Average Error: 1.8 → 0.4
Time: 9.8min
Precision: binary64
Cost: 62976
\[z \leq 0.5\]
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
↓
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\frac{\left(7 - z\right) \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left({\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)}^{3} + {\left(\frac{-176.6150291621406}{4 - z}\right)}^{3}\right) + 12.507343278686905 \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) + -0.13857109526572012 \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right) + 9.984369578019572 \cdot 10^{-06} \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right)}{\left(7 - z\right) \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right)\]
\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^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
↓
\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\frac{\left(7 - z\right) \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left({\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)}^{3} + {\left(\frac{-176.6150291621406}{4 - z}\right)}^{3}\right) + 12.507343278686905 \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) + -0.13857109526572012 \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right) + 9.984369578019572 \cdot 10^{-06} \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right)}{\left(7 - z\right) \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\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-06 (+ (- (- 1.0 z) 1.0) 7.0)))
    (/ 1.5056327351493116e-07 (+ (- (- 1.0 z) 1.0) 8.0))))))
↓
(FPCore (z)
 :precision binary64
 (*
  (/ PI (sin (* PI z)))
  (*
   (* (* (sqrt (* PI 2.0)) (pow (- 7.5 z) (- 0.5 z))) (exp (+ z -7.5)))
   (+
    (/
     (+
      (*
       (- 7.0 z)
       (+
        (*
         (- 6.0 z)
         (+
          (*
           (- 5.0 z)
           (+
            (pow
             (+
              (+
               (/ -1259.1392167224028 (- 2.0 z))
               (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
              (/ 771.3234287776531 (- 3.0 z)))
             3.0)
            (pow (/ -176.6150291621406 (- 4.0 z)) 3.0)))
          (*
           12.507343278686905
           (+
            (*
             (+
              (+
               (/ -1259.1392167224028 (- 2.0 z))
               (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
              (/ 771.3234287776531 (- 3.0 z)))
             (+
              (+
               (/ -1259.1392167224028 (- 2.0 z))
               (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
              (/ 771.3234287776531 (- 3.0 z))))
            (*
             (/ -176.6150291621406 (- 4.0 z))
             (-
              (/ -176.6150291621406 (- 4.0 z))
              (+
               (+
                (/ -1259.1392167224028 (- 2.0 z))
                (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
               (/ 771.3234287776531 (- 3.0 z)))))))))
        (*
         -0.13857109526572012
         (*
          (- 5.0 z)
          (+
           (*
            (+
             (+
              (/ -1259.1392167224028 (- 2.0 z))
              (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
             (/ 771.3234287776531 (- 3.0 z)))
            (+
             (+
              (/ -1259.1392167224028 (- 2.0 z))
              (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
             (/ 771.3234287776531 (- 3.0 z))))
           (*
            (/ -176.6150291621406 (- 4.0 z))
            (-
             (/ -176.6150291621406 (- 4.0 z))
             (+
              (+
               (/ -1259.1392167224028 (- 2.0 z))
               (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
              (/ 771.3234287776531 (- 3.0 z))))))))))
      (*
       9.984369578019572e-06
       (*
        (- 6.0 z)
        (*
         (- 5.0 z)
         (+
          (*
           (+
            (+
             (/ -1259.1392167224028 (- 2.0 z))
             (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
            (/ 771.3234287776531 (- 3.0 z)))
           (+
            (+
             (/ -1259.1392167224028 (- 2.0 z))
             (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
            (/ 771.3234287776531 (- 3.0 z))))
          (*
           (/ -176.6150291621406 (- 4.0 z))
           (-
            (/ -176.6150291621406 (- 4.0 z))
            (+
             (+
              (/ -1259.1392167224028 (- 2.0 z))
              (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
             (/ 771.3234287776531 (- 3.0 z))))))))))
     (*
      (- 7.0 z)
      (*
       (- 6.0 z)
       (*
        (- 5.0 z)
        (+
         (*
          (+
           (+
            (/ -1259.1392167224028 (- 2.0 z))
            (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
           (/ 771.3234287776531 (- 3.0 z)))
          (+
           (+
            (/ -1259.1392167224028 (- 2.0 z))
            (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
           (/ 771.3234287776531 (- 3.0 z))))
         (*
          (/ -176.6150291621406 (- 4.0 z))
          (-
           (/ -176.6150291621406 (- 4.0 z))
           (+
            (+
             (/ -1259.1392167224028 (- 2.0 z))
             (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
            (/ 771.3234287776531 (- 3.0 z))))))))))
    (/ 1.5056327351493116e-07 (- 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-06 / (((1.0 - z) - 1.0) + 7.0))) + (1.5056327351493116e-07 / (((1.0 - z) - 1.0) + 8.0))));
}
↓
double code(double z) {
	return (((double) M_PI) / sin(((double) M_PI) * z)) * (((sqrt(((double) M_PI) * 2.0) * pow((7.5 - z), (0.5 - z))) * exp(z + -7.5)) * (((((7.0 - z) * (((6.0 - z) * (((5.0 - z) * (pow((((-1259.1392167224028 / (2.0 - z)) + (0.9999999999998099 + (676.5203681218851 / (1.0 - z)))) + (771.3234287776531 / (3.0 - z))), 3.0) + pow((-176.6150291621406 / (4.0 - z)), 3.0))) + (12.507343278686905 * (((((-1259.1392167224028 / (2.0 - z)) + (0.9999999999998099 + (676.5203681218851 / (1.0 - z)))) + (771.3234287776531 / (3.0 - z))) * (((-1259.1392167224028 / (2.0 - z)) + (0.9999999999998099 + (676.5203681218851 / (1.0 - z)))) + (771.3234287776531 / (3.0 - z)))) + ((-176.6150291621406 / (4.0 - z)) * ((-176.6150291621406 / (4.0 - z)) - (((-1259.1392167224028 / (2.0 - z)) + (0.9999999999998099 + (676.5203681218851 / (1.0 - z)))) + (771.3234287776531 / (3.0 - z))))))))) + (-0.13857109526572012 * ((5.0 - z) * (((((-1259.1392167224028 / (2.0 - z)) + (0.9999999999998099 + (676.5203681218851 / (1.0 - z)))) + (771.3234287776531 / (3.0 - z))) * (((-1259.1392167224028 / (2.0 - z)) + (0.9999999999998099 + (676.5203681218851 / (1.0 - z)))) + (771.3234287776531 / (3.0 - z)))) + ((-176.6150291621406 / (4.0 - z)) * ((-176.6150291621406 / (4.0 - z)) - (((-1259.1392167224028 / (2.0 - z)) + (0.9999999999998099 + (676.5203681218851 / (1.0 - z)))) + (771.3234287776531 / (3.0 - z)))))))))) + (9.984369578019572e-06 * ((6.0 - z) * ((5.0 - z) * (((((-1259.1392167224028 / (2.0 - z)) + (0.9999999999998099 + (676.5203681218851 / (1.0 - z)))) + (771.3234287776531 / (3.0 - z))) * (((-1259.1392167224028 / (2.0 - z)) + (0.9999999999998099 + (676.5203681218851 / (1.0 - z)))) + (771.3234287776531 / (3.0 - z)))) + ((-176.6150291621406 / (4.0 - z)) * ((-176.6150291621406 / (4.0 - z)) - (((-1259.1392167224028 / (2.0 - z)) + (0.9999999999998099 + (676.5203681218851 / (1.0 - z)))) + (771.3234287776531 / (3.0 - z)))))))))) / ((7.0 - z) * ((6.0 - z) * ((5.0 - z) * (((((-1259.1392167224028 / (2.0 - z)) + (0.9999999999998099 + (676.5203681218851 / (1.0 - z)))) + (771.3234287776531 / (3.0 - z))) * (((-1259.1392167224028 / (2.0 - z)) + (0.9999999999998099 + (676.5203681218851 / (1.0 - z)))) + (771.3234287776531 / (3.0 - z)))) + ((-176.6150291621406 / (4.0 - z)) * ((-176.6150291621406 / (4.0 - z)) - (((-1259.1392167224028 / (2.0 - z)) + (0.9999999999998099 + (676.5203681218851 / (1.0 - z)))) + (771.3234287776531 / (3.0 - z)))))))))) + (1.5056327351493116e-07 / (8.0 - z))));
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error0.4
Cost47424
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \frac{\left(7 - z\right) \cdot \left(\left(6 - z\right) \cdot \left(\left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z}\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z}\right) - \frac{\frac{156.4336358909145}{5 - z}}{5 - z}\right) + -0.13857109526572012 \cdot \left(\left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z}\right) - \frac{12.507343278686905}{5 - z}\right)\right) + 9.984369578019572 \cdot 10^{-06} \cdot \left(\left(6 - z\right) \cdot \left(\left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z}\right) - \frac{12.507343278686905}{5 - z}\right)\right)}{\left(7 - z\right) \cdot \left(\left(6 - z\right) \cdot \left(\left(\frac{-176.6150291621406}{4 - z} + \left(\frac{771.3234287776531}{3 - z} + \frac{\left(-1259.1392167219242 + \frac{-851833.326413742}{\frac{1 - z}{\frac{676.5203681218851}{1 - z} + -0.9999999999998099}}\right) + \left(2 - z\right) \cdot \left(0.9999999999994298 + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}\right)}{\left(2 - z\right) \cdot \left(0.9999999999996199 + \frac{\frac{457679.80848377093}{1 - z} + -676.5203681217565}{1 - z}\right)}\right)\right) - \frac{12.507343278686905}{5 - z}\right)\right)}\right)\right)\]
Alternative 2
Error0.9
Cost34752
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(\left(263.38318696223104 + z \cdot 436.896172553987\right) + \left(z \cdot z\right) \cdot 545.0353078425886\right) + {z}^{3} \cdot 606.676680916724\right)\right)\right)\]
Alternative 3
Error1.0
Cost28032
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(\left(263.38318696223104 + z \cdot 436.896172553987\right) + \left(z \cdot z\right) \cdot 545.0353078425886\right)\right)\right)\]
Alternative 4
Error1.3
Cost27648
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + \left(263.38318696223104 + z \cdot 436.896172553987\right)\right)\right)\]
Alternative 5
Error1.7
Cost27264
\[\frac{\left(e^{z + -7.5} \cdot \left(\sqrt{\pi \cdot 2} \cdot \sqrt{7.5 - z}\right)\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + 263.38318696223104\right)}{z \cdot {\left(7.5 - z\right)}^{z}}\]
Alternative 6
Error1.7
Cost20736
\[\frac{\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\frac{1.5056327351493116 \cdot 10^{-07}}{8 - z} + 263.38318696223104\right)}{z}\]
Alternative 7
Error60.6
Cost385
\[\begin{array}{l} \mathbf{if}\;z \leq 5.471443429802367 \cdot 10^{-309}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]
Alternative 8
Error61.9
Cost64
\[1\]

Error

Time

Derivation

  1. Initial program 1.8

    \[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]

  2. Simplified1.8

    \[\leadsto \color{blue}{\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z}\right) + \frac{12.507343278686905}{5 - z}\right) + \frac{-0.13857109526572012}{6 - z}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right)}\]
  3. Using strategy rm

  4. Applied flip3-+_binary64_14451.2

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\left(\left(\left(\color{blue}{\frac{{\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right)}^{3} + {\left(\frac{-176.6150291621406}{4 - z}\right)}^{3}}{\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}\right)}} + \frac{12.507343278686905}{5 - z}\right) + \frac{-0.13857109526572012}{6 - z}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right)\]

  5. Applied frac-add_binary64_14501.2

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\left(\left(\color{blue}{\frac{\left({\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right)}^{3} + {\left(\frac{-176.6150291621406}{4 - z}\right)}^{3}\right) \cdot \left(5 - z\right) + \left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot 12.507343278686905}{\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(5 - z\right)}} + \frac{-0.13857109526572012}{6 - z}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right)\]

  6. Applied frac-add_binary64_14501.2

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\left(\color{blue}{\frac{\left(\left({\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right)}^{3} + {\left(\frac{-176.6150291621406}{4 - z}\right)}^{3}\right) \cdot \left(5 - z\right) + \left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot 12.507343278686905\right) \cdot \left(6 - z\right) + \left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(5 - z\right)\right) \cdot -0.13857109526572012}{\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(5 - z\right)\right) \cdot \left(6 - z\right)}} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right)\]

  7. Applied frac-add_binary64_14500.4

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\color{blue}{\frac{\left(\left(\left({\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right)}^{3} + {\left(\frac{-176.6150291621406}{4 - z}\right)}^{3}\right) \cdot \left(5 - z\right) + \left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot 12.507343278686905\right) \cdot \left(6 - z\right) + \left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(5 - z\right)\right) \cdot -0.13857109526572012\right) \cdot \left(7 - z\right) + \left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(5 - z\right)\right) \cdot \left(6 - z\right)\right) \cdot 9.984369578019572 \cdot 10^{-06}}{\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(5 - z\right)\right) \cdot \left(6 - z\right)\right) \cdot \left(7 - z\right)}} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right)\]

  8. Simplified0.4

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\frac{\color{blue}{\left(7 - z\right) \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left({\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)}^{3} + {\left(\frac{-176.6150291621406}{4 - z}\right)}^{3}\right) + 12.507343278686905 \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) + -0.13857109526572012 \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right) + 9.984369578019572 \cdot 10^{-06} \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right)}}{\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) + \left(\frac{-176.6150291621406}{4 - z} \cdot \frac{-176.6150291621406}{4 - z} - \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \frac{-176.6150291621406}{4 - z}\right)\right) \cdot \left(5 - z\right)\right) \cdot \left(6 - z\right)\right) \cdot \left(7 - z\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right)\]

  9. Simplified0.4

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\frac{\left(7 - z\right) \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left({\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)}^{3} + {\left(\frac{-176.6150291621406}{4 - z}\right)}^{3}\right) + 12.507343278686905 \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) + -0.13857109526572012 \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right) + 9.984369578019572 \cdot 10^{-06} \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right)}{\color{blue}{\left(7 - z\right) \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right)}} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right)\]
  10. Using strategy rm

  11. Applied +-commutative_binary64_13720.4

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\frac{\left(7 - z\right) \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left({\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)}^{3} + {\left(\frac{-176.6150291621406}{4 - z}\right)}^{3}\right) + 12.507343278686905 \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) + -0.13857109526572012 \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right) + 9.984369578019572 \cdot 10^{-06} \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\color{blue}{\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right)} + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right)}{\left(7 - z\right) \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right)\]

  12. Simplified0.4

    \[\leadsto \color{blue}{\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\frac{\left(7 - z\right) \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left({\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)}^{3} + {\left(\frac{-176.6150291621406}{4 - z}\right)}^{3}\right) + 12.507343278686905 \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) + -0.13857109526572012 \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right) + 9.984369578019572 \cdot 10^{-06} \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right)}{\left(7 - z\right) \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right)}\]

  13. Final simplification0.4

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\frac{\left(7 - z\right) \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left({\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)}^{3} + {\left(\frac{-176.6150291621406}{4 - z}\right)}^{3}\right) + 12.507343278686905 \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right) + -0.13857109526572012 \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right) + 9.984369578019572 \cdot 10^{-06} \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right)}{\left(7 - z\right) \cdot \left(\left(6 - z\right) \cdot \left(\left(5 - z\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) \cdot \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z} \cdot \left(\frac{-176.6150291621406}{4 - z} - \left(\left(\frac{-1259.1392167224028}{2 - z} + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)\right) + \frac{771.3234287776531}{3 - z}\right)\right)\right)\right)\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{8 - z}\right)\right)\]

Reproduce

herbie shell --seed 2021065 
(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-06 (+ (- (- 1.0 z) 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- (- 1.0 z) 1.0) 8.0))))))