Jmat.Real.gamma, branch z less than 0.5

Percentage Accurate: 96.4% → 97.7%

Time: 1.4min

Alternatives: 11

Speedup: 1.1×

• could not determine a ground truth

  1. z = -3.5166441544201094e+123

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: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt[3]{2 \cdot \pi}\\ \left({\left(\left(1 - z\right) + 6.5\right)}^{\left(1 - \left(z + 0.5\right)\right)} \cdot \left(\left(\left|t_0\right| \cdot \sqrt{t_0}\right) \cdot e^{\left(z + -1\right) - 6.5}\right)\right) \cdot \left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \left(\frac{-1259.1392167224028}{3 + \left(-1 - z\right)} + \left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{\left(1 - z\right) + 3}\right)\right)\right) + \left(\left(\frac{12.507343278686905}{\left(1 - z\right) + 4} + \frac{-0.13857109526572012}{1 - \left(z + -5\right)}\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{8 + \left(-1 - z\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{9 + \left(-1 - z\right)}\right)\right)\right) \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right) \end{array} \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (cbrt (* 2.0 PI))))
   (*
    (*
     (pow (+ (- 1.0 z) 6.5) (- 1.0 (+ z 0.5)))
     (* (* (fabs t_0) (sqrt t_0)) (exp (- (+ z -1.0) 6.5))))
    (*
     (+
      (+
       (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))
       (+
        (/ -1259.1392167224028 (+ 3.0 (- -1.0 z)))
        (+
         (/ 771.3234287776531 (- 1.0 (+ z -2.0)))
         (/ -176.6150291621406 (+ (- 1.0 z) 3.0)))))
      (+
       (+
        (/ 12.507343278686905 (+ (- 1.0 z) 4.0))
        (/ -0.13857109526572012 (- 1.0 (+ z -5.0))))
       (+
        (/ 9.984369578019572e-6 (+ 8.0 (- -1.0 z)))
        (/ 1.5056327351493116e-7 (+ 9.0 (- -1.0 z))))))
     (/ PI (sin (* z PI)))))))

C

double code(double z) {
	double t_0 = cbrt((2.0 * ((double) M_PI)));
	return (pow(((1.0 - z) + 6.5), (1.0 - (z + 0.5))) * ((fabs(t_0) * sqrt(t_0)) * exp(((z + -1.0) - 6.5)))) * ((((0.9999999999998099 + (676.5203681218851 / (1.0 - z))) + ((-1259.1392167224028 / (3.0 + (-1.0 - z))) + ((771.3234287776531 / (1.0 - (z + -2.0))) + (-176.6150291621406 / ((1.0 - z) + 3.0))))) + (((12.507343278686905 / ((1.0 - z) + 4.0)) + (-0.13857109526572012 / (1.0 - (z + -5.0)))) + ((9.984369578019572e-6 / (8.0 + (-1.0 - z))) + (1.5056327351493116e-7 / (9.0 + (-1.0 - z)))))) * (((double) M_PI) / sin((z * ((double) M_PI)))));
}

Java

public static double code(double z) {
	double t_0 = Math.cbrt((2.0 * Math.PI));
	return (Math.pow(((1.0 - z) + 6.5), (1.0 - (z + 0.5))) * ((Math.abs(t_0) * Math.sqrt(t_0)) * Math.exp(((z + -1.0) - 6.5)))) * ((((0.9999999999998099 + (676.5203681218851 / (1.0 - z))) + ((-1259.1392167224028 / (3.0 + (-1.0 - z))) + ((771.3234287776531 / (1.0 - (z + -2.0))) + (-176.6150291621406 / ((1.0 - z) + 3.0))))) + (((12.507343278686905 / ((1.0 - z) + 4.0)) + (-0.13857109526572012 / (1.0 - (z + -5.0)))) + ((9.984369578019572e-6 / (8.0 + (-1.0 - z))) + (1.5056327351493116e-7 / (9.0 + (-1.0 - z)))))) * (Math.PI / Math.sin((z * Math.PI))));
}

Julia

function code(z)
	t_0 = cbrt(Float64(2.0 * pi))
	return Float64(Float64((Float64(Float64(1.0 - z) + 6.5) ^ Float64(1.0 - Float64(z + 0.5))) * Float64(Float64(abs(t_0) * sqrt(t_0)) * exp(Float64(Float64(z + -1.0) - 6.5)))) * Float64(Float64(Float64(Float64(0.9999999999998099 + Float64(676.5203681218851 / Float64(1.0 - z))) + Float64(Float64(-1259.1392167224028 / Float64(3.0 + Float64(-1.0 - z))) + Float64(Float64(771.3234287776531 / Float64(1.0 - Float64(z + -2.0))) + Float64(-176.6150291621406 / Float64(Float64(1.0 - z) + 3.0))))) + Float64(Float64(Float64(12.507343278686905 / Float64(Float64(1.0 - z) + 4.0)) + Float64(-0.13857109526572012 / Float64(1.0 - Float64(z + -5.0)))) + Float64(Float64(9.984369578019572e-6 / Float64(8.0 + Float64(-1.0 - z))) + Float64(1.5056327351493116e-7 / Float64(9.0 + Float64(-1.0 - z)))))) * Float64(pi / sin(Float64(z * pi)))))
end

Wolfram

code[z_] := Block[{t$95$0 = N[Power[N[(2.0 * Pi), $MachinePrecision], 1/3], $MachinePrecision]}, N[(N[(N[Power[N[(N[(1.0 - z), $MachinePrecision] + 6.5), $MachinePrecision], N[(1.0 - N[(z + 0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(N[(N[Abs[t$95$0], $MachinePrecision] * N[Sqrt[t$95$0], $MachinePrecision]), $MachinePrecision] * N[Exp[N[(N[(z + -1.0), $MachinePrecision] - 6.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(0.9999999999998099 + N[(676.5203681218851 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-1259.1392167224028 / N[(3.0 + N[(-1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(771.3234287776531 / N[(1.0 - N[(z + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-176.6150291621406 / N[(N[(1.0 - z), $MachinePrecision] + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(12.507343278686905 / N[(N[(1.0 - z), $MachinePrecision] + 4.0), $MachinePrecision]), $MachinePrecision] + N[(-0.13857109526572012 / N[(1.0 - N[(z + -5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(9.984369578019572e-6 / N[(8.0 + N[(-1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(9.0 + N[(-1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(Pi / N[Sin[N[(z * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 99.3%

   \[\left({\left(\left(1 - z\right) + 6.5\right)}^{\left(1 - \left(z + 0.5\right)\right)} \cdot \left(\left(\left|\sqrt[3]{2 \cdot \pi}\right| \cdot \sqrt{\sqrt[3]{2 \cdot \pi}}\right) \cdot e^{\left(z + -1\right) - 6.5}\right)\right) \cdot \left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \left(\frac{-1259.1392167224028}{3 + \left(-1 - z\right)} + \left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{\left(1 - z\right) + 3}\right)\right)\right) + \left(\left(\frac{12.507343278686905}{\left(1 - z\right) + 4} + \frac{-0.13857109526572012}{1 - \left(z + -5\right)}\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{8 + \left(-1 - z\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{9 + \left(-1 - z\right)}\right)\right)\right) \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right) \]

Alternative 2: 98.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right) + {\left({\left(\frac{-0.13857109526572012}{6 - z} + \left(\frac{676.5203681218851}{1 - z} + \left(0.9999999999998099 + \left(\frac{771.3234287776531}{3 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)}^{3}\right)}^{0.3333333333333333}\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right) \cdot \left(e^{z + -7.5} \cdot \frac{\sqrt{2 \cdot \pi} \cdot \left(\pi \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right)}{\sin \left(z \cdot \pi\right)}\right) \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (*
  (+
   (+
    (+ (/ -176.6150291621406 (- 4.0 z)) (/ 12.507343278686905 (- 5.0 z)))
    (pow
     (pow
      (+
       (/ -0.13857109526572012 (- 6.0 z))
       (+
        (/ 676.5203681218851 (- 1.0 z))
        (+
         0.9999999999998099
         (+
          (/ 771.3234287776531 (- 3.0 z))
          (/ -1259.1392167224028 (- 2.0 z))))))
      3.0)
     0.3333333333333333))
   (+ (/ 9.984369578019572e-6 (- 7.0 z)) (/ 1.5056327351493116e-7 (- 8.0 z))))
  (*
   (exp (+ z -7.5))
   (/ (* (sqrt (* 2.0 PI)) (* PI (pow (- 7.5 z) (- 0.5 z)))) (sin (* z PI))))))

C

double code(double z) {
	return ((((-176.6150291621406 / (4.0 - z)) + (12.507343278686905 / (5.0 - z))) + pow(pow(((-0.13857109526572012 / (6.0 - z)) + ((676.5203681218851 / (1.0 - z)) + (0.9999999999998099 + ((771.3234287776531 / (3.0 - z)) + (-1259.1392167224028 / (2.0 - z)))))), 3.0), 0.3333333333333333)) + ((9.984369578019572e-6 / (7.0 - z)) + (1.5056327351493116e-7 / (8.0 - z)))) * (exp((z + -7.5)) * ((sqrt((2.0 * ((double) M_PI))) * (((double) M_PI) * pow((7.5 - z), (0.5 - z)))) / sin((z * ((double) M_PI)))));
}

Java

public static double code(double z) {
	return ((((-176.6150291621406 / (4.0 - z)) + (12.507343278686905 / (5.0 - z))) + Math.pow(Math.pow(((-0.13857109526572012 / (6.0 - z)) + ((676.5203681218851 / (1.0 - z)) + (0.9999999999998099 + ((771.3234287776531 / (3.0 - z)) + (-1259.1392167224028 / (2.0 - z)))))), 3.0), 0.3333333333333333)) + ((9.984369578019572e-6 / (7.0 - z)) + (1.5056327351493116e-7 / (8.0 - z)))) * (Math.exp((z + -7.5)) * ((Math.sqrt((2.0 * Math.PI)) * (Math.PI * Math.pow((7.5 - z), (0.5 - z)))) / Math.sin((z * Math.PI))));
}

Python

def code(z):
	return ((((-176.6150291621406 / (4.0 - z)) + (12.507343278686905 / (5.0 - z))) + math.pow(math.pow(((-0.13857109526572012 / (6.0 - z)) + ((676.5203681218851 / (1.0 - z)) + (0.9999999999998099 + ((771.3234287776531 / (3.0 - z)) + (-1259.1392167224028 / (2.0 - z)))))), 3.0), 0.3333333333333333)) + ((9.984369578019572e-6 / (7.0 - z)) + (1.5056327351493116e-7 / (8.0 - z)))) * (math.exp((z + -7.5)) * ((math.sqrt((2.0 * math.pi)) * (math.pi * math.pow((7.5 - z), (0.5 - z)))) / math.sin((z * math.pi))))

Julia

function code(z)
	return Float64(Float64(Float64(Float64(Float64(-176.6150291621406 / Float64(4.0 - z)) + Float64(12.507343278686905 / Float64(5.0 - z))) + ((Float64(Float64(-0.13857109526572012 / Float64(6.0 - z)) + Float64(Float64(676.5203681218851 / Float64(1.0 - z)) + Float64(0.9999999999998099 + Float64(Float64(771.3234287776531 / Float64(3.0 - z)) + Float64(-1259.1392167224028 / Float64(2.0 - z)))))) ^ 3.0) ^ 0.3333333333333333)) + Float64(Float64(9.984369578019572e-6 / Float64(7.0 - z)) + Float64(1.5056327351493116e-7 / Float64(8.0 - z)))) * Float64(exp(Float64(z + -7.5)) * Float64(Float64(sqrt(Float64(2.0 * pi)) * Float64(pi * (Float64(7.5 - z) ^ Float64(0.5 - z)))) / sin(Float64(z * pi)))))
end

MATLAB

function tmp = code(z)
	tmp = ((((-176.6150291621406 / (4.0 - z)) + (12.507343278686905 / (5.0 - z))) + ((((-0.13857109526572012 / (6.0 - z)) + ((676.5203681218851 / (1.0 - z)) + (0.9999999999998099 + ((771.3234287776531 / (3.0 - z)) + (-1259.1392167224028 / (2.0 - z)))))) ^ 3.0) ^ 0.3333333333333333)) + ((9.984369578019572e-6 / (7.0 - z)) + (1.5056327351493116e-7 / (8.0 - z)))) * (exp((z + -7.5)) * ((sqrt((2.0 * pi)) * (pi * ((7.5 - z) ^ (0.5 - z)))) / sin((z * pi))));
end

Wolfram

code[z_] := N[(N[(N[(N[(N[(-176.6150291621406 / N[(4.0 - z), $MachinePrecision]), $MachinePrecision] + N[(12.507343278686905 / N[(5.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[Power[N[Power[N[(N[(-0.13857109526572012 / N[(6.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(676.5203681218851 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(0.9999999999998099 + N[(N[(771.3234287776531 / N[(3.0 - z), $MachinePrecision]), $MachinePrecision] + N[(-1259.1392167224028 / N[(2.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], 0.3333333333333333], $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] * N[(N[Exp[N[(z + -7.5), $MachinePrecision]], $MachinePrecision] * N[(N[(N[Sqrt[N[(2.0 * Pi), $MachinePrecision]], $MachinePrecision] * N[(Pi * N[Power[N[(7.5 - z), $MachinePrecision], N[(0.5 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Sin[N[(z * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.2%

   \[\left(\left(\left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right) + {\left({\left(\frac{-0.13857109526572012}{6 - z} + \left(\frac{676.5203681218851}{1 - z} + \left(0.9999999999998099 + \left(\frac{771.3234287776531}{3 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)}^{3}\right)}^{0.3333333333333333}\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right) \cdot \left(e^{z + -7.5} \cdot \frac{\sqrt{2 \cdot \pi} \cdot \left(\pi \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right)}{\sin \left(z \cdot \pi\right)}\right) \]

Alternative 3: 97.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \left({\left(\left(1 - z\right) + 6.5\right)}^{\left(1 - \left(z + 0.5\right)\right)} \cdot \left(\sqrt{2 \cdot \pi} \cdot e^{-6.5 + \left(z + -1\right)}\right)\right) \cdot \left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \left(\frac{-1259.1392167224028}{3 + \left(-1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} + \frac{771.3234287776531}{3 - z}\right)\right)\right) + \left(\left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right) + \left(\frac{12.507343278686905}{5 - z} + \frac{-0.13857109526572012}{6 - z}\right)\right)\right)\right) \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (*
  (*
   (pow (+ (- 1.0 z) 6.5) (- 1.0 (+ z 0.5)))
   (* (sqrt (* 2.0 PI)) (exp (+ -6.5 (+ z -1.0)))))
  (*
   (/ PI (sin (* z PI)))
   (+
    (+
     (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))
     (+
      (/ -1259.1392167224028 (+ 3.0 (- -1.0 z)))
      (+ (/ -176.6150291621406 (- 4.0 z)) (/ 771.3234287776531 (- 3.0 z)))))
    (+
     (+ (/ 9.984369578019572e-6 (- 7.0 z)) (/ 1.5056327351493116e-7 (- 8.0 z)))
     (+
      (/ 12.507343278686905 (- 5.0 z))
      (/ -0.13857109526572012 (- 6.0 z))))))))

C

double code(double z) {
	return (pow(((1.0 - z) + 6.5), (1.0 - (z + 0.5))) * (sqrt((2.0 * ((double) M_PI))) * exp((-6.5 + (z + -1.0))))) * ((((double) M_PI) / sin((z * ((double) M_PI)))) * (((0.9999999999998099 + (676.5203681218851 / (1.0 - z))) + ((-1259.1392167224028 / (3.0 + (-1.0 - z))) + ((-176.6150291621406 / (4.0 - z)) + (771.3234287776531 / (3.0 - z))))) + (((9.984369578019572e-6 / (7.0 - z)) + (1.5056327351493116e-7 / (8.0 - z))) + ((12.507343278686905 / (5.0 - z)) + (-0.13857109526572012 / (6.0 - z))))));
}

Java

public static double code(double z) {
	return (Math.pow(((1.0 - z) + 6.5), (1.0 - (z + 0.5))) * (Math.sqrt((2.0 * Math.PI)) * Math.exp((-6.5 + (z + -1.0))))) * ((Math.PI / Math.sin((z * Math.PI))) * (((0.9999999999998099 + (676.5203681218851 / (1.0 - z))) + ((-1259.1392167224028 / (3.0 + (-1.0 - z))) + ((-176.6150291621406 / (4.0 - z)) + (771.3234287776531 / (3.0 - z))))) + (((9.984369578019572e-6 / (7.0 - z)) + (1.5056327351493116e-7 / (8.0 - z))) + ((12.507343278686905 / (5.0 - z)) + (-0.13857109526572012 / (6.0 - z))))));
}

Python

def code(z):
	return (math.pow(((1.0 - z) + 6.5), (1.0 - (z + 0.5))) * (math.sqrt((2.0 * math.pi)) * math.exp((-6.5 + (z + -1.0))))) * ((math.pi / math.sin((z * math.pi))) * (((0.9999999999998099 + (676.5203681218851 / (1.0 - z))) + ((-1259.1392167224028 / (3.0 + (-1.0 - z))) + ((-176.6150291621406 / (4.0 - z)) + (771.3234287776531 / (3.0 - z))))) + (((9.984369578019572e-6 / (7.0 - z)) + (1.5056327351493116e-7 / (8.0 - z))) + ((12.507343278686905 / (5.0 - z)) + (-0.13857109526572012 / (6.0 - z))))))

Julia

function code(z)
	return Float64(Float64((Float64(Float64(1.0 - z) + 6.5) ^ Float64(1.0 - Float64(z + 0.5))) * Float64(sqrt(Float64(2.0 * pi)) * exp(Float64(-6.5 + Float64(z + -1.0))))) * Float64(Float64(pi / sin(Float64(z * pi))) * Float64(Float64(Float64(0.9999999999998099 + Float64(676.5203681218851 / Float64(1.0 - z))) + Float64(Float64(-1259.1392167224028 / Float64(3.0 + Float64(-1.0 - z))) + Float64(Float64(-176.6150291621406 / Float64(4.0 - z)) + Float64(771.3234287776531 / Float64(3.0 - z))))) + Float64(Float64(Float64(9.984369578019572e-6 / Float64(7.0 - z)) + Float64(1.5056327351493116e-7 / Float64(8.0 - z))) + Float64(Float64(12.507343278686905 / Float64(5.0 - z)) + Float64(-0.13857109526572012 / Float64(6.0 - z)))))))
end

MATLAB

function tmp = code(z)
	tmp = ((((1.0 - z) + 6.5) ^ (1.0 - (z + 0.5))) * (sqrt((2.0 * pi)) * exp((-6.5 + (z + -1.0))))) * ((pi / sin((z * pi))) * (((0.9999999999998099 + (676.5203681218851 / (1.0 - z))) + ((-1259.1392167224028 / (3.0 + (-1.0 - z))) + ((-176.6150291621406 / (4.0 - z)) + (771.3234287776531 / (3.0 - z))))) + (((9.984369578019572e-6 / (7.0 - z)) + (1.5056327351493116e-7 / (8.0 - z))) + ((12.507343278686905 / (5.0 - z)) + (-0.13857109526572012 / (6.0 - z))))));
end

Wolfram

code[z_] := N[(N[(N[Power[N[(N[(1.0 - z), $MachinePrecision] + 6.5), $MachinePrecision], N[(1.0 - N[(z + 0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(N[Sqrt[N[(2.0 * Pi), $MachinePrecision]], $MachinePrecision] * N[Exp[N[(-6.5 + N[(z + -1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(Pi / N[Sin[N[(z * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(N[(0.9999999999998099 + N[(676.5203681218851 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-1259.1392167224028 / N[(3.0 + N[(-1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-176.6150291621406 / N[(4.0 - z), $MachinePrecision]), $MachinePrecision] + N[(771.3234287776531 / N[(3.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(9.984369578019572e-6 / N[(7.0 - z), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(8.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(12.507343278686905 / N[(5.0 - z), $MachinePrecision]), $MachinePrecision] + N[(-0.13857109526572012 / N[(6.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.9%

   \[\left({\left(\left(1 - z\right) + 6.5\right)}^{\left(1 - \left(z + 0.5\right)\right)} \cdot \left(\sqrt{2 \cdot \pi} \cdot e^{-6.5 + \left(z + -1\right)}\right)\right) \cdot \left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \left(\frac{-1259.1392167224028}{3 + \left(-1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} + \frac{771.3234287776531}{3 - z}\right)\right)\right) + \left(\left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right) + \left(\frac{12.507343278686905}{5 - z} + \frac{-0.13857109526572012}{6 - z}\right)\right)\right)\right) \]

Alternative 4: 97.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \left({\left(\left(1 - z\right) + 6.5\right)}^{\left(1 - \left(z + 0.5\right)\right)} \cdot \left(e^{\left(z + -1\right) - 6.5} \cdot \sqrt{2 \cdot \pi}\right)\right) \cdot \left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\left(\left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right) + \left(\frac{12.507343278686905}{5 - z} + \frac{-0.13857109526572012}{6 - z}\right)\right) + \left(\left(\frac{-176.6150291621406}{4 - z} + \frac{771.3234287776531}{3 - z}\right) + \left(\frac{676.5203681218851}{1 - z} + \left(0.9999999999998099 + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (*
  (*
   (pow (+ (- 1.0 z) 6.5) (- 1.0 (+ z 0.5)))
   (* (exp (- (+ z -1.0) 6.5)) (sqrt (* 2.0 PI))))
  (*
   (/ PI (sin (* z PI)))
   (+
    (+
     (+ (/ 9.984369578019572e-6 (- 7.0 z)) (/ 1.5056327351493116e-7 (- 8.0 z)))
     (+ (/ 12.507343278686905 (- 5.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
    (+
     (+ (/ -176.6150291621406 (- 4.0 z)) (/ 771.3234287776531 (- 3.0 z)))
     (+
      (/ 676.5203681218851 (- 1.0 z))
      (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2.0 z)))))))))

C

double code(double z) {
	return (pow(((1.0 - z) + 6.5), (1.0 - (z + 0.5))) * (exp(((z + -1.0) - 6.5)) * sqrt((2.0 * ((double) M_PI))))) * ((((double) M_PI) / sin((z * ((double) M_PI)))) * ((((9.984369578019572e-6 / (7.0 - z)) + (1.5056327351493116e-7 / (8.0 - z))) + ((12.507343278686905 / (5.0 - z)) + (-0.13857109526572012 / (6.0 - z)))) + (((-176.6150291621406 / (4.0 - z)) + (771.3234287776531 / (3.0 - z))) + ((676.5203681218851 / (1.0 - z)) + (0.9999999999998099 + (-1259.1392167224028 / (2.0 - z)))))));
}

Java

public static double code(double z) {
	return (Math.pow(((1.0 - z) + 6.5), (1.0 - (z + 0.5))) * (Math.exp(((z + -1.0) - 6.5)) * Math.sqrt((2.0 * Math.PI)))) * ((Math.PI / Math.sin((z * Math.PI))) * ((((9.984369578019572e-6 / (7.0 - z)) + (1.5056327351493116e-7 / (8.0 - z))) + ((12.507343278686905 / (5.0 - z)) + (-0.13857109526572012 / (6.0 - z)))) + (((-176.6150291621406 / (4.0 - z)) + (771.3234287776531 / (3.0 - z))) + ((676.5203681218851 / (1.0 - z)) + (0.9999999999998099 + (-1259.1392167224028 / (2.0 - z)))))));
}

Python

def code(z):
	return (math.pow(((1.0 - z) + 6.5), (1.0 - (z + 0.5))) * (math.exp(((z + -1.0) - 6.5)) * math.sqrt((2.0 * math.pi)))) * ((math.pi / math.sin((z * math.pi))) * ((((9.984369578019572e-6 / (7.0 - z)) + (1.5056327351493116e-7 / (8.0 - z))) + ((12.507343278686905 / (5.0 - z)) + (-0.13857109526572012 / (6.0 - z)))) + (((-176.6150291621406 / (4.0 - z)) + (771.3234287776531 / (3.0 - z))) + ((676.5203681218851 / (1.0 - z)) + (0.9999999999998099 + (-1259.1392167224028 / (2.0 - z)))))))

Julia

function code(z)
	return Float64(Float64((Float64(Float64(1.0 - z) + 6.5) ^ Float64(1.0 - Float64(z + 0.5))) * Float64(exp(Float64(Float64(z + -1.0) - 6.5)) * sqrt(Float64(2.0 * pi)))) * Float64(Float64(pi / sin(Float64(z * pi))) * Float64(Float64(Float64(Float64(9.984369578019572e-6 / Float64(7.0 - z)) + Float64(1.5056327351493116e-7 / Float64(8.0 - z))) + Float64(Float64(12.507343278686905 / Float64(5.0 - z)) + Float64(-0.13857109526572012 / Float64(6.0 - z)))) + Float64(Float64(Float64(-176.6150291621406 / Float64(4.0 - z)) + Float64(771.3234287776531 / Float64(3.0 - z))) + Float64(Float64(676.5203681218851 / Float64(1.0 - z)) + Float64(0.9999999999998099 + Float64(-1259.1392167224028 / Float64(2.0 - z))))))))
end

MATLAB

function tmp = code(z)
	tmp = ((((1.0 - z) + 6.5) ^ (1.0 - (z + 0.5))) * (exp(((z + -1.0) - 6.5)) * sqrt((2.0 * pi)))) * ((pi / sin((z * pi))) * ((((9.984369578019572e-6 / (7.0 - z)) + (1.5056327351493116e-7 / (8.0 - z))) + ((12.507343278686905 / (5.0 - z)) + (-0.13857109526572012 / (6.0 - z)))) + (((-176.6150291621406 / (4.0 - z)) + (771.3234287776531 / (3.0 - z))) + ((676.5203681218851 / (1.0 - z)) + (0.9999999999998099 + (-1259.1392167224028 / (2.0 - z)))))));
end

Wolfram

code[z_] := N[(N[(N[Power[N[(N[(1.0 - z), $MachinePrecision] + 6.5), $MachinePrecision], N[(1.0 - N[(z + 0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(N[Exp[N[(N[(z + -1.0), $MachinePrecision] - 6.5), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(2.0 * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(Pi / N[Sin[N[(z * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(9.984369578019572e-6 / N[(7.0 - z), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(8.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(12.507343278686905 / N[(5.0 - z), $MachinePrecision]), $MachinePrecision] + N[(-0.13857109526572012 / N[(6.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(-176.6150291621406 / N[(4.0 - z), $MachinePrecision]), $MachinePrecision] + N[(771.3234287776531 / N[(3.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(676.5203681218851 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(0.9999999999998099 + N[(-1259.1392167224028 / N[(2.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.9%

   \[\left({\left(\left(1 - z\right) + 6.5\right)}^{\left(1 - \left(z + 0.5\right)\right)} \cdot \left(e^{\left(z + -1\right) - 6.5} \cdot \sqrt{2 \cdot \pi}\right)\right) \cdot \left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\left(\left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right) + \left(\frac{12.507343278686905}{5 - z} + \frac{-0.13857109526572012}{6 - z}\right)\right) + \left(\left(\frac{-176.6150291621406}{4 - z} + \frac{771.3234287776531}{3 - z}\right) + \left(\frac{676.5203681218851}{1 - z} + \left(0.9999999999998099 + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right) \]

Alternative 5: 96.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \left({\left(\left(1 - z\right) + 6.5\right)}^{\left(1 - \left(z + 0.5\right)\right)} \cdot \left(e^{\left(z + -1\right) - 6.5} \cdot \sqrt{2 \cdot \pi}\right)\right) \cdot \left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \left(\frac{-1259.1392167224028}{3 + \left(-1 - z\right)} + \left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{\left(1 - z\right) + 3}\right)\right)\right) + 2.4783749183520145\right)\right) \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (*
  (*
   (pow (+ (- 1.0 z) 6.5) (- 1.0 (+ z 0.5)))
   (* (exp (- (+ z -1.0) 6.5)) (sqrt (* 2.0 PI))))
  (*
   (/ PI (sin (* z PI)))
   (+
    (+
     (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))
     (+
      (/ -1259.1392167224028 (+ 3.0 (- -1.0 z)))
      (+
       (/ 771.3234287776531 (- 1.0 (+ z -2.0)))
       (/ -176.6150291621406 (+ (- 1.0 z) 3.0)))))
    2.4783749183520145))))

C

double code(double z) {
	return (pow(((1.0 - z) + 6.5), (1.0 - (z + 0.5))) * (exp(((z + -1.0) - 6.5)) * sqrt((2.0 * ((double) M_PI))))) * ((((double) M_PI) / sin((z * ((double) M_PI)))) * (((0.9999999999998099 + (676.5203681218851 / (1.0 - z))) + ((-1259.1392167224028 / (3.0 + (-1.0 - z))) + ((771.3234287776531 / (1.0 - (z + -2.0))) + (-176.6150291621406 / ((1.0 - z) + 3.0))))) + 2.4783749183520145));
}

Java

public static double code(double z) {
	return (Math.pow(((1.0 - z) + 6.5), (1.0 - (z + 0.5))) * (Math.exp(((z + -1.0) - 6.5)) * Math.sqrt((2.0 * Math.PI)))) * ((Math.PI / Math.sin((z * Math.PI))) * (((0.9999999999998099 + (676.5203681218851 / (1.0 - z))) + ((-1259.1392167224028 / (3.0 + (-1.0 - z))) + ((771.3234287776531 / (1.0 - (z + -2.0))) + (-176.6150291621406 / ((1.0 - z) + 3.0))))) + 2.4783749183520145));
}

Python

def code(z):
	return (math.pow(((1.0 - z) + 6.5), (1.0 - (z + 0.5))) * (math.exp(((z + -1.0) - 6.5)) * math.sqrt((2.0 * math.pi)))) * ((math.pi / math.sin((z * math.pi))) * (((0.9999999999998099 + (676.5203681218851 / (1.0 - z))) + ((-1259.1392167224028 / (3.0 + (-1.0 - z))) + ((771.3234287776531 / (1.0 - (z + -2.0))) + (-176.6150291621406 / ((1.0 - z) + 3.0))))) + 2.4783749183520145))

Julia

function code(z)
	return Float64(Float64((Float64(Float64(1.0 - z) + 6.5) ^ Float64(1.0 - Float64(z + 0.5))) * Float64(exp(Float64(Float64(z + -1.0) - 6.5)) * sqrt(Float64(2.0 * pi)))) * Float64(Float64(pi / sin(Float64(z * pi))) * Float64(Float64(Float64(0.9999999999998099 + Float64(676.5203681218851 / Float64(1.0 - z))) + Float64(Float64(-1259.1392167224028 / Float64(3.0 + Float64(-1.0 - z))) + Float64(Float64(771.3234287776531 / Float64(1.0 - Float64(z + -2.0))) + Float64(-176.6150291621406 / Float64(Float64(1.0 - z) + 3.0))))) + 2.4783749183520145)))
end

MATLAB

function tmp = code(z)
	tmp = ((((1.0 - z) + 6.5) ^ (1.0 - (z + 0.5))) * (exp(((z + -1.0) - 6.5)) * sqrt((2.0 * pi)))) * ((pi / sin((z * pi))) * (((0.9999999999998099 + (676.5203681218851 / (1.0 - z))) + ((-1259.1392167224028 / (3.0 + (-1.0 - z))) + ((771.3234287776531 / (1.0 - (z + -2.0))) + (-176.6150291621406 / ((1.0 - z) + 3.0))))) + 2.4783749183520145));
end

Wolfram

code[z_] := N[(N[(N[Power[N[(N[(1.0 - z), $MachinePrecision] + 6.5), $MachinePrecision], N[(1.0 - N[(z + 0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(N[Exp[N[(N[(z + -1.0), $MachinePrecision] - 6.5), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(2.0 * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(Pi / N[Sin[N[(z * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(N[(0.9999999999998099 + N[(676.5203681218851 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-1259.1392167224028 / N[(3.0 + N[(-1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(771.3234287776531 / N[(1.0 - N[(z + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-176.6150291621406 / N[(N[(1.0 - z), $MachinePrecision] + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 2.4783749183520145), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

   \[\left({\left(\left(1 - z\right) + 6.5\right)}^{\left(1 - \left(z + 0.5\right)\right)} \cdot \left(e^{\left(z + -1\right) - 6.5} \cdot \sqrt{2 \cdot \pi}\right)\right) \cdot \left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \left(\frac{-1259.1392167224028}{3 + \left(-1 - z\right)} + \left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{\left(1 - z\right) + 3}\right)\right)\right) + 2.4783749183520145\right)\right) \]

Alternative 6: 96.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \left({\left(\left(1 - z\right) + 6.5\right)}^{\left(1 - \left(z + 0.5\right)\right)} \cdot \left(e^{\left(z + -1\right) - 6.5} \cdot \sqrt{2 \cdot \pi}\right)\right) \cdot \left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \left(\frac{-1259.1392167224028}{3 + \left(-1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} + \frac{771.3234287776531}{3 - z}\right)\right)\right) + \left(2.4783749183520145 + z \cdot 0.49644474017195733\right)\right)\right) \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (*
  (*
   (pow (+ (- 1.0 z) 6.5) (- 1.0 (+ z 0.5)))
   (* (exp (- (+ z -1.0) 6.5)) (sqrt (* 2.0 PI))))
  (*
   (/ PI (sin (* z PI)))
   (+
    (+
     (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))
     (+
      (/ -1259.1392167224028 (+ 3.0 (- -1.0 z)))
      (+ (/ -176.6150291621406 (- 4.0 z)) (/ 771.3234287776531 (- 3.0 z)))))
    (+ 2.4783749183520145 (* z 0.49644474017195733))))))

C

double code(double z) {
	return (pow(((1.0 - z) + 6.5), (1.0 - (z + 0.5))) * (exp(((z + -1.0) - 6.5)) * sqrt((2.0 * ((double) M_PI))))) * ((((double) M_PI) / sin((z * ((double) M_PI)))) * (((0.9999999999998099 + (676.5203681218851 / (1.0 - z))) + ((-1259.1392167224028 / (3.0 + (-1.0 - z))) + ((-176.6150291621406 / (4.0 - z)) + (771.3234287776531 / (3.0 - z))))) + (2.4783749183520145 + (z * 0.49644474017195733))));
}

Java

public static double code(double z) {
	return (Math.pow(((1.0 - z) + 6.5), (1.0 - (z + 0.5))) * (Math.exp(((z + -1.0) - 6.5)) * Math.sqrt((2.0 * Math.PI)))) * ((Math.PI / Math.sin((z * Math.PI))) * (((0.9999999999998099 + (676.5203681218851 / (1.0 - z))) + ((-1259.1392167224028 / (3.0 + (-1.0 - z))) + ((-176.6150291621406 / (4.0 - z)) + (771.3234287776531 / (3.0 - z))))) + (2.4783749183520145 + (z * 0.49644474017195733))));
}

Python

def code(z):
	return (math.pow(((1.0 - z) + 6.5), (1.0 - (z + 0.5))) * (math.exp(((z + -1.0) - 6.5)) * math.sqrt((2.0 * math.pi)))) * ((math.pi / math.sin((z * math.pi))) * (((0.9999999999998099 + (676.5203681218851 / (1.0 - z))) + ((-1259.1392167224028 / (3.0 + (-1.0 - z))) + ((-176.6150291621406 / (4.0 - z)) + (771.3234287776531 / (3.0 - z))))) + (2.4783749183520145 + (z * 0.49644474017195733))))

Julia

function code(z)
	return Float64(Float64((Float64(Float64(1.0 - z) + 6.5) ^ Float64(1.0 - Float64(z + 0.5))) * Float64(exp(Float64(Float64(z + -1.0) - 6.5)) * sqrt(Float64(2.0 * pi)))) * Float64(Float64(pi / sin(Float64(z * pi))) * Float64(Float64(Float64(0.9999999999998099 + Float64(676.5203681218851 / Float64(1.0 - z))) + Float64(Float64(-1259.1392167224028 / Float64(3.0 + Float64(-1.0 - z))) + Float64(Float64(-176.6150291621406 / Float64(4.0 - z)) + Float64(771.3234287776531 / Float64(3.0 - z))))) + Float64(2.4783749183520145 + Float64(z * 0.49644474017195733)))))
end

MATLAB

function tmp = code(z)
	tmp = ((((1.0 - z) + 6.5) ^ (1.0 - (z + 0.5))) * (exp(((z + -1.0) - 6.5)) * sqrt((2.0 * pi)))) * ((pi / sin((z * pi))) * (((0.9999999999998099 + (676.5203681218851 / (1.0 - z))) + ((-1259.1392167224028 / (3.0 + (-1.0 - z))) + ((-176.6150291621406 / (4.0 - z)) + (771.3234287776531 / (3.0 - z))))) + (2.4783749183520145 + (z * 0.49644474017195733))));
end

Wolfram

code[z_] := N[(N[(N[Power[N[(N[(1.0 - z), $MachinePrecision] + 6.5), $MachinePrecision], N[(1.0 - N[(z + 0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(N[Exp[N[(N[(z + -1.0), $MachinePrecision] - 6.5), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(2.0 * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(Pi / N[Sin[N[(z * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(N[(0.9999999999998099 + N[(676.5203681218851 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-1259.1392167224028 / N[(3.0 + N[(-1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-176.6150291621406 / N[(4.0 - z), $MachinePrecision]), $MachinePrecision] + N[(771.3234287776531 / N[(3.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(2.4783749183520145 + N[(z * 0.49644474017195733), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.1%

   \[\left({\left(\left(1 - z\right) + 6.5\right)}^{\left(1 - \left(z + 0.5\right)\right)} \cdot \left(e^{\left(z + -1\right) - 6.5} \cdot \sqrt{2 \cdot \pi}\right)\right) \cdot \left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \left(\frac{-1259.1392167224028}{3 + \left(-1 - z\right)} + \left(\frac{-176.6150291621406}{4 - z} + \frac{771.3234287776531}{3 - z}\right)\right)\right) + \left(2.4783749183520145 + z \cdot 0.49644474017195733\right)\right)\right) \]

Alternative 7: 96.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \left({\left(\left(1 - z\right) + 6.5\right)}^{\left(1 - \left(z + 0.5\right)\right)} \cdot \left(e^{\left(z + -1\right) - 6.5} \cdot \sqrt{2 \cdot \pi}\right)\right) \cdot \left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\left(\left(\frac{-176.6150291621406}{4 - z} + \frac{771.3234287776531}{3 - z}\right) + \left(\frac{676.5203681218851}{1 - z} + \left(0.9999999999998099 + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) + 2.4783749183520145\right)\right) \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (*
  (*
   (pow (+ (- 1.0 z) 6.5) (- 1.0 (+ z 0.5)))
   (* (exp (- (+ z -1.0) 6.5)) (sqrt (* 2.0 PI))))
  (*
   (/ PI (sin (* z PI)))
   (+
    (+
     (+ (/ -176.6150291621406 (- 4.0 z)) (/ 771.3234287776531 (- 3.0 z)))
     (+
      (/ 676.5203681218851 (- 1.0 z))
      (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2.0 z)))))
    2.4783749183520145))))

C

double code(double z) {
	return (pow(((1.0 - z) + 6.5), (1.0 - (z + 0.5))) * (exp(((z + -1.0) - 6.5)) * sqrt((2.0 * ((double) M_PI))))) * ((((double) M_PI) / sin((z * ((double) M_PI)))) * ((((-176.6150291621406 / (4.0 - z)) + (771.3234287776531 / (3.0 - z))) + ((676.5203681218851 / (1.0 - z)) + (0.9999999999998099 + (-1259.1392167224028 / (2.0 - z))))) + 2.4783749183520145));
}

Java

public static double code(double z) {
	return (Math.pow(((1.0 - z) + 6.5), (1.0 - (z + 0.5))) * (Math.exp(((z + -1.0) - 6.5)) * Math.sqrt((2.0 * Math.PI)))) * ((Math.PI / Math.sin((z * Math.PI))) * ((((-176.6150291621406 / (4.0 - z)) + (771.3234287776531 / (3.0 - z))) + ((676.5203681218851 / (1.0 - z)) + (0.9999999999998099 + (-1259.1392167224028 / (2.0 - z))))) + 2.4783749183520145));
}

Python

def code(z):
	return (math.pow(((1.0 - z) + 6.5), (1.0 - (z + 0.5))) * (math.exp(((z + -1.0) - 6.5)) * math.sqrt((2.0 * math.pi)))) * ((math.pi / math.sin((z * math.pi))) * ((((-176.6150291621406 / (4.0 - z)) + (771.3234287776531 / (3.0 - z))) + ((676.5203681218851 / (1.0 - z)) + (0.9999999999998099 + (-1259.1392167224028 / (2.0 - z))))) + 2.4783749183520145))

Julia

function code(z)
	return Float64(Float64((Float64(Float64(1.0 - z) + 6.5) ^ Float64(1.0 - Float64(z + 0.5))) * Float64(exp(Float64(Float64(z + -1.0) - 6.5)) * sqrt(Float64(2.0 * pi)))) * Float64(Float64(pi / sin(Float64(z * pi))) * Float64(Float64(Float64(Float64(-176.6150291621406 / Float64(4.0 - z)) + Float64(771.3234287776531 / Float64(3.0 - z))) + Float64(Float64(676.5203681218851 / Float64(1.0 - z)) + Float64(0.9999999999998099 + Float64(-1259.1392167224028 / Float64(2.0 - z))))) + 2.4783749183520145)))
end

MATLAB

function tmp = code(z)
	tmp = ((((1.0 - z) + 6.5) ^ (1.0 - (z + 0.5))) * (exp(((z + -1.0) - 6.5)) * sqrt((2.0 * pi)))) * ((pi / sin((z * pi))) * ((((-176.6150291621406 / (4.0 - z)) + (771.3234287776531 / (3.0 - z))) + ((676.5203681218851 / (1.0 - z)) + (0.9999999999998099 + (-1259.1392167224028 / (2.0 - z))))) + 2.4783749183520145));
end

Wolfram

code[z_] := N[(N[(N[Power[N[(N[(1.0 - z), $MachinePrecision] + 6.5), $MachinePrecision], N[(1.0 - N[(z + 0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(N[Exp[N[(N[(z + -1.0), $MachinePrecision] - 6.5), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(2.0 * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(Pi / N[Sin[N[(z * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(-176.6150291621406 / N[(4.0 - z), $MachinePrecision]), $MachinePrecision] + N[(771.3234287776531 / N[(3.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(676.5203681218851 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(0.9999999999998099 + N[(-1259.1392167224028 / N[(2.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 2.4783749183520145), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

   \[\left({\left(\left(1 - z\right) + 6.5\right)}^{\left(1 - \left(z + 0.5\right)\right)} \cdot \left(e^{\left(z + -1\right) - 6.5} \cdot \sqrt{2 \cdot \pi}\right)\right) \cdot \left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\left(\left(\frac{-176.6150291621406}{4 - z} + \frac{771.3234287776531}{3 - z}\right) + \left(\frac{676.5203681218851}{1 - z} + \left(0.9999999999998099 + \frac{-1259.1392167224028}{2 - z}\right)\right)\right) + 2.4783749183520145\right)\right) \]

Alternative 8: 96.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ 263.3831869810514 \cdot \left(e^{z + -7.5} \cdot \frac{\sqrt{2 \cdot \pi} \cdot \left(\pi \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right)}{\sin \left(z \cdot \pi\right)}\right) \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (*
  263.3831869810514
  (*
   (exp (+ z -7.5))
   (/ (* (sqrt (* 2.0 PI)) (* PI (pow (- 7.5 z) (- 0.5 z)))) (sin (* z PI))))))

C

double code(double z) {
	return 263.3831869810514 * (exp((z + -7.5)) * ((sqrt((2.0 * ((double) M_PI))) * (((double) M_PI) * pow((7.5 - z), (0.5 - z)))) / sin((z * ((double) M_PI)))));
}

Java

public static double code(double z) {
	return 263.3831869810514 * (Math.exp((z + -7.5)) * ((Math.sqrt((2.0 * Math.PI)) * (Math.PI * Math.pow((7.5 - z), (0.5 - z)))) / Math.sin((z * Math.PI))));
}

Python

def code(z):
	return 263.3831869810514 * (math.exp((z + -7.5)) * ((math.sqrt((2.0 * math.pi)) * (math.pi * math.pow((7.5 - z), (0.5 - z)))) / math.sin((z * math.pi))))

Julia

function code(z)
	return Float64(263.3831869810514 * Float64(exp(Float64(z + -7.5)) * Float64(Float64(sqrt(Float64(2.0 * pi)) * Float64(pi * (Float64(7.5 - z) ^ Float64(0.5 - z)))) / sin(Float64(z * pi)))))
end

MATLAB

function tmp = code(z)
	tmp = 263.3831869810514 * (exp((z + -7.5)) * ((sqrt((2.0 * pi)) * (pi * ((7.5 - z) ^ (0.5 - z)))) / sin((z * pi))));
end

Wolfram

code[z_] := N[(263.3831869810514 * N[(N[Exp[N[(z + -7.5), $MachinePrecision]], $MachinePrecision] * N[(N[(N[Sqrt[N[(2.0 * Pi), $MachinePrecision]], $MachinePrecision] * N[(Pi * N[Power[N[(7.5 - z), $MachinePrecision], N[(0.5 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Sin[N[(z * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.5%

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

Alternative 9: 96.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ 263.3831869810514 \cdot \frac{\left({\pi}^{1.5} \cdot \left(e^{z + -7.5} \cdot \sqrt{2}\right)\right) \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}}{\sin \left(z \cdot \pi\right)} \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (*
  263.3831869810514
  (/
   (*
    (* (pow PI 1.5) (* (exp (+ z -7.5)) (sqrt 2.0)))
    (pow (- 7.5 z) (- 0.5 z)))
   (sin (* z PI)))))

C

double code(double z) {
	return 263.3831869810514 * (((pow(((double) M_PI), 1.5) * (exp((z + -7.5)) * sqrt(2.0))) * pow((7.5 - z), (0.5 - z))) / sin((z * ((double) M_PI))));
}

Java

public static double code(double z) {
	return 263.3831869810514 * (((Math.pow(Math.PI, 1.5) * (Math.exp((z + -7.5)) * Math.sqrt(2.0))) * Math.pow((7.5 - z), (0.5 - z))) / Math.sin((z * Math.PI)));
}

Python

def code(z):
	return 263.3831869810514 * (((math.pow(math.pi, 1.5) * (math.exp((z + -7.5)) * math.sqrt(2.0))) * math.pow((7.5 - z), (0.5 - z))) / math.sin((z * math.pi)))

Julia

function code(z)
	return Float64(263.3831869810514 * Float64(Float64(Float64((pi ^ 1.5) * Float64(exp(Float64(z + -7.5)) * sqrt(2.0))) * (Float64(7.5 - z) ^ Float64(0.5 - z))) / sin(Float64(z * pi))))
end

MATLAB

function tmp = code(z)
	tmp = 263.3831869810514 * ((((pi ^ 1.5) * (exp((z + -7.5)) * sqrt(2.0))) * ((7.5 - z) ^ (0.5 - z))) / sin((z * pi)));
end

Wolfram

code[z_] := N[(263.3831869810514 * N[(N[(N[(N[Power[Pi, 1.5], $MachinePrecision] * N[(N[Exp[N[(z + -7.5), $MachinePrecision]], $MachinePrecision] * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Power[N[(7.5 - z), $MachinePrecision], N[(0.5 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[Sin[N[(z * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.6%

   \[263.3831869810514 \cdot \frac{\left({\pi}^{1.5} \cdot \left(e^{z + -7.5} \cdot \sqrt{2}\right)\right) \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}}{\sin \left(z \cdot \pi\right)} \]

Alternative 10: 96.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \sqrt{\pi} \cdot \frac{263.3831869810514 \cdot e^{-7.5}}{\frac{\frac{z}{\sqrt{7.5}}}{\sqrt{2}}} \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (*
  (sqrt PI)
  (/ (* 263.3831869810514 (exp -7.5)) (/ (/ z (sqrt 7.5)) (sqrt 2.0)))))

C

double code(double z) {
	return sqrt(((double) M_PI)) * ((263.3831869810514 * exp(-7.5)) / ((z / sqrt(7.5)) / sqrt(2.0)));
}

Java

public static double code(double z) {
	return Math.sqrt(Math.PI) * ((263.3831869810514 * Math.exp(-7.5)) / ((z / Math.sqrt(7.5)) / Math.sqrt(2.0)));
}

Python

def code(z):
	return math.sqrt(math.pi) * ((263.3831869810514 * math.exp(-7.5)) / ((z / math.sqrt(7.5)) / math.sqrt(2.0)))

Julia

function code(z)
	return Float64(sqrt(pi) * Float64(Float64(263.3831869810514 * exp(-7.5)) / Float64(Float64(z / sqrt(7.5)) / sqrt(2.0))))
end

MATLAB

function tmp = code(z)
	tmp = sqrt(pi) * ((263.3831869810514 * exp(-7.5)) / ((z / sqrt(7.5)) / sqrt(2.0)));
end

Wolfram

code[z_] := N[(N[Sqrt[Pi], $MachinePrecision] * N[(N[(263.3831869810514 * N[Exp[-7.5], $MachinePrecision]), $MachinePrecision] / N[(N[(z / N[Sqrt[7.5], $MachinePrecision]), $MachinePrecision] / N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.2%

   \[\sqrt{\pi} \cdot \frac{263.3831869810514 \cdot e^{-7.5}}{\frac{\frac{z}{\sqrt{7.5}}}{\sqrt{2}}} \]

Alternative 11: 96.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ 263.3831869810514 \cdot \left(\sqrt{\pi} \cdot \left(\frac{e^{-7.5}}{z} \cdot \sqrt{15}\right)\right) \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (* 263.3831869810514 (* (sqrt PI) (* (/ (exp -7.5) z) (sqrt 15.0)))))

C

double code(double z) {
	return 263.3831869810514 * (sqrt(((double) M_PI)) * ((exp(-7.5) / z) * sqrt(15.0)));
}

Java

public static double code(double z) {
	return 263.3831869810514 * (Math.sqrt(Math.PI) * ((Math.exp(-7.5) / z) * Math.sqrt(15.0)));
}

Python

def code(z):
	return 263.3831869810514 * (math.sqrt(math.pi) * ((math.exp(-7.5) / z) * math.sqrt(15.0)))

Julia

function code(z)
	return Float64(263.3831869810514 * Float64(sqrt(pi) * Float64(Float64(exp(-7.5) / z) * sqrt(15.0))))
end

MATLAB

function tmp = code(z)
	tmp = 263.3831869810514 * (sqrt(pi) * ((exp(-7.5) / z) * sqrt(15.0)));
end

Wolfram

code[z_] := N[(263.3831869810514 * N[(N[Sqrt[Pi], $MachinePrecision] * N[(N[(N[Exp[-7.5], $MachinePrecision] / z), $MachinePrecision] * N[Sqrt[15.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.1%

   \[263.3831869810514 \cdot \left(\sqrt{\pi} \cdot \left(\frac{e^{-7.5}}{z} \cdot \sqrt{15}\right)\right) \]

Reproduce

herbie shell --seed 2023297 
(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))))))