Jmat.Real.gamma, branch z less than 0.5

Percentage Accurate: 96.5% → 99.4%

Time: 13.7s

Alternatives: 7

Speedup: 1.1×

• could not determine a ground truth

  1. z = -6174838915726.792

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: 96.5% 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: 99.4% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (- (- 1.0 z) (- (- 1.0 7.0) 0.5))))
   (/
    (*
     (*
      PI
      (*
       (exp
        (fma
         (log t_0)
         (/
          (- (* (- 1.0 z) (- 1.0 z)) (* (- 1.0 0.5) (- 1.0 0.5)))
          (+ (- 1.0 z) (- 1.0 0.5)))
         (- t_0)))
       (sqrt (+ PI PI))))
     (+
      (/ 1.5056327351493116e-7 (- (- 1.0 z) (- 1.0 8.0)))
      (+
       (+
        (+
         (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))
         (/ -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))))))))
    (sin (* PI z)))))

C

double code(double z) {
	double t_0 = (1.0 - z) - ((1.0 - 7.0) - 0.5);
	return ((((double) M_PI) * (exp(fma(log(t_0), ((((1.0 - z) * (1.0 - z)) - ((1.0 - 0.5) * (1.0 - 0.5))) / ((1.0 - z) + (1.0 - 0.5))), -t_0)) * sqrt((((double) M_PI) + ((double) M_PI))))) * ((1.5056327351493116e-7 / ((1.0 - z) - (1.0 - 8.0))) + ((((0.9999999999998099 + (676.5203681218851 / (1.0 - z))) + (-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)))))))) / sin((((double) M_PI) * z));
}

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

3. Applied rewrites 99.4%

   \[\leadsto \color{blue}{\frac{\left(\pi \cdot \left(e^{\mathsf{fma}\left(\log \left(\left(1 - z\right) - \left(\left(1 - 7\right) - 0.5\right)\right), \left(1 - z\right) - \left(1 - 0.5\right), -\left(\left(1 - z\right) - \left(\left(1 - 7\right) - 0.5\right)\right)\right)} \cdot \sqrt{\pi + \pi}\right)\right) \cdot \left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right) + \left(\frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)}\right)\right) + \left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right) + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-6}}{\left(1 - z\right) - \left(1 - 7\right)}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) - \left(1 - 8\right)}\right)}{\sin \left(\pi \cdot z\right)}} \]

5. Applied rewrites 99.4%

   \[\leadsto \frac{\left(\pi \cdot \left(e^{\mathsf{fma}\left(\log \left(\left(1 - z\right) - \left(\left(1 - 7\right) - 0.5\right)\right), \color{blue}{\frac{\left(1 - z\right) \cdot \left(1 - z\right) - \left(1 - 0.5\right) \cdot \left(1 - 0.5\right)}{\left(1 - z\right) + \left(1 - 0.5\right)}}, -\left(\left(1 - z\right) - \left(\left(1 - 7\right) - 0.5\right)\right)\right)} \cdot \sqrt{\pi + \pi}\right)\right) \cdot \left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right) + \left(\frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)}\right)\right) + \left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right) + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-6}}{\left(1 - z\right) - \left(1 - 7\right)}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) - \left(1 - 8\right)}\right)}{\sin \left(\pi \cdot z\right)} \]

7. Applied rewrites 99.4%

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

Alternative 2: 99.4% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (- (- 1.0 z) (- (- 1.0 7.0) 0.5))))
   (/
    (*
     (*
      PI
      (*
       (exp
        (fma
         (log t_0)
         (/
          (* (- 1.0 (- z (- 1.0 0.5))) (- (- 1.0 z) (- 1.0 0.5)))
          (+ (- 1.0 z) (- 1.0 0.5)))
         (- t_0)))
       (sqrt (+ PI PI))))
     (+
      (/ 1.5056327351493116e-7 (- (- 1.0 z) (- 1.0 8.0)))
      (+
       (+
        (+
         (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))
         (/ -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))))))))
    (sin (* PI z)))))

C

double code(double z) {
	double t_0 = (1.0 - z) - ((1.0 - 7.0) - 0.5);
	return ((((double) M_PI) * (exp(fma(log(t_0), (((1.0 - (z - (1.0 - 0.5))) * ((1.0 - z) - (1.0 - 0.5))) / ((1.0 - z) + (1.0 - 0.5))), -t_0)) * sqrt((((double) M_PI) + ((double) M_PI))))) * ((1.5056327351493116e-7 / ((1.0 - z) - (1.0 - 8.0))) + ((((0.9999999999998099 + (676.5203681218851 / (1.0 - z))) + (-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)))))))) / sin((((double) M_PI) * z));
}

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

3. Applied rewrites 99.4%

   \[\leadsto \color{blue}{\frac{\left(\pi \cdot \left(e^{\mathsf{fma}\left(\log \left(\left(1 - z\right) - \left(\left(1 - 7\right) - 0.5\right)\right), \left(1 - z\right) - \left(1 - 0.5\right), -\left(\left(1 - z\right) - \left(\left(1 - 7\right) - 0.5\right)\right)\right)} \cdot \sqrt{\pi + \pi}\right)\right) \cdot \left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right) + \left(\frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)}\right)\right) + \left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right) + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-6}}{\left(1 - z\right) - \left(1 - 7\right)}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) - \left(1 - 8\right)}\right)}{\sin \left(\pi \cdot z\right)}} \]

5. Applied rewrites 99.4%

   \[\leadsto \frac{\left(\pi \cdot \left(e^{\mathsf{fma}\left(\log \left(\left(1 - z\right) - \left(\left(1 - 7\right) - 0.5\right)\right), \color{blue}{\frac{\left(1 - z\right) \cdot \left(1 - z\right) - \left(1 - 0.5\right) \cdot \left(1 - 0.5\right)}{\left(1 - z\right) + \left(1 - 0.5\right)}}, -\left(\left(1 - z\right) - \left(\left(1 - 7\right) - 0.5\right)\right)\right)} \cdot \sqrt{\pi + \pi}\right)\right) \cdot \left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right) + \left(\frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)}\right)\right) + \left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right) + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-6}}{\left(1 - z\right) - \left(1 - 7\right)}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) - \left(1 - 8\right)}\right)}{\sin \left(\pi \cdot z\right)} \]

7. Applied rewrites 99.4%

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

9. Applied rewrites 99.4%

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

Alternative 3: 99.4% accurate, 1.1× speedup

Math

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

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (- (- 1.0 z) (- (- 1.0 7.0) 0.5))))
   (/
    (*
     (*
      PI
      (*
       (exp (fma (log t_0) (- (- 1.0 z) (- 1.0 0.5)) (- t_0)))
       (sqrt (+ PI PI))))
     (+
      (/ 1.5056327351493116e-7 (- (- 1.0 z) (- 1.0 8.0)))
      (+
       (+
        (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))
        (+
         (/ -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))))))))
    (sin (* PI z)))))

C

double code(double z) {
	double t_0 = (1.0 - z) - ((1.0 - 7.0) - 0.5);
	return ((((double) M_PI) * (exp(fma(log(t_0), ((1.0 - z) - (1.0 - 0.5)), -t_0)) * sqrt((((double) M_PI) + ((double) M_PI))))) * ((1.5056327351493116e-7 / ((1.0 - z) - (1.0 - 8.0))) + (((0.9999999999998099 + (676.5203681218851 / (1.0 - z))) + ((-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)))))))) / sin((((double) M_PI) * z));
}

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

3. Applied rewrites 99.4%

   \[\leadsto \color{blue}{\frac{\left(\pi \cdot \left(e^{\mathsf{fma}\left(\log \left(\left(1 - z\right) - \left(\left(1 - 7\right) - 0.5\right)\right), \left(1 - z\right) - \left(1 - 0.5\right), -\left(\left(1 - z\right) - \left(\left(1 - 7\right) - 0.5\right)\right)\right)} \cdot \sqrt{\pi + \pi}\right)\right) \cdot \left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right) + \left(\frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)}\right)\right) + \left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right) + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-6}}{\left(1 - z\right) - \left(1 - 7\right)}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) - \left(1 - 8\right)}\right)}{\sin \left(\pi \cdot z\right)}} \]

5. Applied rewrites 99.4%

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

Alternative 4: 99.3% accurate, 1.1× speedup

Math

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

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (- (- 1.0 z) (- (- 1.0 7.0) 0.5))))
   (*
    PI
    (*
     (+
      (+
       (+
        (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))
        (+
         (/ -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))))
     (/
      (*
       (exp (fma (log t_0) (- (- 1.0 z) (- 1.0 0.5)) (- t_0)))
       (sqrt (+ PI PI)))
      (sin (* PI z)))))))

C

double code(double z) {
	double t_0 = (1.0 - z) - ((1.0 - 7.0) - 0.5);
	return ((double) M_PI) * (((((0.9999999999998099 + (676.5203681218851 / (1.0 - z))) + ((-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)))) * ((exp(fma(log(t_0), ((1.0 - z) - (1.0 - 0.5)), -t_0)) * sqrt((((double) M_PI) + ((double) M_PI)))) / sin((((double) M_PI) * z))));
}

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

3. Applied rewrites 99.2%

   \[\leadsto \color{blue}{\pi \cdot \frac{\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right) + \left(\frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)}\right)\right) + \left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right) + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-6}}{\left(1 - z\right) - \left(1 - 7\right)}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) - \left(1 - 8\right)}\right) \cdot \left(e^{\mathsf{fma}\left(\log \left(\left(1 - z\right) - \left(\left(1 - 7\right) - 0.5\right)\right), \left(1 - z\right) - \left(1 - 0.5\right), -\left(\left(1 - z\right) - \left(\left(1 - 7\right) - 0.5\right)\right)\right)} \cdot \sqrt{\pi + \pi}\right)}{\sin \left(\pi \cdot z\right)}} \]

5. Applied rewrites 99.3%

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

Alternative 5: 99.2% accurate, 1.1× speedup

Math

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

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (- (- 1.0 z) (- (- 1.0 7.0) 0.5))))
   (*
    (/ PI (sin (* PI z)))
    (*
     (+
      (+
       (+
        (+
         (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))
         (/ -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)))))
       (+
        (/ 9.984369578019572e-6 (- (- 1.0 z) (- 1.0 7.0)))
        (/ 1.5056327351493116e-7 (- (- 1.0 z) (- 1.0 8.0)))))
      (/ -0.13857109526572012 (- (- 1.0 z) (- 1.0 6.0))))
     (*
      (exp (fma (log t_0) (- (- 1.0 z) (- 1.0 0.5)) (- t_0)))
      (sqrt (+ PI PI)))))))

C

double code(double z) {
	double t_0 = (1.0 - z) - ((1.0 - 7.0) - 0.5);
	return (((double) M_PI) / sin((((double) M_PI) * z))) * ((((((0.9999999999998099 + (676.5203681218851 / (1.0 - z))) + (-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))))) + ((9.984369578019572e-6 / ((1.0 - z) - (1.0 - 7.0))) + (1.5056327351493116e-7 / ((1.0 - z) - (1.0 - 8.0))))) + (-0.13857109526572012 / ((1.0 - z) - (1.0 - 6.0)))) * (exp(fma(log(t_0), ((1.0 - z) - (1.0 - 0.5)), -t_0)) * sqrt((((double) M_PI) + ((double) M_PI)))));
}

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

3. Applied rewrites 97.6%

   \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \color{blue}{\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)}\right) + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(1 - z\right) - \left(1 - 7\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) - \left(1 - 8\right)}\right)\right)\right)}\right) \]

5. Applied rewrites 97.8%

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

7. Applied rewrites 99.2%

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

Alternative 6: 97.8% accurate, 1.1× speedup

Math

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

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (- (- 1.0 z) (- (- 1.0 7.0) 0.5))))
   (*
    (/ PI (sin (* PI z)))
    (*
     (+
      (+
       (+
        (+
         (+
          0.9999999999998099
          (+
           (/ 676.5203681218851 (- 1.0 z))
           (/ -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))))
       (+
        (/ 9.984369578019572e-6 (- (- 1.0 z) (- 1.0 7.0)))
        (/ 1.5056327351493116e-7 (- (- 1.0 z) (- 1.0 8.0)))))
      (/ -0.13857109526572012 (- (- 1.0 z) (- 1.0 6.0))))
     (*
      (exp (fma (log t_0) (- (- 1.0 z) (- 1.0 0.5)) (- t_0)))
      (sqrt (+ PI PI)))))))

C

double code(double z) {
	double t_0 = (1.0 - z) - ((1.0 - 7.0) - 0.5);
	return (((double) M_PI) / sin((((double) M_PI) * z))) * ((((((0.9999999999998099 + ((676.5203681218851 / (1.0 - z)) + (-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)))) + ((9.984369578019572e-6 / ((1.0 - z) - (1.0 - 7.0))) + (1.5056327351493116e-7 / ((1.0 - z) - (1.0 - 8.0))))) + (-0.13857109526572012 / ((1.0 - z) - (1.0 - 6.0)))) * (exp(fma(log(t_0), ((1.0 - z) - (1.0 - 0.5)), -t_0)) * sqrt((((double) M_PI) + ((double) M_PI)))));
}

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

3. Applied rewrites 97.6%

   \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \color{blue}{\left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(\left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)}\right) + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right)\right) + \left(\frac{9.984369578019572 \cdot 10^{-6}}{\left(1 - z\right) - \left(1 - 7\right)} + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) - \left(1 - 8\right)}\right)\right)\right)}\right) \]

5. Applied rewrites 97.8%

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

7. Applied rewrites 97.8%

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

Alternative 7: 97.8% accurate, 1.1× speedup

Math

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

FPCore

(FPCore (z)
 :precision binary64
 (let* ((t_0 (- (- 1.0 z) (- (- 1.0 7.0) 0.5))))
   (*
    PI
    (/
     (*
      (+
       (+
        (+
         0.9999999999998099
         (+
          (/ 676.5203681218851 (- 1.0 z))
          (+
           (/ -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))))
      (*
       (exp (fma (log t_0) (- (- 1.0 z) (- 1.0 0.5)) (- t_0)))
       (sqrt (+ PI PI))))
     (sin (* PI z))))))

C

double code(double z) {
	double t_0 = (1.0 - z) - ((1.0 - 7.0) - 0.5);
	return ((double) M_PI) * (((((0.9999999999998099 + ((676.5203681218851 / (1.0 - z)) + ((-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)))) * (exp(fma(log(t_0), ((1.0 - z) - (1.0 - 0.5)), -t_0)) * sqrt((((double) M_PI) + ((double) M_PI))))) / sin((((double) M_PI) * z)));
}

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

3. Applied rewrites 99.2%

   \[\leadsto \color{blue}{\pi \cdot \frac{\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(1 - z\right) - 0}\right) + \left(\frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)} + \frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)}\right)\right) + \left(\left(\frac{-176.6150291621406}{\left(1 - z\right) - \left(1 - 4\right)} + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right) + \left(\frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)} + \frac{9.984369578019572 \cdot 10^{-6}}{\left(1 - z\right) - \left(1 - 7\right)}\right)\right)\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(1 - z\right) - \left(1 - 8\right)}\right) \cdot \left(e^{\mathsf{fma}\left(\log \left(\left(1 - z\right) - \left(\left(1 - 7\right) - 0.5\right)\right), \left(1 - z\right) - \left(1 - 0.5\right), -\left(\left(1 - z\right) - \left(\left(1 - 7\right) - 0.5\right)\right)\right)} \cdot \sqrt{\pi + \pi}\right)}{\sin \left(\pi \cdot z\right)}} \]

5. Applied rewrites 97.8%

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

Reproduce

herbie shell --seed 2025121 
(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))))))