Jmat.Real.gamma, branch z less than 0.5

Percentage Accurate: 96.3% → 99.0%

Time: 1.4min

Alternatives: 14

Speedup: 1.2×

• could not determine a ground truth

  1. z = -2.156503718089976e+26

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: 96.3% 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: 99.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\pi}{\sin \left(z \cdot \pi\right)}\\ t_1 := \sqrt{2 \cdot \pi}\\ \mathbf{if}\;z \leq -1000:\\ \;\;\;\;\left(t_0 \cdot \left(t_1 \cdot e^{\left(z + \log \left(7.5 - z\right) \cdot \left(0.5 - z\right)\right) - 7.5}\right)\right) \cdot 263.3831869810514\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(1 - z\right) + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) + 7}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) + 2} + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right) + \left(0.9999999999998099 + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{1 + \left(1 - z\right)}\right)\right)\right)\right) \cdot \left(t_0 \cdot \left(t_1 \cdot \frac{{\left(7.5 - z\right)}^{\left(0.5 - z\right)}}{e^{7.5 - z}}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (/ PI (sin (* z PI)))) (t_1 (sqrt (* 2.0 PI))))
   (if (<= z -1000.0)
     (*
      (* t_0 (* t_1 (exp (- (+ z (* (log (- 7.5 z)) (- 0.5 z))) 7.5))))
      263.3831869810514)
     (*
      (+
       (+
        (/ -0.13857109526572012 (+ (- 1.0 z) 5.0))
        (+
         (/ 9.984369578019572e-6 (+ (- 1.0 z) 6.0))
         (/ 1.5056327351493116e-7 (+ (- 1.0 z) 7.0))))
       (+
        (+
         (/ 771.3234287776531 (+ (- 1.0 z) 2.0))
         (+
          (/ -176.6150291621406 (+ (- 1.0 z) 3.0))
          (/ 12.507343278686905 (+ (- 1.0 z) 4.0))))
        (+
         0.9999999999998099
         (+
          (/ 676.5203681218851 (- 1.0 z))
          (/ -1259.1392167224028 (+ 1.0 (- 1.0 z)))))))
      (* t_0 (* t_1 (/ (pow (- 7.5 z) (- 0.5 z)) (exp (- 7.5 z)))))))))

C

double code(double z) {
	double t_0 = ((double) M_PI) / sin((z * ((double) M_PI)));
	double t_1 = sqrt((2.0 * ((double) M_PI)));
	double tmp;
	if (z <= -1000.0) {
		tmp = (t_0 * (t_1 * exp(((z + (log((7.5 - z)) * (0.5 - z))) - 7.5)))) * 263.3831869810514;
	} else {
		tmp = (((-0.13857109526572012 / ((1.0 - z) + 5.0)) + ((9.984369578019572e-6 / ((1.0 - z) + 6.0)) + (1.5056327351493116e-7 / ((1.0 - z) + 7.0)))) + (((771.3234287776531 / ((1.0 - z) + 2.0)) + ((-176.6150291621406 / ((1.0 - z) + 3.0)) + (12.507343278686905 / ((1.0 - z) + 4.0)))) + (0.9999999999998099 + ((676.5203681218851 / (1.0 - z)) + (-1259.1392167224028 / (1.0 + (1.0 - z))))))) * (t_0 * (t_1 * (pow((7.5 - z), (0.5 - z)) / exp((7.5 - z)))));
	}
	return tmp;
}

Java

public static double code(double z) {
	double t_0 = Math.PI / Math.sin((z * Math.PI));
	double t_1 = Math.sqrt((2.0 * Math.PI));
	double tmp;
	if (z <= -1000.0) {
		tmp = (t_0 * (t_1 * Math.exp(((z + (Math.log((7.5 - z)) * (0.5 - z))) - 7.5)))) * 263.3831869810514;
	} else {
		tmp = (((-0.13857109526572012 / ((1.0 - z) + 5.0)) + ((9.984369578019572e-6 / ((1.0 - z) + 6.0)) + (1.5056327351493116e-7 / ((1.0 - z) + 7.0)))) + (((771.3234287776531 / ((1.0 - z) + 2.0)) + ((-176.6150291621406 / ((1.0 - z) + 3.0)) + (12.507343278686905 / ((1.0 - z) + 4.0)))) + (0.9999999999998099 + ((676.5203681218851 / (1.0 - z)) + (-1259.1392167224028 / (1.0 + (1.0 - z))))))) * (t_0 * (t_1 * (Math.pow((7.5 - z), (0.5 - z)) / Math.exp((7.5 - z)))));
	}
	return tmp;
}

Python

def code(z):
	t_0 = math.pi / math.sin((z * math.pi))
	t_1 = math.sqrt((2.0 * math.pi))
	tmp = 0
	if z <= -1000.0:
		tmp = (t_0 * (t_1 * math.exp(((z + (math.log((7.5 - z)) * (0.5 - z))) - 7.5)))) * 263.3831869810514
	else:
		tmp = (((-0.13857109526572012 / ((1.0 - z) + 5.0)) + ((9.984369578019572e-6 / ((1.0 - z) + 6.0)) + (1.5056327351493116e-7 / ((1.0 - z) + 7.0)))) + (((771.3234287776531 / ((1.0 - z) + 2.0)) + ((-176.6150291621406 / ((1.0 - z) + 3.0)) + (12.507343278686905 / ((1.0 - z) + 4.0)))) + (0.9999999999998099 + ((676.5203681218851 / (1.0 - z)) + (-1259.1392167224028 / (1.0 + (1.0 - z))))))) * (t_0 * (t_1 * (math.pow((7.5 - z), (0.5 - z)) / math.exp((7.5 - z)))))
	return tmp

Julia

function code(z)
	t_0 = Float64(pi / sin(Float64(z * pi)))
	t_1 = sqrt(Float64(2.0 * pi))
	tmp = 0.0
	if (z <= -1000.0)
		tmp = Float64(Float64(t_0 * Float64(t_1 * exp(Float64(Float64(z + Float64(log(Float64(7.5 - z)) * Float64(0.5 - z))) - 7.5)))) * 263.3831869810514);
	else
		tmp = Float64(Float64(Float64(Float64(-0.13857109526572012 / Float64(Float64(1.0 - z) + 5.0)) + Float64(Float64(9.984369578019572e-6 / Float64(Float64(1.0 - z) + 6.0)) + Float64(1.5056327351493116e-7 / Float64(Float64(1.0 - z) + 7.0)))) + Float64(Float64(Float64(771.3234287776531 / Float64(Float64(1.0 - z) + 2.0)) + Float64(Float64(-176.6150291621406 / Float64(Float64(1.0 - z) + 3.0)) + Float64(12.507343278686905 / Float64(Float64(1.0 - z) + 4.0)))) + Float64(0.9999999999998099 + Float64(Float64(676.5203681218851 / Float64(1.0 - z)) + Float64(-1259.1392167224028 / Float64(1.0 + Float64(1.0 - z))))))) * Float64(t_0 * Float64(t_1 * Float64((Float64(7.5 - z) ^ Float64(0.5 - z)) / exp(Float64(7.5 - z))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z)
	t_0 = pi / sin((z * pi));
	t_1 = sqrt((2.0 * pi));
	tmp = 0.0;
	if (z <= -1000.0)
		tmp = (t_0 * (t_1 * exp(((z + (log((7.5 - z)) * (0.5 - z))) - 7.5)))) * 263.3831869810514;
	else
		tmp = (((-0.13857109526572012 / ((1.0 - z) + 5.0)) + ((9.984369578019572e-6 / ((1.0 - z) + 6.0)) + (1.5056327351493116e-7 / ((1.0 - z) + 7.0)))) + (((771.3234287776531 / ((1.0 - z) + 2.0)) + ((-176.6150291621406 / ((1.0 - z) + 3.0)) + (12.507343278686905 / ((1.0 - z) + 4.0)))) + (0.9999999999998099 + ((676.5203681218851 / (1.0 - z)) + (-1259.1392167224028 / (1.0 + (1.0 - z))))))) * (t_0 * (t_1 * (((7.5 - z) ^ (0.5 - z)) / exp((7.5 - z)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[z_] := Block[{t$95$0 = N[(Pi / N[Sin[N[(z * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(2.0 * Pi), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, -1000.0], N[(N[(t$95$0 * N[(t$95$1 * N[Exp[N[(N[(z + N[(N[Log[N[(7.5 - z), $MachinePrecision]], $MachinePrecision] * N[(0.5 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 263.3831869810514), $MachinePrecision], N[(N[(N[(N[(-0.13857109526572012 / N[(N[(1.0 - z), $MachinePrecision] + 5.0), $MachinePrecision]), $MachinePrecision] + N[(N[(9.984369578019572e-6 / N[(N[(1.0 - z), $MachinePrecision] + 6.0), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(N[(1.0 - z), $MachinePrecision] + 7.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(771.3234287776531 / N[(N[(1.0 - z), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] + N[(N[(-176.6150291621406 / N[(N[(1.0 - z), $MachinePrecision] + 3.0), $MachinePrecision]), $MachinePrecision] + N[(12.507343278686905 / N[(N[(1.0 - z), $MachinePrecision] + 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.9999999999998099 + N[(N[(676.5203681218851 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(-1259.1392167224028 / N[(1.0 + N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 * N[(t$95$1 * N[(N[Power[N[(7.5 - z), $MachinePrecision], N[(0.5 - z), $MachinePrecision]], $MachinePrecision] / N[Exp[N[(7.5 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(0.9999999999998099 + \frac{93.9015195213674 + 582.6188486005177 \cdot z}{\left(1 - z\right) \cdot \left(2 - z\right)}\right) + \left(\frac{771.3234287776531}{\left(1 - z\right) + 2} + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right)\right) + \left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(1 - z\right) + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) + 7}\right)\right)\right) \cdot \left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\sqrt{2 \cdot \pi} \cdot e^{\left(z + \log \left(7.5 - z\right) \cdot \left(0.5 - z\right)\right) - 7.5}\right)\right) \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (*
  (+
   (+
    (+
     0.9999999999998099
     (/ (+ 93.9015195213674 (* 582.6188486005177 z)) (* (- 1.0 z) (- 2.0 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 (+ (- 1.0 z) 6.0))
     (/ 1.5056327351493116e-7 (+ (- 1.0 z) 7.0)))))
  (*
   (/ PI (sin (* z PI)))
   (* (sqrt (* 2.0 PI)) (exp (- (+ z (* (log (- 7.5 z)) (- 0.5 z))) 7.5))))))

C

double code(double z) {
	return (((0.9999999999998099 + ((93.9015195213674 + (582.6188486005177 * z)) / ((1.0 - z) * (2.0 - 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 / ((1.0 - z) + 6.0)) + (1.5056327351493116e-7 / ((1.0 - z) + 7.0))))) * ((((double) M_PI) / sin((z * ((double) M_PI)))) * (sqrt((2.0 * ((double) M_PI))) * exp(((z + (log((7.5 - z)) * (0.5 - z))) - 7.5))));
}

Java

public static double code(double z) {
	return (((0.9999999999998099 + ((93.9015195213674 + (582.6188486005177 * z)) / ((1.0 - z) * (2.0 - 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 / ((1.0 - z) + 6.0)) + (1.5056327351493116e-7 / ((1.0 - z) + 7.0))))) * ((Math.PI / Math.sin((z * Math.PI))) * (Math.sqrt((2.0 * Math.PI)) * Math.exp(((z + (Math.log((7.5 - z)) * (0.5 - z))) - 7.5))));
}

Python

def code(z):
	return (((0.9999999999998099 + ((93.9015195213674 + (582.6188486005177 * z)) / ((1.0 - z) * (2.0 - 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 / ((1.0 - z) + 6.0)) + (1.5056327351493116e-7 / ((1.0 - z) + 7.0))))) * ((math.pi / math.sin((z * math.pi))) * (math.sqrt((2.0 * math.pi)) * math.exp(((z + (math.log((7.5 - z)) * (0.5 - z))) - 7.5))))

Julia

function code(z)
	return Float64(Float64(Float64(Float64(0.9999999999998099 + Float64(Float64(93.9015195213674 + Float64(582.6188486005177 * z)) / Float64(Float64(1.0 - z) * Float64(2.0 - z)))) + Float64(Float64(771.3234287776531 / Float64(Float64(1.0 - z) + 2.0)) + Float64(Float64(-176.6150291621406 / Float64(Float64(1.0 - z) + 3.0)) + Float64(12.507343278686905 / Float64(Float64(1.0 - z) + 4.0))))) + Float64(Float64(-0.13857109526572012 / Float64(Float64(1.0 - z) + 5.0)) + Float64(Float64(9.984369578019572e-6 / Float64(Float64(1.0 - z) + 6.0)) + Float64(1.5056327351493116e-7 / Float64(Float64(1.0 - z) + 7.0))))) * Float64(Float64(pi / sin(Float64(z * pi))) * Float64(sqrt(Float64(2.0 * pi)) * exp(Float64(Float64(z + Float64(log(Float64(7.5 - z)) * Float64(0.5 - z))) - 7.5)))))
end

MATLAB

function tmp = code(z)
	tmp = (((0.9999999999998099 + ((93.9015195213674 + (582.6188486005177 * z)) / ((1.0 - z) * (2.0 - 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 / ((1.0 - z) + 6.0)) + (1.5056327351493116e-7 / ((1.0 - z) + 7.0))))) * ((pi / sin((z * pi))) * (sqrt((2.0 * pi)) * exp(((z + (log((7.5 - z)) * (0.5 - z))) - 7.5))));
end

Wolfram

code[z_] := N[(N[(N[(N[(0.9999999999998099 + N[(N[(93.9015195213674 + N[(582.6188486005177 * z), $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 - z), $MachinePrecision] * N[(2.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(771.3234287776531 / N[(N[(1.0 - z), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] + N[(N[(-176.6150291621406 / N[(N[(1.0 - z), $MachinePrecision] + 3.0), $MachinePrecision]), $MachinePrecision] + N[(12.507343278686905 / N[(N[(1.0 - z), $MachinePrecision] + 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-0.13857109526572012 / N[(N[(1.0 - z), $MachinePrecision] + 5.0), $MachinePrecision]), $MachinePrecision] + N[(N[(9.984369578019572e-6 / N[(N[(1.0 - z), $MachinePrecision] + 6.0), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(N[(1.0 - z), $MachinePrecision] + 7.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(Pi / N[Sin[N[(z * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[N[(2.0 * Pi), $MachinePrecision]], $MachinePrecision] * N[Exp[N[(N[(z + N[(N[Log[N[(7.5 - z), $MachinePrecision]], $MachinePrecision] * N[(0.5 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(1 - z\right) + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) + 7}\right)\right) + \left(\left(0.9999999999998099 + \frac{93.9015195213674 + 582.6188486005177 \cdot z}{\left(1 - z\right) \cdot \left(2 - z\right)}\right) + \left(\frac{771.3234287776531}{3 - z} + \left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right)\right)\right)\right) \cdot \left(\frac{\pi}{\sin \left(z \cdot \pi\right)} \cdot \left(\sqrt{2 \cdot \pi} \cdot e^{\left(\left(z + -1\right) - 6.5\right) + \left(0.5 - z\right) \cdot \log \left(\left(1 - z\right) + 6.5\right)}\right)\right) \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (*
  (+
   (+
    (/ -0.13857109526572012 (+ (- 1.0 z) 5.0))
    (+
     (/ 9.984369578019572e-6 (+ (- 1.0 z) 6.0))
     (/ 1.5056327351493116e-7 (+ (- 1.0 z) 7.0))))
   (+
    (+
     0.9999999999998099
     (/ (+ 93.9015195213674 (* 582.6188486005177 z)) (* (- 1.0 z) (- 2.0 z))))
    (+
     (/ 771.3234287776531 (- 3.0 z))
     (+ (/ -176.6150291621406 (- 4.0 z)) (/ 12.507343278686905 (- 5.0 z))))))
  (*
   (/ PI (sin (* z PI)))
   (*
    (sqrt (* 2.0 PI))
    (exp (+ (- (+ z -1.0) 6.5) (* (- 0.5 z) (log (+ (- 1.0 z) 6.5)))))))))

C

double code(double z) {
	return (((-0.13857109526572012 / ((1.0 - z) + 5.0)) + ((9.984369578019572e-6 / ((1.0 - z) + 6.0)) + (1.5056327351493116e-7 / ((1.0 - z) + 7.0)))) + ((0.9999999999998099 + ((93.9015195213674 + (582.6188486005177 * z)) / ((1.0 - z) * (2.0 - z)))) + ((771.3234287776531 / (3.0 - z)) + ((-176.6150291621406 / (4.0 - z)) + (12.507343278686905 / (5.0 - z)))))) * ((((double) M_PI) / sin((z * ((double) M_PI)))) * (sqrt((2.0 * ((double) M_PI))) * exp((((z + -1.0) - 6.5) + ((0.5 - z) * log(((1.0 - z) + 6.5)))))));
}

Java

public static double code(double z) {
	return (((-0.13857109526572012 / ((1.0 - z) + 5.0)) + ((9.984369578019572e-6 / ((1.0 - z) + 6.0)) + (1.5056327351493116e-7 / ((1.0 - z) + 7.0)))) + ((0.9999999999998099 + ((93.9015195213674 + (582.6188486005177 * z)) / ((1.0 - z) * (2.0 - z)))) + ((771.3234287776531 / (3.0 - z)) + ((-176.6150291621406 / (4.0 - z)) + (12.507343278686905 / (5.0 - z)))))) * ((Math.PI / Math.sin((z * Math.PI))) * (Math.sqrt((2.0 * Math.PI)) * Math.exp((((z + -1.0) - 6.5) + ((0.5 - z) * Math.log(((1.0 - z) + 6.5)))))));
}

Python

def code(z):
	return (((-0.13857109526572012 / ((1.0 - z) + 5.0)) + ((9.984369578019572e-6 / ((1.0 - z) + 6.0)) + (1.5056327351493116e-7 / ((1.0 - z) + 7.0)))) + ((0.9999999999998099 + ((93.9015195213674 + (582.6188486005177 * z)) / ((1.0 - z) * (2.0 - z)))) + ((771.3234287776531 / (3.0 - z)) + ((-176.6150291621406 / (4.0 - z)) + (12.507343278686905 / (5.0 - z)))))) * ((math.pi / math.sin((z * math.pi))) * (math.sqrt((2.0 * math.pi)) * math.exp((((z + -1.0) - 6.5) + ((0.5 - z) * math.log(((1.0 - z) + 6.5)))))))

Julia

function code(z)
	return Float64(Float64(Float64(Float64(-0.13857109526572012 / Float64(Float64(1.0 - z) + 5.0)) + Float64(Float64(9.984369578019572e-6 / Float64(Float64(1.0 - z) + 6.0)) + Float64(1.5056327351493116e-7 / Float64(Float64(1.0 - z) + 7.0)))) + Float64(Float64(0.9999999999998099 + Float64(Float64(93.9015195213674 + Float64(582.6188486005177 * z)) / Float64(Float64(1.0 - z) * Float64(2.0 - z)))) + Float64(Float64(771.3234287776531 / Float64(3.0 - z)) + Float64(Float64(-176.6150291621406 / Float64(4.0 - z)) + Float64(12.507343278686905 / Float64(5.0 - z)))))) * Float64(Float64(pi / sin(Float64(z * pi))) * Float64(sqrt(Float64(2.0 * pi)) * exp(Float64(Float64(Float64(z + -1.0) - 6.5) + Float64(Float64(0.5 - z) * log(Float64(Float64(1.0 - z) + 6.5))))))))
end

MATLAB

function tmp = code(z)
	tmp = (((-0.13857109526572012 / ((1.0 - z) + 5.0)) + ((9.984369578019572e-6 / ((1.0 - z) + 6.0)) + (1.5056327351493116e-7 / ((1.0 - z) + 7.0)))) + ((0.9999999999998099 + ((93.9015195213674 + (582.6188486005177 * z)) / ((1.0 - z) * (2.0 - z)))) + ((771.3234287776531 / (3.0 - z)) + ((-176.6150291621406 / (4.0 - z)) + (12.507343278686905 / (5.0 - z)))))) * ((pi / sin((z * pi))) * (sqrt((2.0 * pi)) * exp((((z + -1.0) - 6.5) + ((0.5 - z) * log(((1.0 - z) + 6.5)))))));
end

Wolfram

code[z_] := N[(N[(N[(N[(-0.13857109526572012 / N[(N[(1.0 - z), $MachinePrecision] + 5.0), $MachinePrecision]), $MachinePrecision] + N[(N[(9.984369578019572e-6 / N[(N[(1.0 - z), $MachinePrecision] + 6.0), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(N[(1.0 - z), $MachinePrecision] + 7.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(0.9999999999998099 + N[(N[(93.9015195213674 + N[(582.6188486005177 * z), $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 - z), $MachinePrecision] * N[(2.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(771.3234287776531 / N[(3.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(-176.6150291621406 / N[(4.0 - z), $MachinePrecision]), $MachinePrecision] + N[(12.507343278686905 / N[(5.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(Pi / N[Sin[N[(z * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[N[(2.0 * Pi), $MachinePrecision]], $MachinePrecision] * N[Exp[N[(N[(N[(z + -1.0), $MachinePrecision] - 6.5), $MachinePrecision] + N[(N[(0.5 - z), $MachinePrecision] * N[Log[N[(N[(1.0 - z), $MachinePrecision] + 6.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 98.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\pi}{\sin \left(z \cdot \pi\right)}\\ t_1 := \sqrt{2 \cdot \pi}\\ \mathbf{if}\;z \leq 2.75 \cdot 10^{-17}:\\ \;\;\;\;\left(t_0 \cdot \left(t_1 \cdot e^{\left(z + \log \left(7.5 - z\right) \cdot \left(0.5 - z\right)\right) - 7.5}\right)\right) \cdot 263.3831869810514\\ \mathbf{else}:\\ \;\;\;\;\left(t_1 \cdot \left({\left(7.5 - z\right)}^{\left(0.5 - z\right)} \cdot e^{z + -7.5}\right)\right) \cdot \left(t_0 \cdot \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-7}}{8 - z} + \frac{9.984369578019572 \cdot 10^{-6}}{7 - z}\right) + \left(\frac{771.3234287776531}{3 - z} + \left(0.9999999999998099 + \left(\frac{676.5203681218851}{1 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right) + \left(\left(\frac{-176.6150291621406}{4 - z} + \frac{12.507343278686905}{5 - z}\right) + \frac{-0.13857109526572012}{6 - z}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (/ PI (sin (* z PI)))) (t_1 (sqrt (* 2.0 PI))))
   (if (<= z 2.75e-17)
     (*
      (* t_0 (* t_1 (exp (- (+ z (* (log (- 7.5 z)) (- 0.5 z))) 7.5))))
      263.3831869810514)
     (*
      (* t_1 (* (pow (- 7.5 z) (- 0.5 z)) (exp (+ z -7.5))))
      (*
       t_0
       (+
        (+
         (+
          (/ 1.5056327351493116e-7 (- 8.0 z))
          (/ 9.984369578019572e-6 (- 7.0 z)))
         (+
          (/ 771.3234287776531 (- 3.0 z))
          (+
           0.9999999999998099
           (+
            (/ 676.5203681218851 (- 1.0 z))
            (/ -1259.1392167224028 (- 2.0 z))))))
        (+
         (+ (/ -176.6150291621406 (- 4.0 z)) (/ 12.507343278686905 (- 5.0 z)))
         (/ -0.13857109526572012 (- 6.0 z)))))))))

C

double code(double z) {
	double t_0 = ((double) M_PI) / sin((z * ((double) M_PI)));
	double t_1 = sqrt((2.0 * ((double) M_PI)));
	double tmp;
	if (z <= 2.75e-17) {
		tmp = (t_0 * (t_1 * exp(((z + (log((7.5 - z)) * (0.5 - z))) - 7.5)))) * 263.3831869810514;
	} else {
		tmp = (t_1 * (pow((7.5 - z), (0.5 - z)) * exp((z + -7.5)))) * (t_0 * ((((1.5056327351493116e-7 / (8.0 - z)) + (9.984369578019572e-6 / (7.0 - z))) + ((771.3234287776531 / (3.0 - z)) + (0.9999999999998099 + ((676.5203681218851 / (1.0 - z)) + (-1259.1392167224028 / (2.0 - z)))))) + (((-176.6150291621406 / (4.0 - z)) + (12.507343278686905 / (5.0 - z))) + (-0.13857109526572012 / (6.0 - z)))));
	}
	return tmp;
}

Java

public static double code(double z) {
	double t_0 = Math.PI / Math.sin((z * Math.PI));
	double t_1 = Math.sqrt((2.0 * Math.PI));
	double tmp;
	if (z <= 2.75e-17) {
		tmp = (t_0 * (t_1 * Math.exp(((z + (Math.log((7.5 - z)) * (0.5 - z))) - 7.5)))) * 263.3831869810514;
	} else {
		tmp = (t_1 * (Math.pow((7.5 - z), (0.5 - z)) * Math.exp((z + -7.5)))) * (t_0 * ((((1.5056327351493116e-7 / (8.0 - z)) + (9.984369578019572e-6 / (7.0 - z))) + ((771.3234287776531 / (3.0 - z)) + (0.9999999999998099 + ((676.5203681218851 / (1.0 - z)) + (-1259.1392167224028 / (2.0 - z)))))) + (((-176.6150291621406 / (4.0 - z)) + (12.507343278686905 / (5.0 - z))) + (-0.13857109526572012 / (6.0 - z)))));
	}
	return tmp;
}

Python

def code(z):
	t_0 = math.pi / math.sin((z * math.pi))
	t_1 = math.sqrt((2.0 * math.pi))
	tmp = 0
	if z <= 2.75e-17:
		tmp = (t_0 * (t_1 * math.exp(((z + (math.log((7.5 - z)) * (0.5 - z))) - 7.5)))) * 263.3831869810514
	else:
		tmp = (t_1 * (math.pow((7.5 - z), (0.5 - z)) * math.exp((z + -7.5)))) * (t_0 * ((((1.5056327351493116e-7 / (8.0 - z)) + (9.984369578019572e-6 / (7.0 - z))) + ((771.3234287776531 / (3.0 - z)) + (0.9999999999998099 + ((676.5203681218851 / (1.0 - z)) + (-1259.1392167224028 / (2.0 - z)))))) + (((-176.6150291621406 / (4.0 - z)) + (12.507343278686905 / (5.0 - z))) + (-0.13857109526572012 / (6.0 - z)))))
	return tmp

Julia

function code(z)
	t_0 = Float64(pi / sin(Float64(z * pi)))
	t_1 = sqrt(Float64(2.0 * pi))
	tmp = 0.0
	if (z <= 2.75e-17)
		tmp = Float64(Float64(t_0 * Float64(t_1 * exp(Float64(Float64(z + Float64(log(Float64(7.5 - z)) * Float64(0.5 - z))) - 7.5)))) * 263.3831869810514);
	else
		tmp = Float64(Float64(t_1 * Float64((Float64(7.5 - z) ^ Float64(0.5 - z)) * exp(Float64(z + -7.5)))) * Float64(t_0 * Float64(Float64(Float64(Float64(1.5056327351493116e-7 / Float64(8.0 - z)) + Float64(9.984369578019572e-6 / Float64(7.0 - z))) + Float64(Float64(771.3234287776531 / Float64(3.0 - z)) + Float64(0.9999999999998099 + Float64(Float64(676.5203681218851 / Float64(1.0 - z)) + Float64(-1259.1392167224028 / Float64(2.0 - z)))))) + Float64(Float64(Float64(-176.6150291621406 / Float64(4.0 - z)) + Float64(12.507343278686905 / Float64(5.0 - z))) + Float64(-0.13857109526572012 / Float64(6.0 - z))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z)
	t_0 = pi / sin((z * pi));
	t_1 = sqrt((2.0 * pi));
	tmp = 0.0;
	if (z <= 2.75e-17)
		tmp = (t_0 * (t_1 * exp(((z + (log((7.5 - z)) * (0.5 - z))) - 7.5)))) * 263.3831869810514;
	else
		tmp = (t_1 * (((7.5 - z) ^ (0.5 - z)) * exp((z + -7.5)))) * (t_0 * ((((1.5056327351493116e-7 / (8.0 - z)) + (9.984369578019572e-6 / (7.0 - z))) + ((771.3234287776531 / (3.0 - z)) + (0.9999999999998099 + ((676.5203681218851 / (1.0 - z)) + (-1259.1392167224028 / (2.0 - z)))))) + (((-176.6150291621406 / (4.0 - z)) + (12.507343278686905 / (5.0 - z))) + (-0.13857109526572012 / (6.0 - z)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[z_] := Block[{t$95$0 = N[(Pi / N[Sin[N[(z * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(2.0 * Pi), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, 2.75e-17], N[(N[(t$95$0 * N[(t$95$1 * N[Exp[N[(N[(z + N[(N[Log[N[(7.5 - z), $MachinePrecision]], $MachinePrecision] * N[(0.5 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 263.3831869810514), $MachinePrecision], N[(N[(t$95$1 * N[(N[Power[N[(7.5 - z), $MachinePrecision], N[(0.5 - z), $MachinePrecision]], $MachinePrecision] * N[Exp[N[(z + -7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 * N[(N[(N[(N[(1.5056327351493116e-7 / N[(8.0 - z), $MachinePrecision]), $MachinePrecision] + N[(9.984369578019572e-6 / N[(7.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(771.3234287776531 / N[(3.0 - z), $MachinePrecision]), $MachinePrecision] + N[(0.9999999999998099 + N[(N[(676.5203681218851 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(-1259.1392167224028 / N[(2.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(-176.6150291621406 / N[(4.0 - z), $MachinePrecision]), $MachinePrecision] + N[(12.507343278686905 / N[(5.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.13857109526572012 / N[(6.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 98.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\pi}{\sin \left(z \cdot \pi\right)}\\ t_1 := \sqrt{2 \cdot \pi}\\ \mathbf{if}\;z \leq -1000:\\ \;\;\;\;\left(t_0 \cdot \left(t_1 \cdot e^{\left(z + \log \left(7.5 - z\right) \cdot \left(0.5 - z\right)\right) - 7.5}\right)\right) \cdot 263.3831869810514\\ \mathbf{else}:\\ \;\;\;\;\left(t_1 \cdot \left({\left(7.5 - z\right)}^{\left(0.5 - z\right)} \cdot e^{z + -7.5}\right)\right) \cdot \left(t_0 \cdot \left(\left(\frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} + \frac{-0.13857109526572012}{6 - z}\right)\right) + \left(\frac{1.5056327351493116 \cdot 10^{-7}}{8 - z} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} + \left(\frac{676.5203681218851}{1 - z} + \left(\frac{771.3234287776531}{3 - z} + \left(0.9999999999998099 + \frac{-1259.1392167224028}{2 - z}\right)\right)\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (/ PI (sin (* z PI)))) (t_1 (sqrt (* 2.0 PI))))
   (if (<= z -1000.0)
     (*
      (* t_0 (* t_1 (exp (- (+ z (* (log (- 7.5 z)) (- 0.5 z))) 7.5))))
      263.3831869810514)
     (*
      (* t_1 (* (pow (- 7.5 z) (- 0.5 z)) (exp (+ z -7.5))))
      (*
       t_0
       (+
        (+
         (/ -176.6150291621406 (- 4.0 z))
         (+
          (/ 12.507343278686905 (- 5.0 z))
          (/ -0.13857109526572012 (- 6.0 z))))
        (+
         (/ 1.5056327351493116e-7 (- 8.0 z))
         (+
          (/ 9.984369578019572e-6 (- 7.0 z))
          (+
           (/ 676.5203681218851 (- 1.0 z))
           (+
            (/ 771.3234287776531 (- 3.0 z))
            (+ 0.9999999999998099 (/ -1259.1392167224028 (- 2.0 z)))))))))))))

C

double code(double z) {
	double t_0 = ((double) M_PI) / sin((z * ((double) M_PI)));
	double t_1 = sqrt((2.0 * ((double) M_PI)));
	double tmp;
	if (z <= -1000.0) {
		tmp = (t_0 * (t_1 * exp(((z + (log((7.5 - z)) * (0.5 - z))) - 7.5)))) * 263.3831869810514;
	} else {
		tmp = (t_1 * (pow((7.5 - z), (0.5 - z)) * exp((z + -7.5)))) * (t_0 * (((-176.6150291621406 / (4.0 - z)) + ((12.507343278686905 / (5.0 - z)) + (-0.13857109526572012 / (6.0 - z)))) + ((1.5056327351493116e-7 / (8.0 - z)) + ((9.984369578019572e-6 / (7.0 - z)) + ((676.5203681218851 / (1.0 - z)) + ((771.3234287776531 / (3.0 - z)) + (0.9999999999998099 + (-1259.1392167224028 / (2.0 - z)))))))));
	}
	return tmp;
}

Java

public static double code(double z) {
	double t_0 = Math.PI / Math.sin((z * Math.PI));
	double t_1 = Math.sqrt((2.0 * Math.PI));
	double tmp;
	if (z <= -1000.0) {
		tmp = (t_0 * (t_1 * Math.exp(((z + (Math.log((7.5 - z)) * (0.5 - z))) - 7.5)))) * 263.3831869810514;
	} else {
		tmp = (t_1 * (Math.pow((7.5 - z), (0.5 - z)) * Math.exp((z + -7.5)))) * (t_0 * (((-176.6150291621406 / (4.0 - z)) + ((12.507343278686905 / (5.0 - z)) + (-0.13857109526572012 / (6.0 - z)))) + ((1.5056327351493116e-7 / (8.0 - z)) + ((9.984369578019572e-6 / (7.0 - z)) + ((676.5203681218851 / (1.0 - z)) + ((771.3234287776531 / (3.0 - z)) + (0.9999999999998099 + (-1259.1392167224028 / (2.0 - z)))))))));
	}
	return tmp;
}

Python

def code(z):
	t_0 = math.pi / math.sin((z * math.pi))
	t_1 = math.sqrt((2.0 * math.pi))
	tmp = 0
	if z <= -1000.0:
		tmp = (t_0 * (t_1 * math.exp(((z + (math.log((7.5 - z)) * (0.5 - z))) - 7.5)))) * 263.3831869810514
	else:
		tmp = (t_1 * (math.pow((7.5 - z), (0.5 - z)) * math.exp((z + -7.5)))) * (t_0 * (((-176.6150291621406 / (4.0 - z)) + ((12.507343278686905 / (5.0 - z)) + (-0.13857109526572012 / (6.0 - z)))) + ((1.5056327351493116e-7 / (8.0 - z)) + ((9.984369578019572e-6 / (7.0 - z)) + ((676.5203681218851 / (1.0 - z)) + ((771.3234287776531 / (3.0 - z)) + (0.9999999999998099 + (-1259.1392167224028 / (2.0 - z)))))))))
	return tmp

Julia

function code(z)
	t_0 = Float64(pi / sin(Float64(z * pi)))
	t_1 = sqrt(Float64(2.0 * pi))
	tmp = 0.0
	if (z <= -1000.0)
		tmp = Float64(Float64(t_0 * Float64(t_1 * exp(Float64(Float64(z + Float64(log(Float64(7.5 - z)) * Float64(0.5 - z))) - 7.5)))) * 263.3831869810514);
	else
		tmp = Float64(Float64(t_1 * Float64((Float64(7.5 - z) ^ Float64(0.5 - z)) * exp(Float64(z + -7.5)))) * Float64(t_0 * Float64(Float64(Float64(-176.6150291621406 / Float64(4.0 - z)) + Float64(Float64(12.507343278686905 / Float64(5.0 - z)) + Float64(-0.13857109526572012 / Float64(6.0 - z)))) + Float64(Float64(1.5056327351493116e-7 / Float64(8.0 - z)) + Float64(Float64(9.984369578019572e-6 / Float64(7.0 - z)) + Float64(Float64(676.5203681218851 / Float64(1.0 - z)) + Float64(Float64(771.3234287776531 / Float64(3.0 - z)) + Float64(0.9999999999998099 + Float64(-1259.1392167224028 / Float64(2.0 - z))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z)
	t_0 = pi / sin((z * pi));
	t_1 = sqrt((2.0 * pi));
	tmp = 0.0;
	if (z <= -1000.0)
		tmp = (t_0 * (t_1 * exp(((z + (log((7.5 - z)) * (0.5 - z))) - 7.5)))) * 263.3831869810514;
	else
		tmp = (t_1 * (((7.5 - z) ^ (0.5 - z)) * exp((z + -7.5)))) * (t_0 * (((-176.6150291621406 / (4.0 - z)) + ((12.507343278686905 / (5.0 - z)) + (-0.13857109526572012 / (6.0 - z)))) + ((1.5056327351493116e-7 / (8.0 - z)) + ((9.984369578019572e-6 / (7.0 - z)) + ((676.5203681218851 / (1.0 - z)) + ((771.3234287776531 / (3.0 - z)) + (0.9999999999998099 + (-1259.1392167224028 / (2.0 - z)))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[z_] := Block[{t$95$0 = N[(Pi / N[Sin[N[(z * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(2.0 * Pi), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, -1000.0], N[(N[(t$95$0 * N[(t$95$1 * N[Exp[N[(N[(z + N[(N[Log[N[(7.5 - z), $MachinePrecision]], $MachinePrecision] * N[(0.5 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 263.3831869810514), $MachinePrecision], N[(N[(t$95$1 * N[(N[Power[N[(7.5 - z), $MachinePrecision], N[(0.5 - z), $MachinePrecision]], $MachinePrecision] * N[Exp[N[(z + -7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 * N[(N[(N[(-176.6150291621406 / N[(4.0 - z), $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[(1.5056327351493116e-7 / N[(8.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(9.984369578019572e-6 / N[(7.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(676.5203681218851 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(771.3234287776531 / N[(3.0 - z), $MachinePrecision]), $MachinePrecision] + N[(0.9999999999998099 + N[(-1259.1392167224028 / N[(2.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 98.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\pi}{\sin \left(z \cdot \pi\right)}\\ t_1 := \sqrt{2 \cdot \pi}\\ \mathbf{if}\;z \leq -1000:\\ \;\;\;\;\left(t_0 \cdot \left(t_1 \cdot e^{\left(z + \log \left(7.5 - z\right) \cdot \left(0.5 - z\right)\right) - 7.5}\right)\right) \cdot 263.3831869810514\\ \mathbf{else}:\\ \;\;\;\;\left(t_0 \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-7}}{8 - z} + \left(\left(0.9999999999998099 + \left(\frac{771.3234287776531}{3 - z} + \frac{-1259.1392167224028}{2 - z}\right)\right) + \left(\frac{676.5203681218851}{1 - z} + \frac{9.984369578019572 \cdot 10^{-6}}{7 - z}\right)\right)\right) + \left(\frac{-176.6150291621406}{4 - z} + \left(\frac{12.507343278686905}{5 - z} + \frac{-0.13857109526572012}{6 - z}\right)\right)\right)\right) \cdot \left(t_1 \cdot \left({\left(7.5 - z\right)}^{\left(0.5 - z\right)} \cdot e^{z + -7.5}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (/ PI (sin (* z PI)))) (t_1 (sqrt (* 2.0 PI))))
   (if (<= z -1000.0)
     (*
      (* t_0 (* t_1 (exp (- (+ z (* (log (- 7.5 z)) (- 0.5 z))) 7.5))))
      263.3831869810514)
     (*
      (*
       t_0
       (+
        (+
         (/ 1.5056327351493116e-7 (- 8.0 z))
         (+
          (+
           0.9999999999998099
           (+
            (/ 771.3234287776531 (- 3.0 z))
            (/ -1259.1392167224028 (- 2.0 z))))
          (+
           (/ 676.5203681218851 (- 1.0 z))
           (/ 9.984369578019572e-6 (- 7.0 z)))))
        (+
         (/ -176.6150291621406 (- 4.0 z))
         (+
          (/ 12.507343278686905 (- 5.0 z))
          (/ -0.13857109526572012 (- 6.0 z))))))
      (* t_1 (* (pow (- 7.5 z) (- 0.5 z)) (exp (+ z -7.5))))))))

C

double code(double z) {
	double t_0 = ((double) M_PI) / sin((z * ((double) M_PI)));
	double t_1 = sqrt((2.0 * ((double) M_PI)));
	double tmp;
	if (z <= -1000.0) {
		tmp = (t_0 * (t_1 * exp(((z + (log((7.5 - z)) * (0.5 - z))) - 7.5)))) * 263.3831869810514;
	} else {
		tmp = (t_0 * (((1.5056327351493116e-7 / (8.0 - z)) + ((0.9999999999998099 + ((771.3234287776531 / (3.0 - z)) + (-1259.1392167224028 / (2.0 - z)))) + ((676.5203681218851 / (1.0 - z)) + (9.984369578019572e-6 / (7.0 - z))))) + ((-176.6150291621406 / (4.0 - z)) + ((12.507343278686905 / (5.0 - z)) + (-0.13857109526572012 / (6.0 - z)))))) * (t_1 * (pow((7.5 - z), (0.5 - z)) * exp((z + -7.5))));
	}
	return tmp;
}

Java

public static double code(double z) {
	double t_0 = Math.PI / Math.sin((z * Math.PI));
	double t_1 = Math.sqrt((2.0 * Math.PI));
	double tmp;
	if (z <= -1000.0) {
		tmp = (t_0 * (t_1 * Math.exp(((z + (Math.log((7.5 - z)) * (0.5 - z))) - 7.5)))) * 263.3831869810514;
	} else {
		tmp = (t_0 * (((1.5056327351493116e-7 / (8.0 - z)) + ((0.9999999999998099 + ((771.3234287776531 / (3.0 - z)) + (-1259.1392167224028 / (2.0 - z)))) + ((676.5203681218851 / (1.0 - z)) + (9.984369578019572e-6 / (7.0 - z))))) + ((-176.6150291621406 / (4.0 - z)) + ((12.507343278686905 / (5.0 - z)) + (-0.13857109526572012 / (6.0 - z)))))) * (t_1 * (Math.pow((7.5 - z), (0.5 - z)) * Math.exp((z + -7.5))));
	}
	return tmp;
}

Python

def code(z):
	t_0 = math.pi / math.sin((z * math.pi))
	t_1 = math.sqrt((2.0 * math.pi))
	tmp = 0
	if z <= -1000.0:
		tmp = (t_0 * (t_1 * math.exp(((z + (math.log((7.5 - z)) * (0.5 - z))) - 7.5)))) * 263.3831869810514
	else:
		tmp = (t_0 * (((1.5056327351493116e-7 / (8.0 - z)) + ((0.9999999999998099 + ((771.3234287776531 / (3.0 - z)) + (-1259.1392167224028 / (2.0 - z)))) + ((676.5203681218851 / (1.0 - z)) + (9.984369578019572e-6 / (7.0 - z))))) + ((-176.6150291621406 / (4.0 - z)) + ((12.507343278686905 / (5.0 - z)) + (-0.13857109526572012 / (6.0 - z)))))) * (t_1 * (math.pow((7.5 - z), (0.5 - z)) * math.exp((z + -7.5))))
	return tmp

Julia

function code(z)
	t_0 = Float64(pi / sin(Float64(z * pi)))
	t_1 = sqrt(Float64(2.0 * pi))
	tmp = 0.0
	if (z <= -1000.0)
		tmp = Float64(Float64(t_0 * Float64(t_1 * exp(Float64(Float64(z + Float64(log(Float64(7.5 - z)) * Float64(0.5 - z))) - 7.5)))) * 263.3831869810514);
	else
		tmp = Float64(Float64(t_0 * Float64(Float64(Float64(1.5056327351493116e-7 / Float64(8.0 - z)) + Float64(Float64(0.9999999999998099 + Float64(Float64(771.3234287776531 / Float64(3.0 - z)) + Float64(-1259.1392167224028 / Float64(2.0 - z)))) + Float64(Float64(676.5203681218851 / Float64(1.0 - z)) + Float64(9.984369578019572e-6 / Float64(7.0 - z))))) + Float64(Float64(-176.6150291621406 / Float64(4.0 - z)) + Float64(Float64(12.507343278686905 / Float64(5.0 - z)) + Float64(-0.13857109526572012 / Float64(6.0 - z)))))) * Float64(t_1 * Float64((Float64(7.5 - z) ^ Float64(0.5 - z)) * exp(Float64(z + -7.5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z)
	t_0 = pi / sin((z * pi));
	t_1 = sqrt((2.0 * pi));
	tmp = 0.0;
	if (z <= -1000.0)
		tmp = (t_0 * (t_1 * exp(((z + (log((7.5 - z)) * (0.5 - z))) - 7.5)))) * 263.3831869810514;
	else
		tmp = (t_0 * (((1.5056327351493116e-7 / (8.0 - z)) + ((0.9999999999998099 + ((771.3234287776531 / (3.0 - z)) + (-1259.1392167224028 / (2.0 - z)))) + ((676.5203681218851 / (1.0 - z)) + (9.984369578019572e-6 / (7.0 - z))))) + ((-176.6150291621406 / (4.0 - z)) + ((12.507343278686905 / (5.0 - z)) + (-0.13857109526572012 / (6.0 - z)))))) * (t_1 * (((7.5 - z) ^ (0.5 - z)) * exp((z + -7.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[z_] := Block[{t$95$0 = N[(Pi / N[Sin[N[(z * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(2.0 * Pi), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, -1000.0], N[(N[(t$95$0 * N[(t$95$1 * N[Exp[N[(N[(z + N[(N[Log[N[(7.5 - z), $MachinePrecision]], $MachinePrecision] * N[(0.5 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 263.3831869810514), $MachinePrecision], N[(N[(t$95$0 * N[(N[(N[(1.5056327351493116e-7 / N[(8.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(0.9999999999998099 + N[(N[(771.3234287776531 / N[(3.0 - z), $MachinePrecision]), $MachinePrecision] + N[(-1259.1392167224028 / N[(2.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(676.5203681218851 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(9.984369578019572e-6 / N[(7.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-176.6150291621406 / N[(4.0 - z), $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] * N[(t$95$1 * N[(N[Power[N[(7.5 - z), $MachinePrecision], N[(0.5 - z), $MachinePrecision]], $MachinePrecision] * N[Exp[N[(z + -7.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 96.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(0.9999999999998099 + \frac{93.9015195213674 + 582.6188486005177 \cdot z}{\left(1 - z\right) \cdot \left(2 - z\right)}\right) + \left(\frac{771.3234287776531}{\left(1 - z\right) + 2} + \left(\frac{-176.6150291621406}{\left(1 - z\right) + 3} + \frac{12.507343278686905}{\left(1 - z\right) + 4}\right)\right)\right) + \left(\frac{-0.13857109526572012}{\left(1 - z\right) + 5} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(1 - z\right) + 6} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) + 7}\right)\right)\right) \cdot \left(\left(\sqrt{2 \cdot \pi} \cdot e^{\left(\left(z + -1\right) - 6.5\right) + \left(0.5 - z\right) \cdot \log \left(\left(1 - z\right) + 6.5\right)}\right) \cdot \frac{\pi}{z \cdot \pi}\right) \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (*
  (+
   (+
    (+
     0.9999999999998099
     (/ (+ 93.9015195213674 (* 582.6188486005177 z)) (* (- 1.0 z) (- 2.0 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 (+ (- 1.0 z) 6.0))
     (/ 1.5056327351493116e-7 (+ (- 1.0 z) 7.0)))))
  (*
   (*
    (sqrt (* 2.0 PI))
    (exp (+ (- (+ z -1.0) 6.5) (* (- 0.5 z) (log (+ (- 1.0 z) 6.5))))))
   (/ PI (* z PI)))))

C

double code(double z) {
	return (((0.9999999999998099 + ((93.9015195213674 + (582.6188486005177 * z)) / ((1.0 - z) * (2.0 - 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 / ((1.0 - z) + 6.0)) + (1.5056327351493116e-7 / ((1.0 - z) + 7.0))))) * ((sqrt((2.0 * ((double) M_PI))) * exp((((z + -1.0) - 6.5) + ((0.5 - z) * log(((1.0 - z) + 6.5)))))) * (((double) M_PI) / (z * ((double) M_PI))));
}

Java

public static double code(double z) {
	return (((0.9999999999998099 + ((93.9015195213674 + (582.6188486005177 * z)) / ((1.0 - z) * (2.0 - 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 / ((1.0 - z) + 6.0)) + (1.5056327351493116e-7 / ((1.0 - z) + 7.0))))) * ((Math.sqrt((2.0 * Math.PI)) * Math.exp((((z + -1.0) - 6.5) + ((0.5 - z) * Math.log(((1.0 - z) + 6.5)))))) * (Math.PI / (z * Math.PI)));
}

Python

def code(z):
	return (((0.9999999999998099 + ((93.9015195213674 + (582.6188486005177 * z)) / ((1.0 - z) * (2.0 - 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 / ((1.0 - z) + 6.0)) + (1.5056327351493116e-7 / ((1.0 - z) + 7.0))))) * ((math.sqrt((2.0 * math.pi)) * math.exp((((z + -1.0) - 6.5) + ((0.5 - z) * math.log(((1.0 - z) + 6.5)))))) * (math.pi / (z * math.pi)))

Julia

function code(z)
	return Float64(Float64(Float64(Float64(0.9999999999998099 + Float64(Float64(93.9015195213674 + Float64(582.6188486005177 * z)) / Float64(Float64(1.0 - z) * Float64(2.0 - z)))) + Float64(Float64(771.3234287776531 / Float64(Float64(1.0 - z) + 2.0)) + Float64(Float64(-176.6150291621406 / Float64(Float64(1.0 - z) + 3.0)) + Float64(12.507343278686905 / Float64(Float64(1.0 - z) + 4.0))))) + Float64(Float64(-0.13857109526572012 / Float64(Float64(1.0 - z) + 5.0)) + Float64(Float64(9.984369578019572e-6 / Float64(Float64(1.0 - z) + 6.0)) + Float64(1.5056327351493116e-7 / Float64(Float64(1.0 - z) + 7.0))))) * Float64(Float64(sqrt(Float64(2.0 * pi)) * exp(Float64(Float64(Float64(z + -1.0) - 6.5) + Float64(Float64(0.5 - z) * log(Float64(Float64(1.0 - z) + 6.5)))))) * Float64(pi / Float64(z * pi))))
end

MATLAB

function tmp = code(z)
	tmp = (((0.9999999999998099 + ((93.9015195213674 + (582.6188486005177 * z)) / ((1.0 - z) * (2.0 - 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 / ((1.0 - z) + 6.0)) + (1.5056327351493116e-7 / ((1.0 - z) + 7.0))))) * ((sqrt((2.0 * pi)) * exp((((z + -1.0) - 6.5) + ((0.5 - z) * log(((1.0 - z) + 6.5)))))) * (pi / (z * pi)));
end

Wolfram

code[z_] := N[(N[(N[(N[(0.9999999999998099 + N[(N[(93.9015195213674 + N[(582.6188486005177 * z), $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 - z), $MachinePrecision] * N[(2.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(771.3234287776531 / N[(N[(1.0 - z), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] + N[(N[(-176.6150291621406 / N[(N[(1.0 - z), $MachinePrecision] + 3.0), $MachinePrecision]), $MachinePrecision] + N[(12.507343278686905 / N[(N[(1.0 - z), $MachinePrecision] + 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-0.13857109526572012 / N[(N[(1.0 - z), $MachinePrecision] + 5.0), $MachinePrecision]), $MachinePrecision] + N[(N[(9.984369578019572e-6 / N[(N[(1.0 - z), $MachinePrecision] + 6.0), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(N[(1.0 - z), $MachinePrecision] + 7.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[Sqrt[N[(2.0 * Pi), $MachinePrecision]], $MachinePrecision] * N[Exp[N[(N[(N[(z + -1.0), $MachinePrecision] - 6.5), $MachinePrecision] + N[(N[(0.5 - z), $MachinePrecision] * N[Log[N[(N[(1.0 - z), $MachinePrecision] + 6.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(Pi / N[(z * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 96.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \left(\sqrt{2 \cdot \pi} \cdot e^{\left(z + -7.5\right) + \log \left({\left(\mathsf{fma}\left(-1, z, 7.5\right)\right)}^{\left(0.5 - z\right)}\right)}\right) \cdot \frac{263.3831869810514}{z} \end{array} \]

FPCore

(FPCore (z)
 :precision binary64
 (*
  (*
   (sqrt (* 2.0 PI))
   (exp (+ (+ z -7.5) (log (pow (fma -1.0 z 7.5) (- 0.5 z))))))
  (/ 263.3831869810514 z)))

C

double code(double z) {
	return (sqrt((2.0 * ((double) M_PI))) * exp(((z + -7.5) + log(pow(fma(-1.0, z, 7.5), (0.5 - z)))))) * (263.3831869810514 / z);
}

Julia

function code(z)
	return Float64(Float64(sqrt(Float64(2.0 * pi)) * exp(Float64(Float64(z + -7.5) + log((fma(-1.0, z, 7.5) ^ Float64(0.5 - z)))))) * Float64(263.3831869810514 / z))
end

Wolfram

code[z_] := N[(N[(N[Sqrt[N[(2.0 * Pi), $MachinePrecision]], $MachinePrecision] * N[Exp[N[(N[(z + -7.5), $MachinePrecision] + N[Log[N[Power[N[(-1.0 * z + 7.5), $MachinePrecision], N[(0.5 - z), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(263.3831869810514 / z), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 95.8% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 11: 95.9% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 12: 96.1% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 13: 94.4% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 14: 95.1% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2023340 
(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))))))