) - ((771.3234287776531 / (z - 3.0)) - (-176.6150291621406 / (4.0 - z)))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - ((9.984369578019572e-6 / (7.0 - z)) - (-1.5056327351493116e-7 / (8.0 - z)))))) * ((Math.exp((z - 7.5)) * Math.PI) / t_4);
	} else {
		tmp = (t_3 * Math.pow(-(z - 7.5), (0.5 - z))) * ((263.3831869810514 * Math.exp(-7.5)) * t_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.sqrt((math.pi + math.pi))
	t_4 = math.sin((math.pi * z))
	t_5 = math.pi / t_4
	tmp = 0
	if (t_5 * (((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+304:
		tmp = ((t_3 * math.pow((7.5 - z), (0.5 - z))) * (((((-676.5203681218851 / (z - 1.0)) - -0.9999999999998099) - (-1259.1392167224028 / (z - 2.0))) - ((771.3234287776531 / (z - 3.0)) - (-176.6150291621406 / (4.0 - z)))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - ((9.984369578019572e-6 / (7.0 - z)) - (-1.5056327351493116e-7 / (8.0 - z)))))) * ((math.exp((z - 7.5)) * math.pi) / t_4)
	else:
		tmp = (t_3 * math.pow(-(z - 7.5), (0.5 - z))) * ((263.3831869810514 * math.exp(-7.5)) * t_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 = sqrt(Float64(pi + pi))
	t_4 = sin(Float64(pi * z))
	t_5 = Float64(pi / t_4)
	tmp = 0.0
	if (Float64(t_5 * 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+304)
		tmp = Float64(Float64(Float64(t_3 * (Float64(7.5 - z) ^ Float64(0.5 - z))) * Float64(Float64(Float64(Float64(Float64(-676.5203681218851 / Float64(z - 1.0)) - -0.9999999999998099) - Float64(-1259.1392167224028 / Float64(z - 2.0))) - Float64(Float64(771.3234287776531 / Float64(z - 3.0)) - Float64(-176.6150291621406 / Float64(4.0 - z)))) - Float64(Float64(Float64(12.507343278686905 / Float64(z - 5.0)) - Float64(-0.13857109526572012 / Float64(6.0 - z))) - Float64(Float64(9.984369578019572e-6 / Float64(7.0 - z)) - Float64(-1.5056327351493116e-7 / Float64(8.0 - z)))))) * Float64(Float64(exp(Float64(z - 7.5)) * pi) / t_4));
	else
		tmp = Float64(Float64(t_3 * (Float64(-Float64(z - 7.5)) ^ Float64(0.5 - z))) * Float64(Float64(263.3831869810514 * exp(-7.5)) * t_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 = sqrt((pi + pi));
	t_4 = sin((pi * z));
	t_5 = pi / t_4;
	tmp = 0.0;
	if ((t_5 * (((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+304)
		tmp = ((t_3 * ((7.5 - z) ^ (0.5 - z))) * (((((-676.5203681218851 / (z - 1.0)) - -0.9999999999998099) - (-1259.1392167224028 / (z - 2.0))) - ((771.3234287776531 / (z - 3.0)) - (-176.6150291621406 / (4.0 - z)))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - ((9.984369578019572e-6 / (7.0 - z)) - (-1.5056327351493116e-7 / (8.0 - z)))))) * ((exp((z - 7.5)) * pi) / t_4);
	else
		tmp = (t_3 * (-(z - 7.5) ^ (0.5 - z))) * ((263.3831869810514 * exp(-7.5)) * t_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[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$5 = N[(Pi / t$95$4), $MachinePrecision]}, If[LessEqual[N[(t$95$5 * 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+304], N[(N[(N[(t$95$3 * N[Power[N[(7.5 - z), $MachinePrecision], N[(0.5 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(N[(-676.5203681218851 / N[(z - 1.0), $MachinePrecision]), $MachinePrecision] - -0.9999999999998099), $MachinePrecision] - N[(-1259.1392167224028 / N[(z - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(771.3234287776531 / N[(z - 3.0), $MachinePrecision]), $MachinePrecision] - N[(-176.6150291621406 / N[(4.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(12.507343278686905 / N[(z - 5.0), $MachinePrecision]), $MachinePrecision] - N[(-0.13857109526572012 / N[(6.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(9.984369578019572e-6 / N[(7.0 - z), $MachinePrecision]), $MachinePrecision] - N[(-1.5056327351493116e-7 / N[(8.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[Exp[N[(z - 7.5), $MachinePrecision]], $MachinePrecision] * Pi), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$3 * N[Power[(-N[(z - 7.5), $MachinePrecision]), N[(0.5 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(263.3831869810514 * N[Exp[-7.5], $MachinePrecision]), $MachinePrecision] * t$95$5), $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)))))) < 1.9999999999999999e304

   1. Initial program 96.4%

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

   3. Applied rewrites 98.2%

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

   5. Applied rewrites 98.2%

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

   7. Applied rewrites 98.3%

      \[\leadsto \color{blue}{\left(\left(\sqrt{\pi + \pi} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \left(\frac{771.3234287776531}{z - 3} - \frac{-176.6150291621406}{4 - z}\right)\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right)\right) \cdot \frac{e^{z - 7.5} \cdot \pi}{\sin \left(\pi \cdot z\right)}} \]

   if 1.9999999999999999e304 < (*.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 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 96.2%

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

Alternative 6: 99.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - z\right) - 1\\ t_1 := \frac{\pi}{\sin \left(\pi \cdot z\right)}\\ t_2 := t\_0 + 7\\ t_3 := t\_2 + 0.5\\ t_4 := \sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\\ \mathbf{if}\;t\_1 \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {t\_3}^{\left(t\_0 + 0.5\right)}\right) \cdot e^{-t\_3}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{t\_0 + 1}\right) + \frac{-1259.1392167224028}{t\_0 + 2}\right) + \frac{771.3234287776531}{t\_0 + 3}\right) + \frac{-176.6150291621406}{t\_0 + 4}\right) + \frac{12.507343278686905}{t\_0 + 5}\right) + \frac{-0.13857109526572012}{t\_0 + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t\_2}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{t\_0 + 8}\right)\right) \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_4 \cdot \left(\left(\left(\left(\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(1.4451589203350195 \cdot 10^{-6} + z \cdot \left(2.0611519559804982 \cdot 10^{-7} + 2.9403018100637997 \cdot 10^{-8} \cdot z\right)\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4 \cdot \left(\left(263.3831869810514 \cdot e^{-7.5}\right) \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (- (- 1.0 z) 1.0))
        (t_1 (/ PI (sin (* PI z))))
        (t_2 (+ t_0 7.0))
        (t_3 (+ t_2 0.5))
        (t_4 (* (sqrt (+ PI PI)) (pow (- (- z 7.5)) (- 0.5 z)))))
   (if (<=
        (*
         t_1
         (*
          (* (* (sqrt (* PI 2.0)) (pow t_3 (+ t_0 0.5))) (exp (- t_3)))
          (+
           (+
            (+
             (+
              (+
               (+
                (+
                 (+ 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_2))
           (/ 1.5056327351493116e-7 (+ t_0 8.0)))))
        2e+304)
     (*
      t_4
      (*
       (*
        (-
         (-
          (-
           (/ -771.3234287776531 (- z 3.0))
           (-
            (-
             (/ -1259.1392167224028 (- z 2.0))
             (/ -676.5203681218851 (- z 1.0)))
            0.9999999999998099))
          (/ 176.6150291621406 (- 4.0 z)))
         (-
          (-
           (/ 12.507343278686905 (- z 5.0))
           (/ -0.13857109526572012 (- 6.0 z)))
          (+
           1.4451589203350195e-6
           (* z (+ 2.0611519559804982e-7 (* 2.9403018100637997e-8 z))))))
        (exp (- z 7.5)))
       t_1))
     (* t_4 (* (* 263.3831869810514 (exp -7.5)) t_1)))))

C

double code(double z) {
	double t_0 = (1.0 - z) - 1.0;
	double t_1 = ((double) M_PI) / sin((((double) M_PI) * z));
	double t_2 = t_0 + 7.0;
	double t_3 = t_2 + 0.5;
	double t_4 = sqrt((((double) M_PI) + ((double) M_PI))) * pow(-(z - 7.5), (0.5 - z));
	double tmp;
	if ((t_1 * (((sqrt((((double) M_PI) * 2.0)) * pow(t_3, (t_0 + 0.5))) * exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304) {
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - (1.4451589203350195e-6 + (z * (2.0611519559804982e-7 + (2.9403018100637997e-8 * z)))))) * exp((z - 7.5))) * t_1);
	} else {
		tmp = t_4 * ((263.3831869810514 * exp(-7.5)) * t_1);
	}
	return tmp;
}

Java

public static double code(double z) {
	double t_0 = (1.0 - z) - 1.0;
	double t_1 = Math.PI / Math.sin((Math.PI * z));
	double t_2 = t_0 + 7.0;
	double t_3 = t_2 + 0.5;
	double t_4 = Math.sqrt((Math.PI + Math.PI)) * Math.pow(-(z - 7.5), (0.5 - z));
	double tmp;
	if ((t_1 * (((Math.sqrt((Math.PI * 2.0)) * Math.pow(t_3, (t_0 + 0.5))) * Math.exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304) {
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - (1.4451589203350195e-6 + (z * (2.0611519559804982e-7 + (2.9403018100637997e-8 * z)))))) * Math.exp((z - 7.5))) * t_1);
	} else {
		tmp = t_4 * ((263.3831869810514 * Math.exp(-7.5)) * t_1);
	}
	return tmp;
}

Python

def code(z):
	t_0 = (1.0 - z) - 1.0
	t_1 = math.pi / math.sin((math.pi * z))
	t_2 = t_0 + 7.0
	t_3 = t_2 + 0.5
	t_4 = math.sqrt((math.pi + math.pi)) * math.pow(-(z - 7.5), (0.5 - z))
	tmp = 0
	if (t_1 * (((math.sqrt((math.pi * 2.0)) * math.pow(t_3, (t_0 + 0.5))) * math.exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304:
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - (1.4451589203350195e-6 + (z * (2.0611519559804982e-7 + (2.9403018100637997e-8 * z)))))) * math.exp((z - 7.5))) * t_1)
	else:
		tmp = t_4 * ((263.3831869810514 * math.exp(-7.5)) * t_1)
	return tmp

Julia

function code(z)
	t_0 = Float64(Float64(1.0 - z) - 1.0)
	t_1 = Float64(pi / sin(Float64(pi * z)))
	t_2 = Float64(t_0 + 7.0)
	t_3 = Float64(t_2 + 0.5)
	t_4 = Float64(sqrt(Float64(pi + pi)) * (Float64(-Float64(z - 7.5)) ^ Float64(0.5 - z)))
	tmp = 0.0
	if (Float64(t_1 * Float64(Float64(Float64(sqrt(Float64(pi * 2.0)) * (t_3 ^ Float64(t_0 + 0.5))) * exp(Float64(-t_3))) * 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_2)) + Float64(1.5056327351493116e-7 / Float64(t_0 + 8.0))))) <= 2e+304)
		tmp = Float64(t_4 * Float64(Float64(Float64(Float64(Float64(Float64(-771.3234287776531 / Float64(z - 3.0)) - Float64(Float64(Float64(-1259.1392167224028 / Float64(z - 2.0)) - Float64(-676.5203681218851 / Float64(z - 1.0))) - 0.9999999999998099)) - Float64(176.6150291621406 / Float64(4.0 - z))) - Float64(Float64(Float64(12.507343278686905 / Float64(z - 5.0)) - Float64(-0.13857109526572012 / Float64(6.0 - z))) - Float64(1.4451589203350195e-6 + Float64(z * Float64(2.0611519559804982e-7 + Float64(2.9403018100637997e-8 * z)))))) * exp(Float64(z - 7.5))) * t_1));
	else
		tmp = Float64(t_4 * Float64(Float64(263.3831869810514 * exp(-7.5)) * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z)
	t_0 = (1.0 - z) - 1.0;
	t_1 = pi / sin((pi * z));
	t_2 = t_0 + 7.0;
	t_3 = t_2 + 0.5;
	t_4 = sqrt((pi + pi)) * (-(z - 7.5) ^ (0.5 - z));
	tmp = 0.0;
	if ((t_1 * (((sqrt((pi * 2.0)) * (t_3 ^ (t_0 + 0.5))) * exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304)
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - (1.4451589203350195e-6 + (z * (2.0611519559804982e-7 + (2.9403018100637997e-8 * z)))))) * exp((z - 7.5))) * t_1);
	else
		tmp = t_4 * ((263.3831869810514 * exp(-7.5)) * t_1);
	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[(Pi / N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + 7.0), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + 0.5), $MachinePrecision]}, Block[{t$95$4 = N[(N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision] * N[Power[(-N[(z - 7.5), $MachinePrecision]), N[(0.5 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 * N[(N[(N[(N[Sqrt[N[(Pi * 2.0), $MachinePrecision]], $MachinePrecision] * N[Power[t$95$3, N[(t$95$0 + 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Exp[(-t$95$3)], $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$2), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(t$95$0 + 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e+304], N[(t$95$4 * N[(N[(N[(N[(N[(N[(-771.3234287776531 / N[(z - 3.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(-1259.1392167224028 / N[(z - 2.0), $MachinePrecision]), $MachinePrecision] - N[(-676.5203681218851 / N[(z - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 0.9999999999998099), $MachinePrecision]), $MachinePrecision] - N[(176.6150291621406 / N[(4.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(12.507343278686905 / N[(z - 5.0), $MachinePrecision]), $MachinePrecision] - N[(-0.13857109526572012 / N[(6.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(1.4451589203350195e-6 + N[(z * N[(2.0611519559804982e-7 + N[(2.9403018100637997e-8 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Exp[N[(z - 7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$4 * N[(N[(263.3831869810514 * N[Exp[-7.5], $MachinePrecision]), $MachinePrecision] * t$95$1), $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)))))) < 1.9999999999999999e304

   1. Initial program 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   7. Applied rewrites 98.3%

      \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\color{blue}{\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right)} - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - \frac{15}{2}\right)\right)}^{\left(\frac{1}{2} - z\right)}\right) \cdot \left(\left(\left(\left(\left(\frac{\frac{-7713234287776531}{10000000000000}}{z - 3} - \left(\left(\frac{\frac{-3147848041806007}{2500000000000}}{z - 2} - \frac{\frac{-6765203681218851}{10000000000000}}{z - 1}\right) - \frac{9999999999998099}{10000000000000000}\right)\right) - \frac{\frac{883075145810703}{5000000000000}}{4 - z}\right) - \left(\left(\frac{\frac{2501468655737381}{200000000000000}}{z - 5} - \frac{\frac{-3464277381643003}{25000000000000000}}{6 - z}\right) - \color{blue}{\left(\frac{2023222488469027353}{1400000000000000000000000} + z \cdot \left(\frac{16159431334887105871}{78400000000000000000000000} + \frac{129091010669041056297}{4390400000000000000000000000} \cdot z\right)\right)}\right)\right) \cdot e^{z - \frac{15}{2}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   10. Applied rewrites 98.1%

       \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \color{blue}{\left(1.4451589203350195 \cdot 10^{-6} + z \cdot \left(2.0611519559804982 \cdot 10^{-7} + 2.9403018100637997 \cdot 10^{-8} \cdot z\right)\right)}\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   if 1.9999999999999999e304 < (*.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 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 96.2%

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

Alternative 7: 99.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\pi}{\sin \left(\pi \cdot z\right)}\\ t_1 := \left(1 - z\right) - 1\\ t_2 := t\_1 + 7\\ t_3 := t\_2 + 0.5\\ t_4 := \sqrt{\pi + \pi}\\ \mathbf{if}\;t\_0 \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {t\_3}^{\left(t\_1 + 0.5\right)}\right) \cdot e^{-t\_3}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{t\_1 + 1}\right) + \frac{-1259.1392167224028}{t\_1 + 2}\right) + \frac{771.3234287776531}{t\_1 + 3}\right) + \frac{-176.6150291621406}{t\_1 + 4}\right) + \frac{12.507343278686905}{t\_1 + 5}\right) + \frac{-0.13857109526572012}{t\_1 + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t\_2}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{t\_1 + 8}\right)\right) \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\left(t\_4 \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \left(\frac{771.3234287776531}{z - 3} - \frac{176.6150291621406}{z - 4}\right)\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \mathsf{fma}\left(\mathsf{fma}\left(z, 2.9403018100637997 \cdot 10^{-8}, 2.0611519559804982 \cdot 10^{-7}\right), z, 1.4451589203350195 \cdot 10^{-6}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t\_4 \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(263.3831869810514 \cdot e^{-7.5}\right) \cdot t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (/ PI (sin (* PI z))))
        (t_1 (- (- 1.0 z) 1.0))
        (t_2 (+ t_1 7.0))
        (t_3 (+ t_2 0.5))
        (t_4 (sqrt (+ PI PI))))
   (if (<=
        (*
         t_0
         (*
          (* (* (sqrt (* PI 2.0)) (pow t_3 (+ t_1 0.5))) (exp (- t_3)))
          (+
           (+
            (+
             (+
              (+
               (+
                (+
                 (+ 0.9999999999998099 (/ 676.5203681218851 (+ t_1 1.0)))
                 (/ -1259.1392167224028 (+ t_1 2.0)))
                (/ 771.3234287776531 (+ t_1 3.0)))
               (/ -176.6150291621406 (+ t_1 4.0)))
              (/ 12.507343278686905 (+ t_1 5.0)))
             (/ -0.13857109526572012 (+ t_1 6.0)))
            (/ 9.984369578019572e-6 t_2))
           (/ 1.5056327351493116e-7 (+ t_1 8.0)))))
        2e+304)
     (*
      (* t_4 (pow (- 7.5 z) (- 0.5 z)))
      (*
       (*
        (-
         (-
          (-
           (- (/ -676.5203681218851 (- z 1.0)) -0.9999999999998099)
           (/ -1259.1392167224028 (- z 2.0)))
          (- (/ 771.3234287776531 (- z 3.0)) (/ 176.6150291621406 (- z 4.0))))
         (-
          (-
           (/ 12.507343278686905 (- z 5.0))
           (/ -0.13857109526572012 (- 6.0 z)))
          (fma
           (fma z 2.9403018100637997e-8 2.0611519559804982e-7)
           z
           1.4451589203350195e-6)))
        (exp (- z 7.5)))
       t_0))
     (*
      (* t_4 (pow (- (- z 7.5)) (- 0.5 z)))
      (* (* 263.3831869810514 (exp -7.5)) t_0)))))

C

double code(double z) {
	double t_0 = ((double) M_PI) / sin((((double) M_PI) * z));
	double t_1 = (1.0 - z) - 1.0;
	double t_2 = t_1 + 7.0;
	double t_3 = t_2 + 0.5;
	double t_4 = sqrt((((double) M_PI) + ((double) M_PI)));
	double tmp;
	if ((t_0 * (((sqrt((((double) M_PI) * 2.0)) * pow(t_3, (t_1 + 0.5))) * exp(-t_3)) * ((((((((0.9999999999998099 + (676.5203681218851 / (t_1 + 1.0))) + (-1259.1392167224028 / (t_1 + 2.0))) + (771.3234287776531 / (t_1 + 3.0))) + (-176.6150291621406 / (t_1 + 4.0))) + (12.507343278686905 / (t_1 + 5.0))) + (-0.13857109526572012 / (t_1 + 6.0))) + (9.984369578019572e-6 / t_2)) + (1.5056327351493116e-7 / (t_1 + 8.0))))) <= 2e+304) {
		tmp = (t_4 * pow((7.5 - z), (0.5 - z))) * (((((((-676.5203681218851 / (z - 1.0)) - -0.9999999999998099) - (-1259.1392167224028 / (z - 2.0))) - ((771.3234287776531 / (z - 3.0)) - (176.6150291621406 / (z - 4.0)))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - fma(fma(z, 2.9403018100637997e-8, 2.0611519559804982e-7), z, 1.4451589203350195e-6))) * exp((z - 7.5))) * t_0);
	} else {
		tmp = (t_4 * pow(-(z - 7.5), (0.5 - z))) * ((263.3831869810514 * exp(-7.5)) * t_0);
	}
	return tmp;
}

Julia

function code(z)
	t_0 = Float64(pi / sin(Float64(pi * z)))
	t_1 = Float64(Float64(1.0 - z) - 1.0)
	t_2 = Float64(t_1 + 7.0)
	t_3 = Float64(t_2 + 0.5)
	t_4 = sqrt(Float64(pi + pi))
	tmp = 0.0
	if (Float64(t_0 * Float64(Float64(Float64(sqrt(Float64(pi * 2.0)) * (t_3 ^ Float64(t_1 + 0.5))) * exp(Float64(-t_3))) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(0.9999999999998099 + Float64(676.5203681218851 / Float64(t_1 + 1.0))) + Float64(-1259.1392167224028 / Float64(t_1 + 2.0))) + Float64(771.3234287776531 / Float64(t_1 + 3.0))) + Float64(-176.6150291621406 / Float64(t_1 + 4.0))) + Float64(12.507343278686905 / Float64(t_1 + 5.0))) + Float64(-0.13857109526572012 / Float64(t_1 + 6.0))) + Float64(9.984369578019572e-6 / t_2)) + Float64(1.5056327351493116e-7 / Float64(t_1 + 8.0))))) <= 2e+304)
		tmp = Float64(Float64(t_4 * (Float64(7.5 - z) ^ Float64(0.5 - z))) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(-676.5203681218851 / Float64(z - 1.0)) - -0.9999999999998099) - Float64(-1259.1392167224028 / Float64(z - 2.0))) - Float64(Float64(771.3234287776531 / Float64(z - 3.0)) - Float64(176.6150291621406 / Float64(z - 4.0)))) - Float64(Float64(Float64(12.507343278686905 / Float64(z - 5.0)) - Float64(-0.13857109526572012 / Float64(6.0 - z))) - fma(fma(z, 2.9403018100637997e-8, 2.0611519559804982e-7), z, 1.4451589203350195e-6))) * exp(Float64(z - 7.5))) * t_0));
	else
		tmp = Float64(Float64(t_4 * (Float64(-Float64(z - 7.5)) ^ Float64(0.5 - z))) * Float64(Float64(263.3831869810514 * exp(-7.5)) * t_0));
	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] - 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + 7.0), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + 0.5), $MachinePrecision]}, Block[{t$95$4 = N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(t$95$0 * N[(N[(N[(N[Sqrt[N[(Pi * 2.0), $MachinePrecision]], $MachinePrecision] * N[Power[t$95$3, N[(t$95$1 + 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Exp[(-t$95$3)], $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(0.9999999999998099 + N[(676.5203681218851 / N[(t$95$1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1259.1392167224028 / N[(t$95$1 + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(771.3234287776531 / N[(t$95$1 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-176.6150291621406 / N[(t$95$1 + 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(12.507343278686905 / N[(t$95$1 + 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.13857109526572012 / N[(t$95$1 + 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(9.984369578019572e-6 / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(t$95$1 + 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e+304], N[(N[(t$95$4 * N[Power[N[(7.5 - z), $MachinePrecision], N[(0.5 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(-676.5203681218851 / N[(z - 1.0), $MachinePrecision]), $MachinePrecision] - -0.9999999999998099), $MachinePrecision] - N[(-1259.1392167224028 / N[(z - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(771.3234287776531 / N[(z - 3.0), $MachinePrecision]), $MachinePrecision] - N[(176.6150291621406 / N[(z - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(12.507343278686905 / N[(z - 5.0), $MachinePrecision]), $MachinePrecision] - N[(-0.13857109526572012 / N[(6.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 2.9403018100637997e-8 + 2.0611519559804982e-7), $MachinePrecision] * z + 1.4451589203350195e-6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Exp[N[(z - 7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$4 * N[Power[(-N[(z - 7.5), $MachinePrecision]), N[(0.5 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(263.3831869810514 * N[Exp[-7.5], $MachinePrecision]), $MachinePrecision] * t$95$0), $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)))))) < 1.9999999999999999e304

   1. Initial program 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - \frac{15}{2}\right)\right)}^{\left(\frac{1}{2} - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{\frac{-6765203681218851}{10000000000000}}{z - 1} - \frac{-9999999999998099}{10000000000000000}\right) - \frac{\frac{-3147848041806007}{2500000000000}}{z - 2}\right) - \frac{\frac{7713234287776531}{10000000000000}}{z - 3}\right) - \frac{\frac{883075145810703}{5000000000000}}{4 - z}\right) - \left(\left(\frac{\frac{2501468655737381}{200000000000000}}{z - 5} - \frac{\frac{-3464277381643003}{25000000000000000}}{6 - z}\right) - \color{blue}{\left(\frac{2023222488469027353}{1400000000000000000000000} + z \cdot \left(\frac{16159431334887105871}{78400000000000000000000000} + \frac{129091010669041056297}{4390400000000000000000000000} \cdot z\right)\right)}\right)\right) \cdot e^{z - \frac{15}{2}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   8. Applied rewrites 97.3%

      \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \color{blue}{\left(1.4451589203350195 \cdot 10^{-6} + z \cdot \left(2.0611519559804982 \cdot 10^{-7} + 2.9403018100637997 \cdot 10^{-8} \cdot z\right)\right)}\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   10. Applied rewrites 98.1%

       \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \left(\frac{771.3234287776531}{z - 3} - \frac{176.6150291621406}{z - 4}\right)\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \mathsf{fma}\left(\mathsf{fma}\left(z, 2.9403018100637997 \cdot 10^{-8}, 2.0611519559804982 \cdot 10^{-7}\right), z, 1.4451589203350195 \cdot 10^{-6}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   if 1.9999999999999999e304 < (*.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 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 96.2%

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

Alternative 8: 99.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - z\right) - 1\\ t_1 := \frac{\pi}{\sin \left(\pi \cdot z\right)}\\ t_2 := t\_0 + 7\\ t_3 := t\_2 + 0.5\\ t_4 := \sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\\ \mathbf{if}\;t\_1 \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {t\_3}^{\left(t\_0 + 0.5\right)}\right) \cdot e^{-t\_3}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{t\_0 + 1}\right) + \frac{-1259.1392167224028}{t\_0 + 2}\right) + \frac{771.3234287776531}{t\_0 + 3}\right) + \frac{-176.6150291621406}{t\_0 + 4}\right) + \frac{12.507343278686905}{t\_0 + 5}\right) + \frac{-0.13857109526572012}{t\_0 + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t\_2}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{t\_0 + 8}\right)\right) \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_4 \cdot \left(\left(\left(\left(\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(1.4451589203350195 \cdot 10^{-6} + 2.0611519559804982 \cdot 10^{-7} \cdot z\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4 \cdot \left(\left(263.3831869810514 \cdot e^{-7.5}\right) \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (- (- 1.0 z) 1.0))
        (t_1 (/ PI (sin (* PI z))))
        (t_2 (+ t_0 7.0))
        (t_3 (+ t_2 0.5))
        (t_4 (* (sqrt (+ PI PI)) (pow (- (- z 7.5)) (- 0.5 z)))))
   (if (<=
        (*
         t_1
         (*
          (* (* (sqrt (* PI 2.0)) (pow t_3 (+ t_0 0.5))) (exp (- t_3)))
          (+
           (+
            (+
             (+
              (+
               (+
                (+
                 (+ 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_2))
           (/ 1.5056327351493116e-7 (+ t_0 8.0)))))
        2e+304)
     (*
      t_4
      (*
       (*
        (-
         (-
          (-
           (/ -771.3234287776531 (- z 3.0))
           (-
            (-
             (/ -1259.1392167224028 (- z 2.0))
             (/ -676.5203681218851 (- z 1.0)))
            0.9999999999998099))
          (/ 176.6150291621406 (- 4.0 z)))
         (-
          (-
           (/ 12.507343278686905 (- z 5.0))
           (/ -0.13857109526572012 (- 6.0 z)))
          (+ 1.4451589203350195e-6 (* 2.0611519559804982e-7 z))))
        (exp (- z 7.5)))
       t_1))
     (* t_4 (* (* 263.3831869810514 (exp -7.5)) t_1)))))

C

double code(double z) {
	double t_0 = (1.0 - z) - 1.0;
	double t_1 = ((double) M_PI) / sin((((double) M_PI) * z));
	double t_2 = t_0 + 7.0;
	double t_3 = t_2 + 0.5;
	double t_4 = sqrt((((double) M_PI) + ((double) M_PI))) * pow(-(z - 7.5), (0.5 - z));
	double tmp;
	if ((t_1 * (((sqrt((((double) M_PI) * 2.0)) * pow(t_3, (t_0 + 0.5))) * exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304) {
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - (1.4451589203350195e-6 + (2.0611519559804982e-7 * z)))) * exp((z - 7.5))) * t_1);
	} else {
		tmp = t_4 * ((263.3831869810514 * exp(-7.5)) * t_1);
	}
	return tmp;
}

Java

public static double code(double z) {
	double t_0 = (1.0 - z) - 1.0;
	double t_1 = Math.PI / Math.sin((Math.PI * z));
	double t_2 = t_0 + 7.0;
	double t_3 = t_2 + 0.5;
	double t_4 = Math.sqrt((Math.PI + Math.PI)) * Math.pow(-(z - 7.5), (0.5 - z));
	double tmp;
	if ((t_1 * (((Math.sqrt((Math.PI * 2.0)) * Math.pow(t_3, (t_0 + 0.5))) * Math.exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304) {
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - (1.4451589203350195e-6 + (2.0611519559804982e-7 * z)))) * Math.exp((z - 7.5))) * t_1);
	} else {
		tmp = t_4 * ((263.3831869810514 * Math.exp(-7.5)) * t_1);
	}
	return tmp;
}

Python

def code(z):
	t_0 = (1.0 - z) - 1.0
	t_1 = math.pi / math.sin((math.pi * z))
	t_2 = t_0 + 7.0
	t_3 = t_2 + 0.5
	t_4 = math.sqrt((math.pi + math.pi)) * math.pow(-(z - 7.5), (0.5 - z))
	tmp = 0
	if (t_1 * (((math.sqrt((math.pi * 2.0)) * math.pow(t_3, (t_0 + 0.5))) * math.exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304:
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - (1.4451589203350195e-6 + (2.0611519559804982e-7 * z)))) * math.exp((z - 7.5))) * t_1)
	else:
		tmp = t_4 * ((263.3831869810514 * math.exp(-7.5)) * t_1)
	return tmp

Julia

function code(z)
	t_0 = Float64(Float64(1.0 - z) - 1.0)
	t_1 = Float64(pi / sin(Float64(pi * z)))
	t_2 = Float64(t_0 + 7.0)
	t_3 = Float64(t_2 + 0.5)
	t_4 = Float64(sqrt(Float64(pi + pi)) * (Float64(-Float64(z - 7.5)) ^ Float64(0.5 - z)))
	tmp = 0.0
	if (Float64(t_1 * Float64(Float64(Float64(sqrt(Float64(pi * 2.0)) * (t_3 ^ Float64(t_0 + 0.5))) * exp(Float64(-t_3))) * 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_2)) + Float64(1.5056327351493116e-7 / Float64(t_0 + 8.0))))) <= 2e+304)
		tmp = Float64(t_4 * Float64(Float64(Float64(Float64(Float64(Float64(-771.3234287776531 / Float64(z - 3.0)) - Float64(Float64(Float64(-1259.1392167224028 / Float64(z - 2.0)) - Float64(-676.5203681218851 / Float64(z - 1.0))) - 0.9999999999998099)) - Float64(176.6150291621406 / Float64(4.0 - z))) - Float64(Float64(Float64(12.507343278686905 / Float64(z - 5.0)) - Float64(-0.13857109526572012 / Float64(6.0 - z))) - Float64(1.4451589203350195e-6 + Float64(2.0611519559804982e-7 * z)))) * exp(Float64(z - 7.5))) * t_1));
	else
		tmp = Float64(t_4 * Float64(Float64(263.3831869810514 * exp(-7.5)) * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z)
	t_0 = (1.0 - z) - 1.0;
	t_1 = pi / sin((pi * z));
	t_2 = t_0 + 7.0;
	t_3 = t_2 + 0.5;
	t_4 = sqrt((pi + pi)) * (-(z - 7.5) ^ (0.5 - z));
	tmp = 0.0;
	if ((t_1 * (((sqrt((pi * 2.0)) * (t_3 ^ (t_0 + 0.5))) * exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304)
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - (1.4451589203350195e-6 + (2.0611519559804982e-7 * z)))) * exp((z - 7.5))) * t_1);
	else
		tmp = t_4 * ((263.3831869810514 * exp(-7.5)) * t_1);
	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[(Pi / N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + 7.0), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + 0.5), $MachinePrecision]}, Block[{t$95$4 = N[(N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision] * N[Power[(-N[(z - 7.5), $MachinePrecision]), N[(0.5 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 * N[(N[(N[(N[Sqrt[N[(Pi * 2.0), $MachinePrecision]], $MachinePrecision] * N[Power[t$95$3, N[(t$95$0 + 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Exp[(-t$95$3)], $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$2), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(t$95$0 + 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e+304], N[(t$95$4 * N[(N[(N[(N[(N[(N[(-771.3234287776531 / N[(z - 3.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(-1259.1392167224028 / N[(z - 2.0), $MachinePrecision]), $MachinePrecision] - N[(-676.5203681218851 / N[(z - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 0.9999999999998099), $MachinePrecision]), $MachinePrecision] - N[(176.6150291621406 / N[(4.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(12.507343278686905 / N[(z - 5.0), $MachinePrecision]), $MachinePrecision] - N[(-0.13857109526572012 / N[(6.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(1.4451589203350195e-6 + N[(2.0611519559804982e-7 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Exp[N[(z - 7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$4 * N[(N[(263.3831869810514 * N[Exp[-7.5], $MachinePrecision]), $MachinePrecision] * t$95$1), $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)))))) < 1.9999999999999999e304

   1. Initial program 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   7. Applied rewrites 98.3%

      \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\color{blue}{\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right)} - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - \frac{15}{2}\right)\right)}^{\left(\frac{1}{2} - z\right)}\right) \cdot \left(\left(\left(\left(\left(\frac{\frac{-7713234287776531}{10000000000000}}{z - 3} - \left(\left(\frac{\frac{-3147848041806007}{2500000000000}}{z - 2} - \frac{\frac{-6765203681218851}{10000000000000}}{z - 1}\right) - \frac{9999999999998099}{10000000000000000}\right)\right) - \frac{\frac{883075145810703}{5000000000000}}{4 - z}\right) - \left(\left(\frac{\frac{2501468655737381}{200000000000000}}{z - 5} - \frac{\frac{-3464277381643003}{25000000000000000}}{6 - z}\right) - \color{blue}{\left(\frac{2023222488469027353}{1400000000000000000000000} + \frac{16159431334887105871}{78400000000000000000000000} \cdot z\right)}\right)\right) \cdot e^{z - \frac{15}{2}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   10. Applied rewrites 98.0%

       \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \color{blue}{\left(1.4451589203350195 \cdot 10^{-6} + 2.0611519559804982 \cdot 10^{-7} \cdot z\right)}\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   if 1.9999999999999999e304 < (*.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 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 96.2%

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

Alternative 9: 98.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - z\right) - 1\\ t_1 := \frac{\pi}{\sin \left(\pi \cdot z\right)}\\ t_2 := t\_0 + 7\\ t_3 := t\_2 + 0.5\\ t_4 := \sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\\ \mathbf{if}\;t\_1 \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {t\_3}^{\left(t\_0 + 0.5\right)}\right) \cdot e^{-t\_3}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{t\_0 + 1}\right) + \frac{-1259.1392167224028}{t\_0 + 2}\right) + \frac{771.3234287776531}{t\_0 + 3}\right) + \frac{-176.6150291621406}{t\_0 + 4}\right) + \frac{12.507343278686905}{t\_0 + 5}\right) + \frac{-0.13857109526572012}{t\_0 + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t\_2}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{t\_0 + 8}\right)\right) \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_4 \cdot \left(\left(\left(\left(\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - 1.4451589203350195 \cdot 10^{-6}\right)\right) \cdot e^{z - 7.5}\right) \cdot t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4 \cdot \left(\left(263.3831869810514 \cdot e^{-7.5}\right) \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (- (- 1.0 z) 1.0))
        (t_1 (/ PI (sin (* PI z))))
        (t_2 (+ t_0 7.0))
        (t_3 (+ t_2 0.5))
        (t_4 (* (sqrt (+ PI PI)) (pow (- (- z 7.5)) (- 0.5 z)))))
   (if (<=
        (*
         t_1
         (*
          (* (* (sqrt (* PI 2.0)) (pow t_3 (+ t_0 0.5))) (exp (- t_3)))
          (+
           (+
            (+
             (+
              (+
               (+
                (+
                 (+ 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_2))
           (/ 1.5056327351493116e-7 (+ t_0 8.0)))))
        2e+304)
     (*
      t_4
      (*
       (*
        (-
         (-
          (-
           (/ -771.3234287776531 (- z 3.0))
           (-
            (-
             (/ -1259.1392167224028 (- z 2.0))
             (/ -676.5203681218851 (- z 1.0)))
            0.9999999999998099))
          (/ 176.6150291621406 (- 4.0 z)))
         (-
          (-
           (/ 12.507343278686905 (- z 5.0))
           (/ -0.13857109526572012 (- 6.0 z)))
          1.4451589203350195e-6))
        (exp (- z 7.5)))
       t_1))
     (* t_4 (* (* 263.3831869810514 (exp -7.5)) t_1)))))

C

double code(double z) {
	double t_0 = (1.0 - z) - 1.0;
	double t_1 = ((double) M_PI) / sin((((double) M_PI) * z));
	double t_2 = t_0 + 7.0;
	double t_3 = t_2 + 0.5;
	double t_4 = sqrt((((double) M_PI) + ((double) M_PI))) * pow(-(z - 7.5), (0.5 - z));
	double tmp;
	if ((t_1 * (((sqrt((((double) M_PI) * 2.0)) * pow(t_3, (t_0 + 0.5))) * exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304) {
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - 1.4451589203350195e-6)) * exp((z - 7.5))) * t_1);
	} else {
		tmp = t_4 * ((263.3831869810514 * exp(-7.5)) * t_1);
	}
	return tmp;
}

Java

public static double code(double z) {
	double t_0 = (1.0 - z) - 1.0;
	double t_1 = Math.PI / Math.sin((Math.PI * z));
	double t_2 = t_0 + 7.0;
	double t_3 = t_2 + 0.5;
	double t_4 = Math.sqrt((Math.PI + Math.PI)) * Math.pow(-(z - 7.5), (0.5 - z));
	double tmp;
	if ((t_1 * (((Math.sqrt((Math.PI * 2.0)) * Math.pow(t_3, (t_0 + 0.5))) * Math.exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304) {
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - 1.4451589203350195e-6)) * Math.exp((z - 7.5))) * t_1);
	} else {
		tmp = t_4 * ((263.3831869810514 * Math.exp(-7.5)) * t_1);
	}
	return tmp;
}

Python

def code(z):
	t_0 = (1.0 - z) - 1.0
	t_1 = math.pi / math.sin((math.pi * z))
	t_2 = t_0 + 7.0
	t_3 = t_2 + 0.5
	t_4 = math.sqrt((math.pi + math.pi)) * math.pow(-(z - 7.5), (0.5 - z))
	tmp = 0
	if (t_1 * (((math.sqrt((math.pi * 2.0)) * math.pow(t_3, (t_0 + 0.5))) * math.exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304:
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - 1.4451589203350195e-6)) * math.exp((z - 7.5))) * t_1)
	else:
		tmp = t_4 * ((263.3831869810514 * math.exp(-7.5)) * t_1)
	return tmp

Julia

function code(z)
	t_0 = Float64(Float64(1.0 - z) - 1.0)
	t_1 = Float64(pi / sin(Float64(pi * z)))
	t_2 = Float64(t_0 + 7.0)
	t_3 = Float64(t_2 + 0.5)
	t_4 = Float64(sqrt(Float64(pi + pi)) * (Float64(-Float64(z - 7.5)) ^ Float64(0.5 - z)))
	tmp = 0.0
	if (Float64(t_1 * Float64(Float64(Float64(sqrt(Float64(pi * 2.0)) * (t_3 ^ Float64(t_0 + 0.5))) * exp(Float64(-t_3))) * 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_2)) + Float64(1.5056327351493116e-7 / Float64(t_0 + 8.0))))) <= 2e+304)
		tmp = Float64(t_4 * Float64(Float64(Float64(Float64(Float64(Float64(-771.3234287776531 / Float64(z - 3.0)) - Float64(Float64(Float64(-1259.1392167224028 / Float64(z - 2.0)) - Float64(-676.5203681218851 / Float64(z - 1.0))) - 0.9999999999998099)) - Float64(176.6150291621406 / Float64(4.0 - z))) - Float64(Float64(Float64(12.507343278686905 / Float64(z - 5.0)) - Float64(-0.13857109526572012 / Float64(6.0 - z))) - 1.4451589203350195e-6)) * exp(Float64(z - 7.5))) * t_1));
	else
		tmp = Float64(t_4 * Float64(Float64(263.3831869810514 * exp(-7.5)) * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z)
	t_0 = (1.0 - z) - 1.0;
	t_1 = pi / sin((pi * z));
	t_2 = t_0 + 7.0;
	t_3 = t_2 + 0.5;
	t_4 = sqrt((pi + pi)) * (-(z - 7.5) ^ (0.5 - z));
	tmp = 0.0;
	if ((t_1 * (((sqrt((pi * 2.0)) * (t_3 ^ (t_0 + 0.5))) * exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304)
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - (((12.507343278686905 / (z - 5.0)) - (-0.13857109526572012 / (6.0 - z))) - 1.4451589203350195e-6)) * exp((z - 7.5))) * t_1);
	else
		tmp = t_4 * ((263.3831869810514 * exp(-7.5)) * t_1);
	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[(Pi / N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + 7.0), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + 0.5), $MachinePrecision]}, Block[{t$95$4 = N[(N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision] * N[Power[(-N[(z - 7.5), $MachinePrecision]), N[(0.5 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 * N[(N[(N[(N[Sqrt[N[(Pi * 2.0), $MachinePrecision]], $MachinePrecision] * N[Power[t$95$3, N[(t$95$0 + 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Exp[(-t$95$3)], $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$2), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(t$95$0 + 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e+304], N[(t$95$4 * N[(N[(N[(N[(N[(N[(-771.3234287776531 / N[(z - 3.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(-1259.1392167224028 / N[(z - 2.0), $MachinePrecision]), $MachinePrecision] - N[(-676.5203681218851 / N[(z - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 0.9999999999998099), $MachinePrecision]), $MachinePrecision] - N[(176.6150291621406 / N[(4.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(12.507343278686905 / N[(z - 5.0), $MachinePrecision]), $MachinePrecision] - N[(-0.13857109526572012 / N[(6.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.4451589203350195e-6), $MachinePrecision]), $MachinePrecision] * N[Exp[N[(z - 7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$4 * N[(N[(263.3831869810514 * N[Exp[-7.5], $MachinePrecision]), $MachinePrecision] * t$95$1), $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)))))) < 1.9999999999999999e304

   1. Initial program 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   7. Applied rewrites 98.3%

      \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\color{blue}{\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right)} - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - \frac{15}{2}\right)\right)}^{\left(\frac{1}{2} - z\right)}\right) \cdot \left(\left(\left(\left(\left(\frac{\frac{-7713234287776531}{10000000000000}}{z - 3} - \left(\left(\frac{\frac{-3147848041806007}{2500000000000}}{z - 2} - \frac{\frac{-6765203681218851}{10000000000000}}{z - 1}\right) - \frac{9999999999998099}{10000000000000000}\right)\right) - \frac{\frac{883075145810703}{5000000000000}}{4 - z}\right) - \left(\left(\frac{\frac{2501468655737381}{200000000000000}}{z - 5} - \frac{\frac{-3464277381643003}{25000000000000000}}{6 - z}\right) - \color{blue}{\frac{2023222488469027353}{1400000000000000000000000}}\right)\right) \cdot e^{z - \frac{15}{2}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   10. Applied rewrites 97.8%

       \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \color{blue}{1.4451589203350195 \cdot 10^{-6}}\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   if 1.9999999999999999e304 < (*.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 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 96.2%

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

Alternative 10: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - z\right) - 1\\ t_1 := \frac{\pi}{\sin \left(\pi \cdot z\right)}\\ t_2 := t\_0 + 7\\ t_3 := t\_2 + 0.5\\ t_4 := \sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\\ \mathbf{if}\;t\_1 \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {t\_3}^{\left(t\_0 + 0.5\right)}\right) \cdot e^{-t\_3}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{t\_0 + 1}\right) + \frac{-1259.1392167224028}{t\_0 + 2}\right) + \frac{771.3234287776531}{t\_0 + 3}\right) + \frac{-176.6150291621406}{t\_0 + 4}\right) + \frac{12.507343278686905}{t\_0 + 5}\right) + \frac{-0.13857109526572012}{t\_0 + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t\_2}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{t\_0 + 8}\right)\right) \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_4 \cdot \left(\left(\left(\left(\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right) - \frac{176.6150291621406}{4 - z}\right) - \left(z \cdot \left(z \cdot \left(-0.01990483129967024 \cdot z - 0.09941724278406093\right) - 0.49644474017195733\right) - 2.4783749183520145\right)\right) \cdot e^{z - 7.5}\right) \cdot t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4 \cdot \left(\left(263.3831869810514 \cdot e^{-7.5}\right) \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (- (- 1.0 z) 1.0))
        (t_1 (/ PI (sin (* PI z))))
        (t_2 (+ t_0 7.0))
        (t_3 (+ t_2 0.5))
        (t_4 (* (sqrt (+ PI PI)) (pow (- (- z 7.5)) (- 0.5 z)))))
   (if (<=
        (*
         t_1
         (*
          (* (* (sqrt (* PI 2.0)) (pow t_3 (+ t_0 0.5))) (exp (- t_3)))
          (+
           (+
            (+
             (+
              (+
               (+
                (+
                 (+ 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_2))
           (/ 1.5056327351493116e-7 (+ t_0 8.0)))))
        2e+304)
     (*
      t_4
      (*
       (*
        (-
         (-
          (-
           (/ -771.3234287776531 (- z 3.0))
           (-
            (-
             (/ -1259.1392167224028 (- z 2.0))
             (/ -676.5203681218851 (- z 1.0)))
            0.9999999999998099))
          (/ 176.6150291621406 (- 4.0 z)))
         (-
          (*
           z
           (-
            (* z (- (* -0.01990483129967024 z) 0.09941724278406093))
            0.49644474017195733))
          2.4783749183520145))
        (exp (- z 7.5)))
       t_1))
     (* t_4 (* (* 263.3831869810514 (exp -7.5)) t_1)))))

C

double code(double z) {
	double t_0 = (1.0 - z) - 1.0;
	double t_1 = ((double) M_PI) / sin((((double) M_PI) * z));
	double t_2 = t_0 + 7.0;
	double t_3 = t_2 + 0.5;
	double t_4 = sqrt((((double) M_PI) + ((double) M_PI))) * pow(-(z - 7.5), (0.5 - z));
	double tmp;
	if ((t_1 * (((sqrt((((double) M_PI) * 2.0)) * pow(t_3, (t_0 + 0.5))) * exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304) {
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - ((z * ((z * ((-0.01990483129967024 * z) - 0.09941724278406093)) - 0.49644474017195733)) - 2.4783749183520145)) * exp((z - 7.5))) * t_1);
	} else {
		tmp = t_4 * ((263.3831869810514 * exp(-7.5)) * t_1);
	}
	return tmp;
}

Java

public static double code(double z) {
	double t_0 = (1.0 - z) - 1.0;
	double t_1 = Math.PI / Math.sin((Math.PI * z));
	double t_2 = t_0 + 7.0;
	double t_3 = t_2 + 0.5;
	double t_4 = Math.sqrt((Math.PI + Math.PI)) * Math.pow(-(z - 7.5), (0.5 - z));
	double tmp;
	if ((t_1 * (((Math.sqrt((Math.PI * 2.0)) * Math.pow(t_3, (t_0 + 0.5))) * Math.exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304) {
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - ((z * ((z * ((-0.01990483129967024 * z) - 0.09941724278406093)) - 0.49644474017195733)) - 2.4783749183520145)) * Math.exp((z - 7.5))) * t_1);
	} else {
		tmp = t_4 * ((263.3831869810514 * Math.exp(-7.5)) * t_1);
	}
	return tmp;
}

Python

def code(z):
	t_0 = (1.0 - z) - 1.0
	t_1 = math.pi / math.sin((math.pi * z))
	t_2 = t_0 + 7.0
	t_3 = t_2 + 0.5
	t_4 = math.sqrt((math.pi + math.pi)) * math.pow(-(z - 7.5), (0.5 - z))
	tmp = 0
	if (t_1 * (((math.sqrt((math.pi * 2.0)) * math.pow(t_3, (t_0 + 0.5))) * math.exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304:
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - ((z * ((z * ((-0.01990483129967024 * z) - 0.09941724278406093)) - 0.49644474017195733)) - 2.4783749183520145)) * math.exp((z - 7.5))) * t_1)
	else:
		tmp = t_4 * ((263.3831869810514 * math.exp(-7.5)) * t_1)
	return tmp

Julia

function code(z)
	t_0 = Float64(Float64(1.0 - z) - 1.0)
	t_1 = Float64(pi / sin(Float64(pi * z)))
	t_2 = Float64(t_0 + 7.0)
	t_3 = Float64(t_2 + 0.5)
	t_4 = Float64(sqrt(Float64(pi + pi)) * (Float64(-Float64(z - 7.5)) ^ Float64(0.5 - z)))
	tmp = 0.0
	if (Float64(t_1 * Float64(Float64(Float64(sqrt(Float64(pi * 2.0)) * (t_3 ^ Float64(t_0 + 0.5))) * exp(Float64(-t_3))) * 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_2)) + Float64(1.5056327351493116e-7 / Float64(t_0 + 8.0))))) <= 2e+304)
		tmp = Float64(t_4 * Float64(Float64(Float64(Float64(Float64(Float64(-771.3234287776531 / Float64(z - 3.0)) - Float64(Float64(Float64(-1259.1392167224028 / Float64(z - 2.0)) - Float64(-676.5203681218851 / Float64(z - 1.0))) - 0.9999999999998099)) - Float64(176.6150291621406 / Float64(4.0 - z))) - Float64(Float64(z * Float64(Float64(z * Float64(Float64(-0.01990483129967024 * z) - 0.09941724278406093)) - 0.49644474017195733)) - 2.4783749183520145)) * exp(Float64(z - 7.5))) * t_1));
	else
		tmp = Float64(t_4 * Float64(Float64(263.3831869810514 * exp(-7.5)) * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z)
	t_0 = (1.0 - z) - 1.0;
	t_1 = pi / sin((pi * z));
	t_2 = t_0 + 7.0;
	t_3 = t_2 + 0.5;
	t_4 = sqrt((pi + pi)) * (-(z - 7.5) ^ (0.5 - z));
	tmp = 0.0;
	if ((t_1 * (((sqrt((pi * 2.0)) * (t_3 ^ (t_0 + 0.5))) * exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304)
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - ((z * ((z * ((-0.01990483129967024 * z) - 0.09941724278406093)) - 0.49644474017195733)) - 2.4783749183520145)) * exp((z - 7.5))) * t_1);
	else
		tmp = t_4 * ((263.3831869810514 * exp(-7.5)) * t_1);
	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[(Pi / N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + 7.0), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + 0.5), $MachinePrecision]}, Block[{t$95$4 = N[(N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision] * N[Power[(-N[(z - 7.5), $MachinePrecision]), N[(0.5 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 * N[(N[(N[(N[Sqrt[N[(Pi * 2.0), $MachinePrecision]], $MachinePrecision] * N[Power[t$95$3, N[(t$95$0 + 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Exp[(-t$95$3)], $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$2), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(t$95$0 + 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e+304], N[(t$95$4 * N[(N[(N[(N[(N[(N[(-771.3234287776531 / N[(z - 3.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(-1259.1392167224028 / N[(z - 2.0), $MachinePrecision]), $MachinePrecision] - N[(-676.5203681218851 / N[(z - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 0.9999999999998099), $MachinePrecision]), $MachinePrecision] - N[(176.6150291621406 / N[(4.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z * N[(N[(z * N[(N[(-0.01990483129967024 * z), $MachinePrecision] - 0.09941724278406093), $MachinePrecision]), $MachinePrecision] - 0.49644474017195733), $MachinePrecision]), $MachinePrecision] - 2.4783749183520145), $MachinePrecision]), $MachinePrecision] * N[Exp[N[(z - 7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$4 * N[(N[(263.3831869810514 * N[Exp[-7.5], $MachinePrecision]), $MachinePrecision] * t$95$1), $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)))))) < 1.9999999999999999e304

   1. Initial program 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   7. Applied rewrites 98.3%

      \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\color{blue}{\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right)} - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - \frac{15}{2}\right)\right)}^{\left(\frac{1}{2} - z\right)}\right) \cdot \left(\left(\left(\left(\left(\frac{\frac{-7713234287776531}{10000000000000}}{z - 3} - \left(\left(\frac{\frac{-3147848041806007}{2500000000000}}{z - 2} - \frac{\frac{-6765203681218851}{10000000000000}}{z - 1}\right) - \frac{9999999999998099}{10000000000000000}\right)\right) - \frac{\frac{883075145810703}{5000000000000}}{4 - z}\right) - \color{blue}{\left(z \cdot \left(z \cdot \left(\frac{-396401817189495604203614369999}{19914854400000000000000000000000} \cdot z - \frac{11784999493416810208044520019}{118540800000000000000000000000}\right) - \frac{350291408665333106351952839}{705600000000000000000000000}\right) - \frac{10409174657078461523082059}{4200000000000000000000000}\right)}\right) \cdot e^{z - \frac{15}{2}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   10. Applied rewrites 97.6%

       \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right) - \frac{176.6150291621406}{4 - z}\right) - \color{blue}{\left(z \cdot \left(z \cdot \left(-0.01990483129967024 \cdot z - 0.09941724278406093\right) - 0.49644474017195733\right) - 2.4783749183520145\right)}\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   if 1.9999999999999999e304 < (*.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 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 96.2%

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

Alternative 11: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - z\right) - 1\\ t_1 := \frac{\pi}{\sin \left(\pi \cdot z\right)}\\ t_2 := t\_0 + 7\\ t_3 := t\_2 + 0.5\\ t_4 := \sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\\ \mathbf{if}\;t\_1 \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {t\_3}^{\left(t\_0 + 0.5\right)}\right) \cdot e^{-t\_3}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{t\_0 + 1}\right) + \frac{-1259.1392167224028}{t\_0 + 2}\right) + \frac{771.3234287776531}{t\_0 + 3}\right) + \frac{-176.6150291621406}{t\_0 + 4}\right) + \frac{12.507343278686905}{t\_0 + 5}\right) + \frac{-0.13857109526572012}{t\_0 + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t\_2}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{t\_0 + 8}\right)\right) \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_4 \cdot \left(\left(\left(\left(\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right) - \frac{176.6150291621406}{4 - z}\right) - \left(z \cdot \left(-0.09941724278406093 \cdot z - 0.49644474017195733\right) - 2.4783749183520145\right)\right) \cdot e^{z - 7.5}\right) \cdot t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4 \cdot \left(\left(263.3831869810514 \cdot e^{-7.5}\right) \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (- (- 1.0 z) 1.0))
        (t_1 (/ PI (sin (* PI z))))
        (t_2 (+ t_0 7.0))
        (t_3 (+ t_2 0.5))
        (t_4 (* (sqrt (+ PI PI)) (pow (- (- z 7.5)) (- 0.5 z)))))
   (if (<=
        (*
         t_1
         (*
          (* (* (sqrt (* PI 2.0)) (pow t_3 (+ t_0 0.5))) (exp (- t_3)))
          (+
           (+
            (+
             (+
              (+
               (+
                (+
                 (+ 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_2))
           (/ 1.5056327351493116e-7 (+ t_0 8.0)))))
        2e+304)
     (*
      t_4
      (*
       (*
        (-
         (-
          (-
           (/ -771.3234287776531 (- z 3.0))
           (-
            (-
             (/ -1259.1392167224028 (- z 2.0))
             (/ -676.5203681218851 (- z 1.0)))
            0.9999999999998099))
          (/ 176.6150291621406 (- 4.0 z)))
         (-
          (* z (- (* -0.09941724278406093 z) 0.49644474017195733))
          2.4783749183520145))
        (exp (- z 7.5)))
       t_1))
     (* t_4 (* (* 263.3831869810514 (exp -7.5)) t_1)))))

C

double code(double z) {
	double t_0 = (1.0 - z) - 1.0;
	double t_1 = ((double) M_PI) / sin((((double) M_PI) * z));
	double t_2 = t_0 + 7.0;
	double t_3 = t_2 + 0.5;
	double t_4 = sqrt((((double) M_PI) + ((double) M_PI))) * pow(-(z - 7.5), (0.5 - z));
	double tmp;
	if ((t_1 * (((sqrt((((double) M_PI) * 2.0)) * pow(t_3, (t_0 + 0.5))) * exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304) {
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - ((z * ((-0.09941724278406093 * z) - 0.49644474017195733)) - 2.4783749183520145)) * exp((z - 7.5))) * t_1);
	} else {
		tmp = t_4 * ((263.3831869810514 * exp(-7.5)) * t_1);
	}
	return tmp;
}

Java

public static double code(double z) {
	double t_0 = (1.0 - z) - 1.0;
	double t_1 = Math.PI / Math.sin((Math.PI * z));
	double t_2 = t_0 + 7.0;
	double t_3 = t_2 + 0.5;
	double t_4 = Math.sqrt((Math.PI + Math.PI)) * Math.pow(-(z - 7.5), (0.5 - z));
	double tmp;
	if ((t_1 * (((Math.sqrt((Math.PI * 2.0)) * Math.pow(t_3, (t_0 + 0.5))) * Math.exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304) {
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - ((z * ((-0.09941724278406093 * z) - 0.49644474017195733)) - 2.4783749183520145)) * Math.exp((z - 7.5))) * t_1);
	} else {
		tmp = t_4 * ((263.3831869810514 * Math.exp(-7.5)) * t_1);
	}
	return tmp;
}

Python

def code(z):
	t_0 = (1.0 - z) - 1.0
	t_1 = math.pi / math.sin((math.pi * z))
	t_2 = t_0 + 7.0
	t_3 = t_2 + 0.5
	t_4 = math.sqrt((math.pi + math.pi)) * math.pow(-(z - 7.5), (0.5 - z))
	tmp = 0
	if (t_1 * (((math.sqrt((math.pi * 2.0)) * math.pow(t_3, (t_0 + 0.5))) * math.exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304:
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - ((z * ((-0.09941724278406093 * z) - 0.49644474017195733)) - 2.4783749183520145)) * math.exp((z - 7.5))) * t_1)
	else:
		tmp = t_4 * ((263.3831869810514 * math.exp(-7.5)) * t_1)
	return tmp

Julia

function code(z)
	t_0 = Float64(Float64(1.0 - z) - 1.0)
	t_1 = Float64(pi / sin(Float64(pi * z)))
	t_2 = Float64(t_0 + 7.0)
	t_3 = Float64(t_2 + 0.5)
	t_4 = Float64(sqrt(Float64(pi + pi)) * (Float64(-Float64(z - 7.5)) ^ Float64(0.5 - z)))
	tmp = 0.0
	if (Float64(t_1 * Float64(Float64(Float64(sqrt(Float64(pi * 2.0)) * (t_3 ^ Float64(t_0 + 0.5))) * exp(Float64(-t_3))) * 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_2)) + Float64(1.5056327351493116e-7 / Float64(t_0 + 8.0))))) <= 2e+304)
		tmp = Float64(t_4 * Float64(Float64(Float64(Float64(Float64(Float64(-771.3234287776531 / Float64(z - 3.0)) - Float64(Float64(Float64(-1259.1392167224028 / Float64(z - 2.0)) - Float64(-676.5203681218851 / Float64(z - 1.0))) - 0.9999999999998099)) - Float64(176.6150291621406 / Float64(4.0 - z))) - Float64(Float64(z * Float64(Float64(-0.09941724278406093 * z) - 0.49644474017195733)) - 2.4783749183520145)) * exp(Float64(z - 7.5))) * t_1));
	else
		tmp = Float64(t_4 * Float64(Float64(263.3831869810514 * exp(-7.5)) * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z)
	t_0 = (1.0 - z) - 1.0;
	t_1 = pi / sin((pi * z));
	t_2 = t_0 + 7.0;
	t_3 = t_2 + 0.5;
	t_4 = sqrt((pi + pi)) * (-(z - 7.5) ^ (0.5 - z));
	tmp = 0.0;
	if ((t_1 * (((sqrt((pi * 2.0)) * (t_3 ^ (t_0 + 0.5))) * exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304)
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - ((z * ((-0.09941724278406093 * z) - 0.49644474017195733)) - 2.4783749183520145)) * exp((z - 7.5))) * t_1);
	else
		tmp = t_4 * ((263.3831869810514 * exp(-7.5)) * t_1);
	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[(Pi / N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + 7.0), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + 0.5), $MachinePrecision]}, Block[{t$95$4 = N[(N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision] * N[Power[(-N[(z - 7.5), $MachinePrecision]), N[(0.5 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 * N[(N[(N[(N[Sqrt[N[(Pi * 2.0), $MachinePrecision]], $MachinePrecision] * N[Power[t$95$3, N[(t$95$0 + 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Exp[(-t$95$3)], $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$2), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(t$95$0 + 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e+304], N[(t$95$4 * N[(N[(N[(N[(N[(N[(-771.3234287776531 / N[(z - 3.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(-1259.1392167224028 / N[(z - 2.0), $MachinePrecision]), $MachinePrecision] - N[(-676.5203681218851 / N[(z - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 0.9999999999998099), $MachinePrecision]), $MachinePrecision] - N[(176.6150291621406 / N[(4.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z * N[(N[(-0.09941724278406093 * z), $MachinePrecision] - 0.49644474017195733), $MachinePrecision]), $MachinePrecision] - 2.4783749183520145), $MachinePrecision]), $MachinePrecision] * N[Exp[N[(z - 7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$4 * N[(N[(263.3831869810514 * N[Exp[-7.5], $MachinePrecision]), $MachinePrecision] * t$95$1), $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)))))) < 1.9999999999999999e304

   1. Initial program 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   7. Applied rewrites 98.3%

      \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\color{blue}{\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right)} - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - \frac{15}{2}\right)\right)}^{\left(\frac{1}{2} - z\right)}\right) \cdot \left(\left(\left(\left(\left(\frac{\frac{-7713234287776531}{10000000000000}}{z - 3} - \left(\left(\frac{\frac{-3147848041806007}{2500000000000}}{z - 2} - \frac{\frac{-6765203681218851}{10000000000000}}{z - 1}\right) - \frac{9999999999998099}{10000000000000000}\right)\right) - \frac{\frac{883075145810703}{5000000000000}}{4 - z}\right) - \color{blue}{\left(z \cdot \left(\frac{-11784999493416810208044520019}{118540800000000000000000000000} \cdot z - \frac{350291408665333106351952839}{705600000000000000000000000}\right) - \frac{10409174657078461523082059}{4200000000000000000000000}\right)}\right) \cdot e^{z - \frac{15}{2}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   10. Applied rewrites 97.7%

       \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right) - \frac{176.6150291621406}{4 - z}\right) - \color{blue}{\left(z \cdot \left(-0.09941724278406093 \cdot z - 0.49644474017195733\right) - 2.4783749183520145\right)}\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   if 1.9999999999999999e304 < (*.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 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 96.2%

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

Alternative 12: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - z\right) - 1\\ t_1 := \frac{\pi}{\sin \left(\pi \cdot z\right)}\\ t_2 := t\_0 + 7\\ t_3 := t\_2 + 0.5\\ t_4 := \sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\\ \mathbf{if}\;t\_1 \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {t\_3}^{\left(t\_0 + 0.5\right)}\right) \cdot e^{-t\_3}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{t\_0 + 1}\right) + \frac{-1259.1392167224028}{t\_0 + 2}\right) + \frac{771.3234287776531}{t\_0 + 3}\right) + \frac{-176.6150291621406}{t\_0 + 4}\right) + \frac{12.507343278686905}{t\_0 + 5}\right) + \frac{-0.13857109526572012}{t\_0 + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t\_2}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{t\_0 + 8}\right)\right) \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_4 \cdot \left(\left(\left(\left(\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right) - \frac{176.6150291621406}{4 - z}\right) - \left(-0.49644474017195733 \cdot z - 2.4783749183520145\right)\right) \cdot e^{z - 7.5}\right) \cdot t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4 \cdot \left(\left(263.3831869810514 \cdot e^{-7.5}\right) \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (- (- 1.0 z) 1.0))
        (t_1 (/ PI (sin (* PI z))))
        (t_2 (+ t_0 7.0))
        (t_3 (+ t_2 0.5))
        (t_4 (* (sqrt (+ PI PI)) (pow (- (- z 7.5)) (- 0.5 z)))))
   (if (<=
        (*
         t_1
         (*
          (* (* (sqrt (* PI 2.0)) (pow t_3 (+ t_0 0.5))) (exp (- t_3)))
          (+
           (+
            (+
             (+
              (+
               (+
                (+
                 (+ 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_2))
           (/ 1.5056327351493116e-7 (+ t_0 8.0)))))
        2e+304)
     (*
      t_4
      (*
       (*
        (-
         (-
          (-
           (/ -771.3234287776531 (- z 3.0))
           (-
            (-
             (/ -1259.1392167224028 (- z 2.0))
             (/ -676.5203681218851 (- z 1.0)))
            0.9999999999998099))
          (/ 176.6150291621406 (- 4.0 z)))
         (- (* -0.49644474017195733 z) 2.4783749183520145))
        (exp (- z 7.5)))
       t_1))
     (* t_4 (* (* 263.3831869810514 (exp -7.5)) t_1)))))

C

double code(double z) {
	double t_0 = (1.0 - z) - 1.0;
	double t_1 = ((double) M_PI) / sin((((double) M_PI) * z));
	double t_2 = t_0 + 7.0;
	double t_3 = t_2 + 0.5;
	double t_4 = sqrt((((double) M_PI) + ((double) M_PI))) * pow(-(z - 7.5), (0.5 - z));
	double tmp;
	if ((t_1 * (((sqrt((((double) M_PI) * 2.0)) * pow(t_3, (t_0 + 0.5))) * exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304) {
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - ((-0.49644474017195733 * z) - 2.4783749183520145)) * exp((z - 7.5))) * t_1);
	} else {
		tmp = t_4 * ((263.3831869810514 * exp(-7.5)) * t_1);
	}
	return tmp;
}

Java

public static double code(double z) {
	double t_0 = (1.0 - z) - 1.0;
	double t_1 = Math.PI / Math.sin((Math.PI * z));
	double t_2 = t_0 + 7.0;
	double t_3 = t_2 + 0.5;
	double t_4 = Math.sqrt((Math.PI + Math.PI)) * Math.pow(-(z - 7.5), (0.5 - z));
	double tmp;
	if ((t_1 * (((Math.sqrt((Math.PI * 2.0)) * Math.pow(t_3, (t_0 + 0.5))) * Math.exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304) {
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - ((-0.49644474017195733 * z) - 2.4783749183520145)) * Math.exp((z - 7.5))) * t_1);
	} else {
		tmp = t_4 * ((263.3831869810514 * Math.exp(-7.5)) * t_1);
	}
	return tmp;
}

Python

def code(z):
	t_0 = (1.0 - z) - 1.0
	t_1 = math.pi / math.sin((math.pi * z))
	t_2 = t_0 + 7.0
	t_3 = t_2 + 0.5
	t_4 = math.sqrt((math.pi + math.pi)) * math.pow(-(z - 7.5), (0.5 - z))
	tmp = 0
	if (t_1 * (((math.sqrt((math.pi * 2.0)) * math.pow(t_3, (t_0 + 0.5))) * math.exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304:
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - ((-0.49644474017195733 * z) - 2.4783749183520145)) * math.exp((z - 7.5))) * t_1)
	else:
		tmp = t_4 * ((263.3831869810514 * math.exp(-7.5)) * t_1)
	return tmp

Julia

function code(z)
	t_0 = Float64(Float64(1.0 - z) - 1.0)
	t_1 = Float64(pi / sin(Float64(pi * z)))
	t_2 = Float64(t_0 + 7.0)
	t_3 = Float64(t_2 + 0.5)
	t_4 = Float64(sqrt(Float64(pi + pi)) * (Float64(-Float64(z - 7.5)) ^ Float64(0.5 - z)))
	tmp = 0.0
	if (Float64(t_1 * Float64(Float64(Float64(sqrt(Float64(pi * 2.0)) * (t_3 ^ Float64(t_0 + 0.5))) * exp(Float64(-t_3))) * 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_2)) + Float64(1.5056327351493116e-7 / Float64(t_0 + 8.0))))) <= 2e+304)
		tmp = Float64(t_4 * Float64(Float64(Float64(Float64(Float64(Float64(-771.3234287776531 / Float64(z - 3.0)) - Float64(Float64(Float64(-1259.1392167224028 / Float64(z - 2.0)) - Float64(-676.5203681218851 / Float64(z - 1.0))) - 0.9999999999998099)) - Float64(176.6150291621406 / Float64(4.0 - z))) - Float64(Float64(-0.49644474017195733 * z) - 2.4783749183520145)) * exp(Float64(z - 7.5))) * t_1));
	else
		tmp = Float64(t_4 * Float64(Float64(263.3831869810514 * exp(-7.5)) * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z)
	t_0 = (1.0 - z) - 1.0;
	t_1 = pi / sin((pi * z));
	t_2 = t_0 + 7.0;
	t_3 = t_2 + 0.5;
	t_4 = sqrt((pi + pi)) * (-(z - 7.5) ^ (0.5 - z));
	tmp = 0.0;
	if ((t_1 * (((sqrt((pi * 2.0)) * (t_3 ^ (t_0 + 0.5))) * exp(-t_3)) * ((((((((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_2)) + (1.5056327351493116e-7 / (t_0 + 8.0))))) <= 2e+304)
		tmp = t_4 * ((((((-771.3234287776531 / (z - 3.0)) - (((-1259.1392167224028 / (z - 2.0)) - (-676.5203681218851 / (z - 1.0))) - 0.9999999999998099)) - (176.6150291621406 / (4.0 - z))) - ((-0.49644474017195733 * z) - 2.4783749183520145)) * exp((z - 7.5))) * t_1);
	else
		tmp = t_4 * ((263.3831869810514 * exp(-7.5)) * t_1);
	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[(Pi / N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + 7.0), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + 0.5), $MachinePrecision]}, Block[{t$95$4 = N[(N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision] * N[Power[(-N[(z - 7.5), $MachinePrecision]), N[(0.5 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 * N[(N[(N[(N[Sqrt[N[(Pi * 2.0), $MachinePrecision]], $MachinePrecision] * N[Power[t$95$3, N[(t$95$0 + 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Exp[(-t$95$3)], $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$2), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(t$95$0 + 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e+304], N[(t$95$4 * N[(N[(N[(N[(N[(N[(-771.3234287776531 / N[(z - 3.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(-1259.1392167224028 / N[(z - 2.0), $MachinePrecision]), $MachinePrecision] - N[(-676.5203681218851 / N[(z - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 0.9999999999998099), $MachinePrecision]), $MachinePrecision] - N[(176.6150291621406 / N[(4.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(-0.49644474017195733 * z), $MachinePrecision] - 2.4783749183520145), $MachinePrecision]), $MachinePrecision] * N[Exp[N[(z - 7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$4 * N[(N[(263.3831869810514 * N[Exp[-7.5], $MachinePrecision]), $MachinePrecision] * t$95$1), $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)))))) < 1.9999999999999999e304

   1. Initial program 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   7. Applied rewrites 98.3%

      \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\color{blue}{\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right)} - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - \frac{15}{2}\right)\right)}^{\left(\frac{1}{2} - z\right)}\right) \cdot \left(\left(\left(\left(\left(\frac{\frac{-7713234287776531}{10000000000000}}{z - 3} - \left(\left(\frac{\frac{-3147848041806007}{2500000000000}}{z - 2} - \frac{\frac{-6765203681218851}{10000000000000}}{z - 1}\right) - \frac{9999999999998099}{10000000000000000}\right)\right) - \frac{\frac{883075145810703}{5000000000000}}{4 - z}\right) - \color{blue}{\left(\frac{-350291408665333106351952839}{705600000000000000000000000} \cdot z - \frac{10409174657078461523082059}{4200000000000000000000000}\right)}\right) \cdot e^{z - \frac{15}{2}}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   10. Applied rewrites 97.2%

       \[\leadsto \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\frac{-771.3234287776531}{z - 3} - \left(\left(\frac{-1259.1392167224028}{z - 2} - \frac{-676.5203681218851}{z - 1}\right) - 0.9999999999998099\right)\right) - \frac{176.6150291621406}{4 - z}\right) - \color{blue}{\left(-0.49644474017195733 \cdot z - 2.4783749183520145\right)}\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \]

   if 1.9999999999999999e304 < (*.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 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 96.2%

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

Alternative 13: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - z\right) - 1\\ t_1 := t\_0 + 7\\ t_2 := t\_1 + 0.5\\ t_3 := \sqrt{\pi + \pi}\\ t_4 := \sin \left(\pi \cdot z\right)\\ t_5 := \frac{\pi}{t\_4}\\ \mathbf{if}\;t\_5 \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {t\_2}^{\left(t\_0 + 0.5\right)}\right) \cdot e^{-t\_2}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{t\_0 + 1}\right) + \frac{-1259.1392167224028}{t\_0 + 2}\right) + \frac{771.3234287776531}{t\_0 + 3}\right) + \frac{-176.6150291621406}{t\_0 + 4}\right) + \frac{12.507343278686905}{t\_0 + 5}\right) + \frac{-0.13857109526572012}{t\_0 + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{t\_1}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{t\_0 + 8}\right)\right) \leq 1.4 \cdot 10^{+304}:\\ \;\;\;\;\frac{\pi \cdot \left(\left(t\_3 \cdot {\left(\left(1 - z\right) - -6.5\right)}^{\left(\left(1 - z\right) - 0.5\right)}\right) \cdot e^{\left(0 + z\right) + -7.5}\right)}{t\_4} \cdot \left(\left(263.3831855358925 + z \cdot \left(436.8961723502244 + 545.0353078134797 \cdot z\right)\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{-6 - \left(1 - z\right)} - \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) - -7}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t\_3 \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(263.3831869810514 \cdot e^{-7.5}\right) \cdot t\_5\right)\\ \end{array} \end{array} \]

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 (sqrt (+ PI PI)))
        (t_4 (sin (* PI z)))
        (t_5 (/ PI t_4)))
   (if (<=
        (*
         t_5
         (*
          (* (* (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)))))
        1.4e+304)
     (*
      (/
       (*
        PI
        (*
         (* t_3 (pow (- (- 1.0 z) -6.5) (- (- 1.0 z) 0.5)))
         (exp (+ (+ 0.0 z) -7.5))))
       t_4)
      (-
       (+
        263.3831855358925
        (* z (+ 436.8961723502244 (* 545.0353078134797 z))))
       (-
        (/ 9.984369578019572e-6 (- -6.0 (- 1.0 z)))
        (/ 1.5056327351493116e-7 (- (- 1.0 z) -7.0)))))
     (*
      (* t_3 (pow (- (- z 7.5)) (- 0.5 z)))
      (* (* 263.3831869810514 (exp -7.5)) t_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 = sqrt((((double) M_PI) + ((double) M_PI)));
	double t_4 = sin((((double) M_PI) * z));
	double t_5 = ((double) M_PI) / t_4;
	double tmp;
	if ((t_5 * (((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))))) <= 1.4e+304) {
		tmp = ((((double) M_PI) * ((t_3 * pow(((1.0 - z) - -6.5), ((1.0 - z) - 0.5))) * exp(((0.0 + z) + -7.5)))) / t_4) * ((263.3831855358925 + (z * (436.8961723502244 + (545.0353078134797 * z)))) - ((9.984369578019572e-6 / (-6.0 - (1.0 - z))) - (1.5056327351493116e-7 / ((1.0 - z) - -7.0))));
	} else {
		tmp = (t_3 * pow(-(z - 7.5), (0.5 - z))) * ((263.3831869810514 * exp(-7.5)) * t_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.sqrt((Math.PI + Math.PI));
	double t_4 = Math.sin((Math.PI * z));
	double t_5 = Math.PI / t_4;
	double tmp;
	if ((t_5 * (((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))))) <= 1.4e+304) {
		tmp = ((Math.PI * ((t_3 * Math.pow(((1.0 - z) - -6.5), ((1.0 - z) - 0.5))) * Math.exp(((0.0 + z) + -7.5)))) / t_4) * ((263.3831855358925 + (z * (436.8961723502244 + (545.0353078134797 * z)))) - ((9.984369578019572e-6 / (-6.0 - (1.0 - z))) - (1.5056327351493116e-7 / ((1.0 - z) - -7.0))));
	} else {
		tmp = (t_3 * Math.pow(-(z - 7.5), (0.5 - z))) * ((263.3831869810514 * Math.exp(-7.5)) * t_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.sqrt((math.pi + math.pi))
	t_4 = math.sin((math.pi * z))
	t_5 = math.pi / t_4
	tmp = 0
	if (t_5 * (((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))))) <= 1.4e+304:
		tmp = ((math.pi * ((t_3 * math.pow(((1.0 - z) - -6.5), ((1.0 - z) - 0.5))) * math.exp(((0.0 + z) + -7.5)))) / t_4) * ((263.3831855358925 + (z * (436.8961723502244 + (545.0353078134797 * z)))) - ((9.984369578019572e-6 / (-6.0 - (1.0 - z))) - (1.5056327351493116e-7 / ((1.0 - z) - -7.0))))
	else:
		tmp = (t_3 * math.pow(-(z - 7.5), (0.5 - z))) * ((263.3831869810514 * math.exp(-7.5)) * t_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 = sqrt(Float64(pi + pi))
	t_4 = sin(Float64(pi * z))
	t_5 = Float64(pi / t_4)
	tmp = 0.0
	if (Float64(t_5 * 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))))) <= 1.4e+304)
		tmp = Float64(Float64(Float64(pi * Float64(Float64(t_3 * (Float64(Float64(1.0 - z) - -6.5) ^ Float64(Float64(1.0 - z) - 0.5))) * exp(Float64(Float64(0.0 + z) + -7.5)))) / t_4) * Float64(Float64(263.3831855358925 + Float64(z * Float64(436.8961723502244 + Float64(545.0353078134797 * z)))) - Float64(Float64(9.984369578019572e-6 / Float64(-6.0 - Float64(1.0 - z))) - Float64(1.5056327351493116e-7 / Float64(Float64(1.0 - z) - -7.0)))));
	else
		tmp = Float64(Float64(t_3 * (Float64(-Float64(z - 7.5)) ^ Float64(0.5 - z))) * Float64(Float64(263.3831869810514 * exp(-7.5)) * t_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 = sqrt((pi + pi));
	t_4 = sin((pi * z));
	t_5 = pi / t_4;
	tmp = 0.0;
	if ((t_5 * (((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))))) <= 1.4e+304)
		tmp = ((pi * ((t_3 * (((1.0 - z) - -6.5) ^ ((1.0 - z) - 0.5))) * exp(((0.0 + z) + -7.5)))) / t_4) * ((263.3831855358925 + (z * (436.8961723502244 + (545.0353078134797 * z)))) - ((9.984369578019572e-6 / (-6.0 - (1.0 - z))) - (1.5056327351493116e-7 / ((1.0 - z) - -7.0))));
	else
		tmp = (t_3 * (-(z - 7.5) ^ (0.5 - z))) * ((263.3831869810514 * exp(-7.5)) * t_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[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$5 = N[(Pi / t$95$4), $MachinePrecision]}, If[LessEqual[N[(t$95$5 * 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], 1.4e+304], N[(N[(N[(Pi * N[(N[(t$95$3 * N[Power[N[(N[(1.0 - z), $MachinePrecision] - -6.5), $MachinePrecision], N[(N[(1.0 - z), $MachinePrecision] - 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Exp[N[(N[(0.0 + z), $MachinePrecision] + -7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision] * N[(N[(263.3831855358925 + N[(z * N[(436.8961723502244 + N[(545.0353078134797 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(9.984369578019572e-6 / N[(-6.0 - N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(1.5056327351493116e-7 / N[(N[(1.0 - z), $MachinePrecision] - -7.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$3 * N[Power[(-N[(z - 7.5), $MachinePrecision]), N[(0.5 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(263.3831869810514 * N[Exp[-7.5], $MachinePrecision]), $MachinePrecision] * t$95$5), $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)))))) < 1.40000000000000006e304

   1. Initial program 96.4%

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

   3. Applied rewrites 98.2%

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

   4. Taylor expanded in z around 0

      \[\leadsto \frac{\pi \cdot \left(\left(\sqrt{\pi + \pi} \cdot {\left(\left(1 - z\right) - \frac{-13}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)}\right) \cdot e^{\left(0 + z\right) + \frac{-15}{2}}\right)}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(\frac{9876869457595968283}{37500000000000000} + z \cdot \left(\frac{131068851705067315609}{300000000000000000} + \frac{367898832774098786021}{675000000000000000} \cdot z\right)\right)} - \left(\frac{\frac{2496092394504893}{250000000000000000000}}{-6 - \left(1 - z\right)} - \frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7}\right)\right) \]

   6. Applied rewrites 97.3%

      \[\leadsto \frac{\pi \cdot \left(\left(\sqrt{\pi + \pi} \cdot {\left(\left(1 - z\right) - -6.5\right)}^{\left(\left(1 - z\right) - 0.5\right)}\right) \cdot e^{\left(0 + z\right) + -7.5}\right)}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(263.3831855358925 + z \cdot \left(436.8961723502244 + 545.0353078134797 \cdot z\right)\right)} - \left(\frac{9.984369578019572 \cdot 10^{-6}}{-6 - \left(1 - z\right)} - \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) - -7}\right)\right) \]

   if 1.40000000000000006e304 < (*.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 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 96.2%

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

Alternative 14: 97.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(\pi \cdot z\right)\\ t_1 := \sqrt{\pi + \pi}\\ t_2 := {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\\ \mathbf{if}\;z \leq -0.52:\\ \;\;\;\;\left(t\_1 \cdot t\_2\right) \cdot \left(\left(263.3831869810514 \cdot e^{-7.5}\right) \cdot \frac{\pi}{t\_0}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(\left(\pi \cdot t\_1\right) \cdot t\_2\right) \cdot e^{z}\right) \cdot e^{-7.5}}{t\_0} \cdot \left(\left(263.3831855358925 + 436.8961723502244 \cdot z\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{-6 - \left(1 - z\right)} - \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) - -7}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (sin (* PI z)))
        (t_1 (sqrt (+ PI PI)))
        (t_2 (pow (- (- z 7.5)) (- 0.5 z))))
   (if (<= z -0.52)
     (* (* t_1 t_2) (* (* 263.3831869810514 (exp -7.5)) (/ PI t_0)))
     (*
      (/ (* (* (* (* PI t_1) t_2) (exp z)) (exp -7.5)) t_0)
      (-
       (+ 263.3831855358925 (* 436.8961723502244 z))
       (-
        (/ 9.984369578019572e-6 (- -6.0 (- 1.0 z)))
        (/ 1.5056327351493116e-7 (- (- 1.0 z) -7.0))))))))

C

double code(double z) {
	double t_0 = sin((((double) M_PI) * z));
	double t_1 = sqrt((((double) M_PI) + ((double) M_PI)));
	double t_2 = pow(-(z - 7.5), (0.5 - z));
	double tmp;
	if (z <= -0.52) {
		tmp = (t_1 * t_2) * ((263.3831869810514 * exp(-7.5)) * (((double) M_PI) / t_0));
	} else {
		tmp = (((((((double) M_PI) * t_1) * t_2) * exp(z)) * exp(-7.5)) / t_0) * ((263.3831855358925 + (436.8961723502244 * z)) - ((9.984369578019572e-6 / (-6.0 - (1.0 - z))) - (1.5056327351493116e-7 / ((1.0 - z) - -7.0))));
	}
	return tmp;
}

Java

public static double code(double z) {
	double t_0 = Math.sin((Math.PI * z));
	double t_1 = Math.sqrt((Math.PI + Math.PI));
	double t_2 = Math.pow(-(z - 7.5), (0.5 - z));
	double tmp;
	if (z <= -0.52) {
		tmp = (t_1 * t_2) * ((263.3831869810514 * Math.exp(-7.5)) * (Math.PI / t_0));
	} else {
		tmp = (((((Math.PI * t_1) * t_2) * Math.exp(z)) * Math.exp(-7.5)) / t_0) * ((263.3831855358925 + (436.8961723502244 * z)) - ((9.984369578019572e-6 / (-6.0 - (1.0 - z))) - (1.5056327351493116e-7 / ((1.0 - z) - -7.0))));
	}
	return tmp;
}

Python

def code(z):
	t_0 = math.sin((math.pi * z))
	t_1 = math.sqrt((math.pi + math.pi))
	t_2 = math.pow(-(z - 7.5), (0.5 - z))
	tmp = 0
	if z <= -0.52:
		tmp = (t_1 * t_2) * ((263.3831869810514 * math.exp(-7.5)) * (math.pi / t_0))
	else:
		tmp = (((((math.pi * t_1) * t_2) * math.exp(z)) * math.exp(-7.5)) / t_0) * ((263.3831855358925 + (436.8961723502244 * z)) - ((9.984369578019572e-6 / (-6.0 - (1.0 - z))) - (1.5056327351493116e-7 / ((1.0 - z) - -7.0))))
	return tmp

Julia

function code(z)
	t_0 = sin(Float64(pi * z))
	t_1 = sqrt(Float64(pi + pi))
	t_2 = Float64(-Float64(z - 7.5)) ^ Float64(0.5 - z)
	tmp = 0.0
	if (z <= -0.52)
		tmp = Float64(Float64(t_1 * t_2) * Float64(Float64(263.3831869810514 * exp(-7.5)) * Float64(pi / t_0)));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(pi * t_1) * t_2) * exp(z)) * exp(-7.5)) / t_0) * Float64(Float64(263.3831855358925 + Float64(436.8961723502244 * z)) - Float64(Float64(9.984369578019572e-6 / Float64(-6.0 - Float64(1.0 - z))) - Float64(1.5056327351493116e-7 / Float64(Float64(1.0 - z) - -7.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z)
	t_0 = sin((pi * z));
	t_1 = sqrt((pi + pi));
	t_2 = -(z - 7.5) ^ (0.5 - z);
	tmp = 0.0;
	if (z <= -0.52)
		tmp = (t_1 * t_2) * ((263.3831869810514 * exp(-7.5)) * (pi / t_0));
	else
		tmp = (((((pi * t_1) * t_2) * exp(z)) * exp(-7.5)) / t_0) * ((263.3831855358925 + (436.8961723502244 * z)) - ((9.984369578019572e-6 / (-6.0 - (1.0 - z))) - (1.5056327351493116e-7 / ((1.0 - z) - -7.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[z_] := Block[{t$95$0 = N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Power[(-N[(z - 7.5), $MachinePrecision]), N[(0.5 - z), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, -0.52], N[(N[(t$95$1 * t$95$2), $MachinePrecision] * N[(N[(263.3831869810514 * N[Exp[-7.5], $MachinePrecision]), $MachinePrecision] * N[(Pi / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(Pi * t$95$1), $MachinePrecision] * t$95$2), $MachinePrecision] * N[Exp[z], $MachinePrecision]), $MachinePrecision] * N[Exp[-7.5], $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] * N[(N[(263.3831855358925 + N[(436.8961723502244 * z), $MachinePrecision]), $MachinePrecision] - N[(N[(9.984369578019572e-6 / N[(-6.0 - N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(1.5056327351493116e-7 / N[(N[(1.0 - z), $MachinePrecision] - -7.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.52000000000000002

   1. Initial program 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 96.2%

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

   if -0.52000000000000002 < z

   1. Initial program 96.4%

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

   3. Applied rewrites 98.2%

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

   5. Applied rewrites 98.2%

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

   6. Taylor expanded in z around 0

      \[\leadsto \frac{\left(\left(\left(\pi \cdot \sqrt{\pi + \pi}\right) \cdot {\left(-\left(z - \frac{15}{2}\right)\right)}^{\left(\frac{1}{2} - z\right)}\right) \cdot e^{z}\right) \cdot e^{\frac{-15}{2}}}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(\frac{9876869457595968283}{37500000000000000} + \frac{131068851705067315609}{300000000000000000} \cdot z\right)} - \left(\frac{\frac{2496092394504893}{250000000000000000000}}{-6 - \left(1 - z\right)} - \frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7}\right)\right) \]

   8. Applied rewrites 96.7%

      \[\leadsto \frac{\left(\left(\left(\pi \cdot \sqrt{\pi + \pi}\right) \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z}\right) \cdot e^{-7.5}}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(263.3831855358925 + 436.8961723502244 \cdot z\right)} - \left(\frac{9.984369578019572 \cdot 10^{-6}}{-6 - \left(1 - z\right)} - \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) - -7}\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 97.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(\pi \cdot z\right)\\ t_1 := \sqrt{\pi + \pi}\\ \mathbf{if}\;z \leq -0.52:\\ \;\;\;\;\left(t\_1 \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(263.3831869810514 \cdot e^{-7.5}\right) \cdot \frac{\pi}{t\_0}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi \cdot \left(\left(t\_1 \cdot {\left(\left(1 - z\right) - -6.5\right)}^{\left(\left(1 - z\right) - 0.5\right)}\right) \cdot e^{\left(0 + z\right) + -7.5}\right)}{t\_0} \cdot \left(\left(263.3831855358925 + 436.8961723502244 \cdot z\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{-6 - \left(1 - z\right)} - \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) - -7}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (sin (* PI z))) (t_1 (sqrt (+ PI PI))))
   (if (<= z -0.52)
     (*
      (* t_1 (pow (- (- z 7.5)) (- 0.5 z)))
      (* (* 263.3831869810514 (exp -7.5)) (/ PI t_0)))
     (*
      (/
       (*
        PI
        (*
         (* t_1 (pow (- (- 1.0 z) -6.5) (- (- 1.0 z) 0.5)))
         (exp (+ (+ 0.0 z) -7.5))))
       t_0)
      (-
       (+ 263.3831855358925 (* 436.8961723502244 z))
       (-
        (/ 9.984369578019572e-6 (- -6.0 (- 1.0 z)))
        (/ 1.5056327351493116e-7 (- (- 1.0 z) -7.0))))))))

C

double code(double z) {
	double t_0 = sin((((double) M_PI) * z));
	double t_1 = sqrt((((double) M_PI) + ((double) M_PI)));
	double tmp;
	if (z <= -0.52) {
		tmp = (t_1 * pow(-(z - 7.5), (0.5 - z))) * ((263.3831869810514 * exp(-7.5)) * (((double) M_PI) / t_0));
	} else {
		tmp = ((((double) M_PI) * ((t_1 * pow(((1.0 - z) - -6.5), ((1.0 - z) - 0.5))) * exp(((0.0 + z) + -7.5)))) / t_0) * ((263.3831855358925 + (436.8961723502244 * z)) - ((9.984369578019572e-6 / (-6.0 - (1.0 - z))) - (1.5056327351493116e-7 / ((1.0 - z) - -7.0))));
	}
	return tmp;
}

Java

public static double code(double z) {
	double t_0 = Math.sin((Math.PI * z));
	double t_1 = Math.sqrt((Math.PI + Math.PI));
	double tmp;
	if (z <= -0.52) {
		tmp = (t_1 * Math.pow(-(z - 7.5), (0.5 - z))) * ((263.3831869810514 * Math.exp(-7.5)) * (Math.PI / t_0));
	} else {
		tmp = ((Math.PI * ((t_1 * Math.pow(((1.0 - z) - -6.5), ((1.0 - z) - 0.5))) * Math.exp(((0.0 + z) + -7.5)))) / t_0) * ((263.3831855358925 + (436.8961723502244 * z)) - ((9.984369578019572e-6 / (-6.0 - (1.0 - z))) - (1.5056327351493116e-7 / ((1.0 - z) - -7.0))));
	}
	return tmp;
}

Python

def code(z):
	t_0 = math.sin((math.pi * z))
	t_1 = math.sqrt((math.pi + math.pi))
	tmp = 0
	if z <= -0.52:
		tmp = (t_1 * math.pow(-(z - 7.5), (0.5 - z))) * ((263.3831869810514 * math.exp(-7.5)) * (math.pi / t_0))
	else:
		tmp = ((math.pi * ((t_1 * math.pow(((1.0 - z) - -6.5), ((1.0 - z) - 0.5))) * math.exp(((0.0 + z) + -7.5)))) / t_0) * ((263.3831855358925 + (436.8961723502244 * z)) - ((9.984369578019572e-6 / (-6.0 - (1.0 - z))) - (1.5056327351493116e-7 / ((1.0 - z) - -7.0))))
	return tmp

Julia

function code(z)
	t_0 = sin(Float64(pi * z))
	t_1 = sqrt(Float64(pi + pi))
	tmp = 0.0
	if (z <= -0.52)
		tmp = Float64(Float64(t_1 * (Float64(-Float64(z - 7.5)) ^ Float64(0.5 - z))) * Float64(Float64(263.3831869810514 * exp(-7.5)) * Float64(pi / t_0)));
	else
		tmp = Float64(Float64(Float64(pi * Float64(Float64(t_1 * (Float64(Float64(1.0 - z) - -6.5) ^ Float64(Float64(1.0 - z) - 0.5))) * exp(Float64(Float64(0.0 + z) + -7.5)))) / t_0) * Float64(Float64(263.3831855358925 + Float64(436.8961723502244 * z)) - Float64(Float64(9.984369578019572e-6 / Float64(-6.0 - Float64(1.0 - z))) - Float64(1.5056327351493116e-7 / Float64(Float64(1.0 - z) - -7.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z)
	t_0 = sin((pi * z));
	t_1 = sqrt((pi + pi));
	tmp = 0.0;
	if (z <= -0.52)
		tmp = (t_1 * (-(z - 7.5) ^ (0.5 - z))) * ((263.3831869810514 * exp(-7.5)) * (pi / t_0));
	else
		tmp = ((pi * ((t_1 * (((1.0 - z) - -6.5) ^ ((1.0 - z) - 0.5))) * exp(((0.0 + z) + -7.5)))) / t_0) * ((263.3831855358925 + (436.8961723502244 * z)) - ((9.984369578019572e-6 / (-6.0 - (1.0 - z))) - (1.5056327351493116e-7 / ((1.0 - z) - -7.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[z_] := Block[{t$95$0 = N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, -0.52], N[(N[(t$95$1 * N[Power[(-N[(z - 7.5), $MachinePrecision]), N[(0.5 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(263.3831869810514 * N[Exp[-7.5], $MachinePrecision]), $MachinePrecision] * N[(Pi / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(Pi * N[(N[(t$95$1 * N[Power[N[(N[(1.0 - z), $MachinePrecision] - -6.5), $MachinePrecision], N[(N[(1.0 - z), $MachinePrecision] - 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Exp[N[(N[(0.0 + z), $MachinePrecision] + -7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] * N[(N[(263.3831855358925 + N[(436.8961723502244 * z), $MachinePrecision]), $MachinePrecision] - N[(N[(9.984369578019572e-6 / N[(-6.0 - N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(1.5056327351493116e-7 / N[(N[(1.0 - z), $MachinePrecision] - -7.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.52000000000000002

   1. Initial program 96.4%

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

   3. Applied rewrites 98.3%

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 96.2%

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

   if -0.52000000000000002 < z

   1. Initial program 96.4%

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

   3. Applied rewrites 98.2%

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

   4. Taylor expanded in z around 0

      \[\leadsto \frac{\pi \cdot \left(\left(\sqrt{\pi + \pi} \cdot {\left(\left(1 - z\right) - \frac{-13}{2}\right)}^{\left(\left(1 - z\right) - \frac{1}{2}\right)}\right) \cdot e^{\left(0 + z\right) + \frac{-15}{2}}\right)}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(\frac{9876869457595968283}{37500000000000000} + \frac{131068851705067315609}{300000000000000000} \cdot z\right)} - \left(\frac{\frac{2496092394504893}{250000000000000000000}}{-6 - \left(1 - z\right)} - \frac{\frac{3764081837873279}{25000000000000000000000}}{\left(1 - z\right) - -7}\right)\right) \]

   6. Applied rewrites 96.7%

      \[\leadsto \frac{\pi \cdot \left(\left(\sqrt{\pi + \pi} \cdot {\left(\left(1 - z\right) - -6.5\right)}^{\left(\left(1 - z\right) - 0.5\right)}\right) \cdot e^{\left(0 + z\right) + -7.5}\right)}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(263.3831855358925 + 436.8961723502244 \cdot z\right)} - \left(\frac{9.984369578019572 \cdot 10^{-6}}{-6 - \left(1 - z\right)} - \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) - -7}\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 96.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(263.3831869810514 \cdot e^{-7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right) \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.4%

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

3. Applied rewrites 98.3%

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

5. Applied rewrites 97.5%

   \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

6. Taylor expanded in z around 0

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

8. Applied rewrites 96.2%

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

Alternative 17: 95.7% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(263.3831869810514 \cdot \frac{e^{-7.5}}{z}\right) \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.4%

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

3. Applied rewrites 98.3%

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

5. Applied rewrites 97.5%

   \[\leadsto \color{blue}{\left(\sqrt{\pi + \pi} \cdot {\left(-\left(z - 7.5\right)\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\frac{-676.5203681218851}{z - 1} - -0.9999999999998099\right) - \frac{-1259.1392167224028}{z - 2}\right) - \frac{771.3234287776531}{z - 3}\right) - \frac{176.6150291621406}{4 - z}\right) - \left(\left(\frac{12.507343278686905}{z - 5} - \frac{-0.13857109526572012}{6 - z}\right) - \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} - \frac{-1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) \cdot e^{z - 7.5}\right) \cdot \frac{\pi}{\sin \left(\pi \cdot z\right)}\right)} \]

6. Taylor expanded in z around 0

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

8. Applied rewrites 95.7%

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

Alternative 18: 95.5% accurate, 8.1× speedup

Math

\[\begin{array}{l} \\ 263.3831869810514 \cdot \frac{e^{-7.5} \cdot \sqrt{\left(\pi + \pi\right) \cdot 7.5}}{z} \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (* 263.3831869810514 (/ (* (exp -7.5) (sqrt (* (+ PI PI) 7.5))) z)))

C

double code(double z) {
	return 263.3831869810514 * ((exp(-7.5) * sqrt(((((double) M_PI) + ((double) M_PI)) * 7.5))) / z);
}

Java

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

Python

def code(z):
	return 263.3831869810514 * ((math.exp(-7.5) * math.sqrt(((math.pi + math.pi) * 7.5))) / z)

Julia

function code(z)
	return Float64(263.3831869810514 * Float64(Float64(exp(-7.5) * sqrt(Float64(Float64(pi + pi) * 7.5))) / z))
end

MATLAB

function tmp = code(z)
	tmp = 263.3831869810514 * ((exp(-7.5) * sqrt(((pi + pi) * 7.5))) / z);
end

Wolfram

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

Derivation

1. Initial program 96.4%

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

2. Taylor expanded in z around 0

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

4. Applied rewrites 95.5%

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

6. Applied rewrites 95.5%

   \[\leadsto 263.3831869810514 \cdot \frac{e^{-7.5} \cdot \sqrt{\left(\pi + \pi\right) \cdot 7.5}}{z} \]
7. Add Preprocessing

Alternative 19: 17.7% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\sqrt{\pi + \pi} \cdot 1975.3739023578855\right) \cdot e^{-7.5}}{z} \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (/ (* (* (sqrt (+ PI PI)) 1975.3739023578855) (exp -7.5)) z))

C

double code(double z) {
	return ((sqrt((((double) M_PI) + ((double) M_PI))) * 1975.3739023578855) * exp(-7.5)) / z;
}

Java

public static double code(double z) {
	return ((Math.sqrt((Math.PI + Math.PI)) * 1975.3739023578855) * Math.exp(-7.5)) / z;
}

Python

def code(z):
	return ((math.sqrt((math.pi + math.pi)) * 1975.3739023578855) * math.exp(-7.5)) / z

Julia

function code(z)
	return Float64(Float64(Float64(sqrt(Float64(pi + pi)) * 1975.3739023578855) * exp(-7.5)) / z)
end

MATLAB

function tmp = code(z)
	tmp = ((sqrt((pi + pi)) * 1975.3739023578855) * exp(-7.5)) / z;
end

Wolfram

code[z_] := N[(N[(N[(N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision] * 1975.3739023578855), $MachinePrecision] * N[Exp[-7.5], $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Derivation

1. Initial program 96.4%

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

2. Taylor expanded in z around 0

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

4. Applied rewrites 95.5%

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

6. Applied rewrites 17.7%

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

8. Applied rewrites 17.7%

   \[\leadsto e^{-7.5} \cdot \color{blue}{\left(\sqrt{\pi + \pi} \cdot \frac{1975.3739023578855}{z}\right)} \]

10. Applied rewrites 17.7%

    \[\leadsto \frac{\left(\sqrt{\pi + \pi} \cdot 1975.3739023578855\right) \cdot e^{-7.5}}{\color{blue}{z}} \]
11. Add Preprocessing

Alternative 20: 17.7% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \left(e^{-7.5} \cdot \frac{1975.3739023578855}{z}\right) \cdot \sqrt{\pi + \pi} \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (* (* (exp -7.5) (/ 1975.3739023578855 z)) (sqrt (+ PI PI))))

C

double code(double z) {
	return (exp(-7.5) * (1975.3739023578855 / z)) * sqrt((((double) M_PI) + ((double) M_PI)));
}

Java

public static double code(double z) {
	return (Math.exp(-7.5) * (1975.3739023578855 / z)) * Math.sqrt((Math.PI + Math.PI));
}

Python

def code(z):
	return (math.exp(-7.5) * (1975.3739023578855 / z)) * math.sqrt((math.pi + math.pi))

Julia

function code(z)
	return Float64(Float64(exp(-7.5) * Float64(1975.3739023578855 / z)) * sqrt(Float64(pi + pi)))
end

MATLAB

function tmp = code(z)
	tmp = (exp(-7.5) * (1975.3739023578855 / z)) * sqrt((pi + pi));
end

Wolfram

code[z_] := N[(N[(N[Exp[-7.5], $MachinePrecision] * N[(1975.3739023578855 / z), $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(Pi + Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.4%

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

2. Taylor expanded in z around 0

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

4. Applied rewrites 95.5%

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

6. Applied rewrites 17.7%

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

8. Applied rewrites 17.7%

   \[\leadsto e^{-7.5} \cdot \color{blue}{\left(\sqrt{\pi + \pi} \cdot \frac{1975.3739023578855}{z}\right)} \]

10. Applied rewrites 17.7%

    \[\leadsto \left(e^{-7.5} \cdot \frac{1975.3739023578855}{z}\right) \cdot \color{blue}{\sqrt{\pi + \pi}} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2025161 
(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))))))