Average Error: 1.7 → 0.5
Time: 1.3min
Precision: binary64
Cost: 49088
\[z \leq 0.5\]
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right) \]
↓
\[\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(e^{z + -7.5} \cdot \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(\frac{771.3234287776531}{3 - z} + \frac{-176.6150291621406}{4 - z}\right)\right) + \left(\frac{12.507343278686905}{5 - z} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} + \left(\frac{-0.13857109526572012}{6 - z} + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right)\right)\right)\right)\right) \]
(FPCore (z)
 :precision binary64
 (*
  (/ 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))))))
↓
(FPCore (z)
 :precision binary64
 (*
  (* (sqrt (* PI 2.0)) (pow (- 7.5 z) (- 0.5 z)))
  (*
   (/ PI (sin (* PI z)))
   (*
    (exp (+ z -7.5))
    (+
     (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))
     (+
      (+
       (/ -1259.1392167224028 (- 2.0 z))
       (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))))
      (+
       (/ 12.507343278686905 (- 5.0 z))
       (+
        (/ 9.984369578019572e-6 (- 7.0 z))
        (+
         (/ -0.13857109526572012 (- 6.0 z))
         (/ 1.5056327351493116e-7 (- 8.0 z)))))))))))
double code(double z) {
	return (((double) M_PI) / sin((((double) M_PI) * z))) * (((sqrt((((double) M_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))));
}
↓
double code(double z) {
	return (sqrt((((double) M_PI) * 2.0)) * pow((7.5 - z), (0.5 - z))) * ((((double) M_PI) / sin((((double) M_PI) * z))) * (exp((z + -7.5)) * ((0.9999999999998099 + (676.5203681218851 / (1.0 - z))) + (((-1259.1392167224028 / (2.0 - z)) + ((771.3234287776531 / (3.0 - z)) + (-176.6150291621406 / (4.0 - z)))) + ((12.507343278686905 / (5.0 - z)) + ((9.984369578019572e-6 / (7.0 - z)) + ((-0.13857109526572012 / (6.0 - z)) + (1.5056327351493116e-7 / (8.0 - z)))))))));
}

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

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

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

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

code[z_] := N[(N[(Pi / N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[Sqrt[N[(Pi * 2.0), $MachinePrecision]], $MachinePrecision] * N[Power[N[(N[(N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision] + 7.0), $MachinePrecision] + 0.5), $MachinePrecision], N[(N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision] + 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Exp[(-N[(N[(N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision] + 7.0), $MachinePrecision] + 0.5), $MachinePrecision])], $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(0.9999999999998099 + N[(676.5203681218851 / N[(N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1259.1392167224028 / N[(N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(771.3234287776531 / N[(N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision] + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-176.6150291621406 / N[(N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision] + 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(12.507343278686905 / N[(N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision] + 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.13857109526572012 / N[(N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision] + 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(9.984369578019572e-6 / N[(N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision] + 7.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(N[(N[(1.0 - z), $MachinePrecision] - 1.0), $MachinePrecision] + 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[z_] := N[(N[(N[Sqrt[N[(Pi * 2.0), $MachinePrecision]], $MachinePrecision] * N[Power[N[(7.5 - z), $MachinePrecision], N[(0.5 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(Pi / N[Sin[N[(Pi * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[Exp[N[(z + -7.5), $MachinePrecision]], $MachinePrecision] * N[(N[(0.9999999999998099 + N[(676.5203681218851 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(-1259.1392167224028 / N[(2.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(771.3234287776531 / N[(3.0 - z), $MachinePrecision]), $MachinePrecision] + N[(-176.6150291621406 / N[(4.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(12.507343278686905 / N[(5.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(9.984369578019572e-6 / N[(7.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(-0.13857109526572012 / N[(6.0 - z), $MachinePrecision]), $MachinePrecision] + N[(1.5056327351493116e-7 / N[(8.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

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

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.7

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

  2. Simplified0.5

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

  3. Final simplification0.5

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

Alternatives

Alternative 1
Error0.7
Cost49088
\[\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot \frac{\pi \cdot \left(e^{z + -7.5} \cdot \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \left(\frac{-1259.1392167224028}{2 - z} + \left(\left(\frac{771.3234287776531}{3 - z} + \frac{-176.6150291621406}{4 - z}\right) + \left(\frac{12.507343278686905}{5 - z} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} + \left(\frac{-0.13857109526572012}{6 - z} + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right)\right)\right)\right)\right)}{\sin \left(\pi \cdot z\right)} \]
Alternative 2
Error1.1
Cost48704
\[\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot \frac{\pi \cdot \left(e^{z + -7.5} \cdot \left(0.9999999999998099 + \left(\frac{676.5203681218851}{1 - z} + \left(\left(\frac{12.507343278686905}{5 - z} + \left(\frac{9.984369578019572 \cdot 10^{-6}}{7 - z} + \left(\frac{-0.13857109526572012}{6 - z} + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)\right) + \left(\frac{-1259.1392167224028}{2 - z} + \left(z \cdot 74.66416387488323 + 212.9540523020159\right)\right)\right)\right)\right)\right)}{\sin \left(\pi \cdot z\right)} \]
Alternative 3
Error1.5
Cost45888
\[\left({\left(7.5 - z\right)}^{\left(0.5 - z\right)} \cdot \left(\sqrt{\pi} \cdot \sqrt{2}\right)\right) \cdot \mathsf{fma}\left(e^{-7.5}, 700.279359537391, e^{-7.5} \cdot \frac{263.3831869810514}{z}\right) \]
Alternative 4
Error1.7
Cost26688
\[\frac{\sqrt{69370.70318429549 \cdot \left(\left(\pi \cdot 2\right) \cdot {\left(7.5 - z\right)}^{\left(2 \cdot \left(0.5 - z\right)\right)}\right)}}{\frac{z}{e^{-7.5}}} \]
Alternative 5
Error2.3
Cost26240
\[\sqrt{7.5} \cdot \left(\frac{263.3831869810514}{z} \cdot \frac{\sqrt{\pi \cdot 2}}{e^{7.5}}\right) \]
Alternative 6
Error2.1
Cost26240
\[\sqrt{7.5} \cdot \left(e^{-7.5} \cdot \frac{\sqrt{\left(\pi \cdot 2\right) \cdot 69370.70318429549}}{z}\right) \]
Alternative 7
Error1.6
Cost26240
\[\left(\sqrt{\left(\pi \cdot 2\right) \cdot 69370.70318429549} \cdot \frac{e^{-7.5}}{z}\right) \cdot \sqrt{7.5} \]

Error

Reproduce

herbie shell --seed 2022284 
(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))))))