Average Error: 61.8 → 2.2
Time: 32.0s
Precision: binary64
\[-\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{e^{\frac{\pi}{4} \cdot f} - e^{-\frac{\pi}{4} \cdot f}}\right)\]
↓
\[\left(\left(0.0625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(0.0625 \cdot f\right)\right)}{\pi \cdot 0.5} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(0.0625 \cdot f\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.0078125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.000244140625 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot -0.25\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.03125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot -0.25\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.00390625 \cdot \frac{f \cdot \left(f \cdot {\pi}^{3}\right)}{\pi \cdot 0.5} + \left(0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.0026041666666666665 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.046875 \cdot \frac{f \cdot \left(0.0625 \cdot \left(f \cdot {\pi}^{4}\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(\left(2 \cdot \left(\log \left(\sqrt[3]{4}\right) + \log \left(\sqrt[3]{\frac{1}{\pi}}\right)\right) + \left(\log \left(\sqrt[3]{\frac{1}{\sqrt[3]{\pi} \cdot \sqrt[3]{\pi}}}\right) + \log \left(\sqrt[3]{\frac{4}{\sqrt[3]{\pi}}}\right)\right)\right) + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\pi}^{3} \cdot 0.125} + \left(0.03125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5} + 0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.5 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{5} \cdot -0.0009765625\right)}{{\pi}^{3} \cdot 0.125} + \left(0.0021158854166666665 \cdot \frac{f \cdot \left(f \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(\left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.001953125 \cdot \frac{-0.25 \cdot \left(\left(f \cdot f\right) \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.015625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot -0.25\right)\right)}{\pi \cdot 0.5} + \left(\log f + \left(0.5416666666666666 \cdot \frac{f \cdot \left({\pi}^{4} \cdot \left(f \cdot 0.00390625\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(3.0517578125 \cdot 10^{-05} \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.25 \cdot \frac{f \cdot \left(f \cdot \left({\pi}^{3} \cdot -0.015625\right)\right)}{\pi \cdot 0.5} + 0.5 \cdot \left(\frac{\left(0.0625 \cdot f\right) \cdot {\pi}^{2}}{\pi \cdot 0.5} + \frac{f \cdot \left({\pi}^{3} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5\right)}^{2}}\right)\right)\right)\right)\right)\right)\right)\right) + 0.0078125 \cdot \left(\frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5\right)}^{2}} + \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right) \cdot \frac{-4}{\pi}\]
-\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{e^{\frac{\pi}{4} \cdot f} - e^{-\frac{\pi}{4} \cdot f}}\right)
↓
\left(\left(0.0625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(0.0625 \cdot f\right)\right)}{\pi \cdot 0.5} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(0.0625 \cdot f\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.0078125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.000244140625 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot -0.25\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.03125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot -0.25\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.00390625 \cdot \frac{f \cdot \left(f \cdot {\pi}^{3}\right)}{\pi \cdot 0.5} + \left(0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.0026041666666666665 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.046875 \cdot \frac{f \cdot \left(0.0625 \cdot \left(f \cdot {\pi}^{4}\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(\left(2 \cdot \left(\log \left(\sqrt[3]{4}\right) + \log \left(\sqrt[3]{\frac{1}{\pi}}\right)\right) + \left(\log \left(\sqrt[3]{\frac{1}{\sqrt[3]{\pi} \cdot \sqrt[3]{\pi}}}\right) + \log \left(\sqrt[3]{\frac{4}{\sqrt[3]{\pi}}}\right)\right)\right) + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\pi}^{3} \cdot 0.125} + \left(0.03125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5} + 0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.5 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{5} \cdot -0.0009765625\right)}{{\pi}^{3} \cdot 0.125} + \left(0.0021158854166666665 \cdot \frac{f \cdot \left(f \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(\left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.001953125 \cdot \frac{-0.25 \cdot \left(\left(f \cdot f\right) \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.015625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot -0.25\right)\right)}{\pi \cdot 0.5} + \left(\log f + \left(0.5416666666666666 \cdot \frac{f \cdot \left({\pi}^{4} \cdot \left(f \cdot 0.00390625\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(3.0517578125 \cdot 10^{-05} \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.25 \cdot \frac{f \cdot \left(f \cdot \left({\pi}^{3} \cdot -0.015625\right)\right)}{\pi \cdot 0.5} + 0.5 \cdot \left(\frac{\left(0.0625 \cdot f\right) \cdot {\pi}^{2}}{\pi \cdot 0.5} + \frac{f \cdot \left({\pi}^{3} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5\right)}^{2}}\right)\right)\right)\right)\right)\right)\right)\right) + 0.0078125 \cdot \left(\frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5\right)}^{2}} + \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right) \cdot \frac{-4}{\pi}
(FPCore (f)
 :precision binary64
 (-
  (*
   (/ 1.0 (/ PI 4.0))
   (log
    (/
     (+ (exp (* (/ PI 4.0) f)) (exp (- (* (/ PI 4.0) f))))
     (- (exp (* (/ PI 4.0) f)) (exp (- (* (/ PI 4.0) f)))))))))
↓
(FPCore (f)
 :precision binary64
 (*
  (-
   (+
    (* 0.0625 (/ (* f (* (pow PI 3.0) (* 0.0625 f))) (* PI 0.5)))
    (+
     (* 0.125 (/ (* (pow PI 3.0) (* 0.0625 f)) (pow (* PI 0.5) 2.0)))
     (+
      (*
       0.0078125
       (/ (* (* f f) (* 0.00390625 (pow PI 6.0))) (pow (* PI 0.5) 4.0)))
      (+
       (*
        0.000244140625
        (/ (* (* f f) (* (pow PI 6.0) -0.25)) (pow (* PI 0.5) 4.0)))
       (+
        (* 0.03125 (/ (* (pow PI 3.0) (* f -0.25)) (pow (* PI 0.5) 2.0)))
        (+
         (* 0.00390625 (/ (* f (* f (pow PI 3.0))) (* PI 0.5)))
         (+
          (*
           0.0625
           (/ (* (* f f) (* -0.015625 (pow PI 5.0))) (* (pow PI 3.0) 0.125)))
          (+
           (*
            0.00048828125
            (/ (* (* f f) (* 0.0625 (pow PI 6.0))) (pow (* PI 0.5) 4.0)))
           (+
            (*
             0.0026041666666666665
             (/ (* (* f f) (* -0.25 (pow PI 4.0))) (pow (* PI 0.5) 2.0)))
            (+
             (*
              0.125
              (/
               (* (* f f) (* 0.00390625 (pow PI 5.0)))
               (* (pow PI 3.0) 0.125)))
             (+
              (*
               0.046875
               (/ (* f (* 0.0625 (* f (pow PI 4.0)))) (pow (* PI 0.5) 2.0)))
              (+
               (*
                0.041666666666666664
                (/
                 (* (* f f) (* -0.015625 (pow PI 4.0)))
                 (pow (* PI 0.5) 2.0)))
               (+
                (+
                 (* 2.0 (+ (log (cbrt 4.0)) (log (cbrt (/ 1.0 PI)))))
                 (+
                  (log (cbrt (/ 1.0 (* (cbrt PI) (cbrt PI)))))
                  (log (cbrt (/ 4.0 (cbrt PI))))))
                (+
                 (*
                  0.00048828125
                  (/ (* (* f f) (pow PI 5.0)) (* (pow PI 3.0) 0.125)))
                 (+
                  (* 0.03125 (/ (* f (pow PI 2.0)) (* PI 0.5)))
                  (*
                   0.0625
                   (/
                    (* (* f f) (* (pow PI 6.0) -0.0009765625))
                    (pow (* PI 0.5) 4.0))))))))))))))))))
   (+
    (*
     0.5
     (/ (* (* f f) (* (pow PI 5.0) -0.0009765625)) (* (pow PI 3.0) 0.125)))
    (+
     (*
      0.0021158854166666665
      (/ (* f (* f (pow PI 4.0))) (pow (* PI 0.5) 2.0)))
     (+
      (*
       0.015625
       (/ (* (* f f) (* 0.0625 (pow PI 5.0))) (* (pow PI 3.0) 0.125)))
      (+
       (+
        (*
         0.125
         (/ (* (* f f) (* (pow PI 6.0) 0.000244140625)) (pow (* PI 0.5) 4.0)))
        (+
         (*
          0.001953125
          (/ (* -0.25 (* (* f f) (pow PI 5.0))) (* (pow PI 3.0) 0.125)))
         (+
          (* 0.015625 (/ (* f (* (pow PI 3.0) (* f -0.25))) (* PI 0.5)))
          (+
           (log f)
           (+
            (*
             0.5416666666666666
             (/ (* f (* (pow PI 4.0) (* f 0.00390625))) (pow (* PI 0.5) 2.0)))
            (+
             (*
              3.0517578125e-05
              (/ (* (* f f) (pow PI 6.0)) (pow (* PI 0.5) 4.0)))
             (+
              (* 0.25 (/ (* f (* f (* (pow PI 3.0) -0.015625))) (* PI 0.5)))
              (*
               0.5
               (+
                (/ (* (* 0.0625 f) (pow PI 2.0)) (* PI 0.5))
                (/
                 (* f (* (pow PI 3.0) -0.015625))
                 (pow (* PI 0.5) 2.0)))))))))))
       (*
        0.0078125
        (+
         (/ (* f (pow PI 3.0)) (pow (* PI 0.5) 2.0))
         (/ (* (* f f) (* (pow PI 6.0) -0.015625)) (pow (* PI 0.5) 4.0)))))))))
  (/ -4.0 PI)))
double code(double f) {
	return -((1.0 / (((double) M_PI) / 4.0)) * log((exp((((double) M_PI) / 4.0) * f) + exp(-((((double) M_PI) / 4.0) * f))) / (exp((((double) M_PI) / 4.0) * f) - exp(-((((double) M_PI) / 4.0) * f)))));
}
↓
double code(double f) {
	return (((0.0625 * ((f * (pow(((double) M_PI), 3.0) * (0.0625 * f))) / (((double) M_PI) * 0.5))) + ((0.125 * ((pow(((double) M_PI), 3.0) * (0.0625 * f)) / pow((((double) M_PI) * 0.5), 2.0))) + ((0.0078125 * (((f * f) * (0.00390625 * pow(((double) M_PI), 6.0))) / pow((((double) M_PI) * 0.5), 4.0))) + ((0.000244140625 * (((f * f) * (pow(((double) M_PI), 6.0) * -0.25)) / pow((((double) M_PI) * 0.5), 4.0))) + ((0.03125 * ((pow(((double) M_PI), 3.0) * (f * -0.25)) / pow((((double) M_PI) * 0.5), 2.0))) + ((0.00390625 * ((f * (f * pow(((double) M_PI), 3.0))) / (((double) M_PI) * 0.5))) + ((0.0625 * (((f * f) * (-0.015625 * pow(((double) M_PI), 5.0))) / (pow(((double) M_PI), 3.0) * 0.125))) + ((0.00048828125 * (((f * f) * (0.0625 * pow(((double) M_PI), 6.0))) / pow((((double) M_PI) * 0.5), 4.0))) + ((0.0026041666666666665 * (((f * f) * (-0.25 * pow(((double) M_PI), 4.0))) / pow((((double) M_PI) * 0.5), 2.0))) + ((0.125 * (((f * f) * (0.00390625 * pow(((double) M_PI), 5.0))) / (pow(((double) M_PI), 3.0) * 0.125))) + ((0.046875 * ((f * (0.0625 * (f * pow(((double) M_PI), 4.0)))) / pow((((double) M_PI) * 0.5), 2.0))) + ((0.041666666666666664 * (((f * f) * (-0.015625 * pow(((double) M_PI), 4.0))) / pow((((double) M_PI) * 0.5), 2.0))) + (((2.0 * (log(cbrt(4.0)) + log(cbrt(1.0 / ((double) M_PI))))) + (log(cbrt(1.0 / (cbrt((double) M_PI) * cbrt((double) M_PI)))) + log(cbrt(4.0 / cbrt((double) M_PI))))) + ((0.00048828125 * (((f * f) * pow(((double) M_PI), 5.0)) / (pow(((double) M_PI), 3.0) * 0.125))) + ((0.03125 * ((f * pow(((double) M_PI), 2.0)) / (((double) M_PI) * 0.5))) + (0.0625 * (((f * f) * (pow(((double) M_PI), 6.0) * -0.0009765625)) / pow((((double) M_PI) * 0.5), 4.0)))))))))))))))))) - ((0.5 * (((f * f) * (pow(((double) M_PI), 5.0) * -0.0009765625)) / (pow(((double) M_PI), 3.0) * 0.125))) + ((0.0021158854166666665 * ((f * (f * pow(((double) M_PI), 4.0))) / pow((((double) M_PI) * 0.5), 2.0))) + ((0.015625 * (((f * f) * (0.0625 * pow(((double) M_PI), 5.0))) / (pow(((double) M_PI), 3.0) * 0.125))) + (((0.125 * (((f * f) * (pow(((double) M_PI), 6.0) * 0.000244140625)) / pow((((double) M_PI) * 0.5), 4.0))) + ((0.001953125 * ((-0.25 * ((f * f) * pow(((double) M_PI), 5.0))) / (pow(((double) M_PI), 3.0) * 0.125))) + ((0.015625 * ((f * (pow(((double) M_PI), 3.0) * (f * -0.25))) / (((double) M_PI) * 0.5))) + (log(f) + ((0.5416666666666666 * ((f * (pow(((double) M_PI), 4.0) * (f * 0.00390625))) / pow((((double) M_PI) * 0.5), 2.0))) + ((3.0517578125e-05 * (((f * f) * pow(((double) M_PI), 6.0)) / pow((((double) M_PI) * 0.5), 4.0))) + ((0.25 * ((f * (f * (pow(((double) M_PI), 3.0) * -0.015625))) / (((double) M_PI) * 0.5))) + (0.5 * ((((0.0625 * f) * pow(((double) M_PI), 2.0)) / (((double) M_PI) * 0.5)) + ((f * (pow(((double) M_PI), 3.0) * -0.015625)) / pow((((double) M_PI) * 0.5), 2.0))))))))))) + (0.0078125 * (((f * pow(((double) M_PI), 3.0)) / pow((((double) M_PI) * 0.5), 2.0)) + (((f * f) * (pow(((double) M_PI), 6.0) * -0.015625)) / pow((((double) M_PI) * 0.5), 4.0))))))))) * (-4.0 / ((double) M_PI));
}

Error

Bits error versus f

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 61.8

    \[-\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{e^{\frac{\pi}{4} \cdot f} - e^{-\frac{\pi}{4} \cdot f}}\right)\]

  2. Simplified61.8

    \[\leadsto \color{blue}{\log \left(\frac{e^{\frac{\pi}{4} \cdot f} + {\left(e^{-0.25}\right)}^{\left(\pi \cdot f\right)}}{e^{\frac{\pi}{4} \cdot f} - {\left(e^{-0.25}\right)}^{\left(\pi \cdot f\right)}}\right) \cdot \frac{-4}{\pi}}\]

  3. Taylor expanded around 0 2.2

    \[\leadsto \color{blue}{\left(\left(0.0625 \cdot \frac{{f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot {\pi}^{3}\right)}{0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot f\right)}{{\left(0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)\right)}^{2}} + \left(0.0078125 \cdot \frac{{f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{4} \cdot {\pi}^{6}\right)}{{\left(0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)\right)}^{4}} + \left(0.000244140625 \cdot \frac{{f}^{2} \cdot \left(\log \left(e^{-0.25}\right) \cdot {\pi}^{6}\right)}{{\left(0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)\right)}^{4}} + \left(0.03125 \cdot \frac{{\pi}^{3} \cdot \left(\log \left(e^{-0.25}\right) \cdot f\right)}{{\left(0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)\right)}^{2}} + \left(0.00390625 \cdot \frac{{f}^{2} \cdot {\pi}^{3}}{0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)} + \left(0.0625 \cdot \frac{{f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{3} \cdot {\pi}^{5}\right)}{{\left(0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)\right)}^{3}} + \left(0.00048828125 \cdot \frac{{f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot {\pi}^{6}\right)}{{\left(0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)\right)}^{4}} + \left(0.0026041666666666665 \cdot \frac{{f}^{2} \cdot \left(\log \left(e^{-0.25}\right) \cdot {\pi}^{4}\right)}{{\left(0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)\right)}^{2}} + \left(0.125 \cdot \frac{{f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{4} \cdot {\pi}^{5}\right)}{{\left(0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)\right)}^{3}} + \left(0.046875 \cdot \frac{{f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot {\pi}^{4}\right)}{{\left(0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{{f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{3} \cdot {\pi}^{4}\right)}{{\left(0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)\right)}^{2}} + \left(\log \left(\frac{2}{0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)}\right) + \left(0.00048828125 \cdot \frac{{f}^{2} \cdot {\pi}^{5}}{{\left(0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)\right)}^{3}} + \left(0.0625 \cdot \frac{{f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{5} \cdot {\pi}^{6}\right)}{{\left(0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)\right)}^{4}} + 0.03125 \cdot \frac{{\pi}^{2} \cdot f}{0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.5 \cdot \frac{{f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{5} \cdot {\pi}^{5}\right)}{{\left(0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)\right)}^{3}} + \left(0.0021158854166666665 \cdot \frac{{f}^{2} \cdot {\pi}^{4}}{{\left(0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)\right)}^{2}} + \left(0.015625 \cdot \frac{{f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot {\pi}^{5}\right)}{{\left(0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)\right)}^{3}} + \left(0.0078125 \cdot \frac{{\pi}^{3} \cdot f}{{\left(0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)\right)}^{2}} + \left(0.0078125 \cdot \frac{{f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{3} \cdot {\pi}^{6}\right)}{{\left(0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)\right)}^{4}} + \left(0.125 \cdot \frac{{f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{6} \cdot {\pi}^{6}\right)}{{\left(0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)\right)}^{4}} + \left(0.001953125 \cdot \frac{{f}^{2} \cdot \left(\log \left(e^{-0.25}\right) \cdot {\pi}^{5}\right)}{{\left(0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)\right)}^{3}} + \left(0.015625 \cdot \frac{{f}^{2} \cdot \left(\log \left(e^{-0.25}\right) \cdot {\pi}^{3}\right)}{0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)} + \left(\log f + \left(0.5416666666666666 \cdot \frac{{f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{4} \cdot {\pi}^{4}\right)}{{\left(0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)\right)}^{2}} + \left(3.0517578125 \cdot 10^{-05} \cdot \frac{{f}^{2} \cdot {\pi}^{6}}{{\left(0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)\right)}^{4}} + \left(0.25 \cdot \frac{{f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{3} \cdot {\pi}^{3}\right)}{0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)} + \left(0.5 \cdot \frac{{\pi}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot f\right)}{0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)} + 0.5 \cdot \frac{{\pi}^{3} \cdot \left({\log \left(e^{-0.25}\right)}^{3} \cdot f\right)}{{\left(0.25 \cdot \pi - \pi \cdot \log \left(e^{-0.25}\right)\right)}^{2}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)} \cdot \frac{-4}{\pi}\]

  4. Simplified2.2

    \[\leadsto \color{blue}{\left(\left(0.0625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot 0.0625\right)\right)}{\pi \cdot 0.5} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot 0.0625\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.0078125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.000244140625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.03125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot -0.25\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.00390625 \cdot \frac{f \cdot \left(f \cdot {\pi}^{3}\right)}{\pi \cdot 0.5} + \left(0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.0026041666666666665 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.046875 \cdot \frac{f \cdot \left(0.0625 \cdot \left(f \cdot {\pi}^{4}\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(\log \left(\frac{2}{\pi \cdot 0.5}\right) + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\pi}^{3} \cdot 0.125} + \left(0.03125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5} + 0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.5 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{5} \cdot -0.0009765625\right)}{{\pi}^{3} \cdot 0.125} + \left(0.0021158854166666665 \cdot \frac{f \cdot \left(f \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(\left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.001953125 \cdot \frac{-0.25 \cdot \left(\left(f \cdot f\right) \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.015625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot -0.25\right)\right)}{\pi \cdot 0.5} + \left(\log f + \left(0.5416666666666666 \cdot \frac{f \cdot \left({\pi}^{4} \cdot \left(f \cdot 0.00390625\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(3.0517578125 \cdot 10^{-05} \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.25 \cdot \frac{f \cdot \left(f \cdot \left({\pi}^{3} \cdot -0.015625\right)\right)}{\pi \cdot 0.5} + 0.5 \cdot \left(\frac{{\pi}^{2} \cdot \left(f \cdot 0.0625\right)}{\pi \cdot 0.5} + \frac{f \cdot \left({\pi}^{3} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5\right)}^{2}}\right)\right)\right)\right)\right)\right)\right)\right) + 0.0078125 \cdot \left(\frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5\right)}^{2}} + \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right)} \cdot \frac{-4}{\pi}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt_binary642.2

    \[\leadsto \left(\left(0.0625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot 0.0625\right)\right)}{\pi \cdot 0.5} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot 0.0625\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.0078125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.000244140625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.03125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot -0.25\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.00390625 \cdot \frac{f \cdot \left(f \cdot {\pi}^{3}\right)}{\pi \cdot 0.5} + \left(0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.0026041666666666665 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.046875 \cdot \frac{f \cdot \left(0.0625 \cdot \left(f \cdot {\pi}^{4}\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(\log \color{blue}{\left(\left(\sqrt[3]{\frac{2}{\pi \cdot 0.5}} \cdot \sqrt[3]{\frac{2}{\pi \cdot 0.5}}\right) \cdot \sqrt[3]{\frac{2}{\pi \cdot 0.5}}\right)} + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\pi}^{3} \cdot 0.125} + \left(0.03125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5} + 0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.5 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{5} \cdot -0.0009765625\right)}{{\pi}^{3} \cdot 0.125} + \left(0.0021158854166666665 \cdot \frac{f \cdot \left(f \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(\left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.001953125 \cdot \frac{-0.25 \cdot \left(\left(f \cdot f\right) \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.015625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot -0.25\right)\right)}{\pi \cdot 0.5} + \left(\log f + \left(0.5416666666666666 \cdot \frac{f \cdot \left({\pi}^{4} \cdot \left(f \cdot 0.00390625\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(3.0517578125 \cdot 10^{-05} \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.25 \cdot \frac{f \cdot \left(f \cdot \left({\pi}^{3} \cdot -0.015625\right)\right)}{\pi \cdot 0.5} + 0.5 \cdot \left(\frac{{\pi}^{2} \cdot \left(f \cdot 0.0625\right)}{\pi \cdot 0.5} + \frac{f \cdot \left({\pi}^{3} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5\right)}^{2}}\right)\right)\right)\right)\right)\right)\right)\right) + 0.0078125 \cdot \left(\frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5\right)}^{2}} + \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right) \cdot \frac{-4}{\pi}\]

  7. Applied log-prod_binary642.2

    \[\leadsto \left(\left(0.0625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot 0.0625\right)\right)}{\pi \cdot 0.5} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot 0.0625\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.0078125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.000244140625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.03125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot -0.25\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.00390625 \cdot \frac{f \cdot \left(f \cdot {\pi}^{3}\right)}{\pi \cdot 0.5} + \left(0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.0026041666666666665 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.046875 \cdot \frac{f \cdot \left(0.0625 \cdot \left(f \cdot {\pi}^{4}\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(\color{blue}{\left(\log \left(\sqrt[3]{\frac{2}{\pi \cdot 0.5}} \cdot \sqrt[3]{\frac{2}{\pi \cdot 0.5}}\right) + \log \left(\sqrt[3]{\frac{2}{\pi \cdot 0.5}}\right)\right)} + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\pi}^{3} \cdot 0.125} + \left(0.03125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5} + 0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.5 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{5} \cdot -0.0009765625\right)}{{\pi}^{3} \cdot 0.125} + \left(0.0021158854166666665 \cdot \frac{f \cdot \left(f \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(\left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.001953125 \cdot \frac{-0.25 \cdot \left(\left(f \cdot f\right) \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.015625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot -0.25\right)\right)}{\pi \cdot 0.5} + \left(\log f + \left(0.5416666666666666 \cdot \frac{f \cdot \left({\pi}^{4} \cdot \left(f \cdot 0.00390625\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(3.0517578125 \cdot 10^{-05} \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.25 \cdot \frac{f \cdot \left(f \cdot \left({\pi}^{3} \cdot -0.015625\right)\right)}{\pi \cdot 0.5} + 0.5 \cdot \left(\frac{{\pi}^{2} \cdot \left(f \cdot 0.0625\right)}{\pi \cdot 0.5} + \frac{f \cdot \left({\pi}^{3} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5\right)}^{2}}\right)\right)\right)\right)\right)\right)\right)\right) + 0.0078125 \cdot \left(\frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5\right)}^{2}} + \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right) \cdot \frac{-4}{\pi}\]

  8. Simplified2.2

    \[\leadsto \left(\left(0.0625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot 0.0625\right)\right)}{\pi \cdot 0.5} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot 0.0625\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.0078125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.000244140625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.03125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot -0.25\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.00390625 \cdot \frac{f \cdot \left(f \cdot {\pi}^{3}\right)}{\pi \cdot 0.5} + \left(0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.0026041666666666665 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.046875 \cdot \frac{f \cdot \left(0.0625 \cdot \left(f \cdot {\pi}^{4}\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(\left(\color{blue}{2 \cdot \log \left(\sqrt[3]{\frac{4}{\pi}}\right)} + \log \left(\sqrt[3]{\frac{2}{\pi \cdot 0.5}}\right)\right) + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\pi}^{3} \cdot 0.125} + \left(0.03125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5} + 0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.5 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{5} \cdot -0.0009765625\right)}{{\pi}^{3} \cdot 0.125} + \left(0.0021158854166666665 \cdot \frac{f \cdot \left(f \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(\left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.001953125 \cdot \frac{-0.25 \cdot \left(\left(f \cdot f\right) \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.015625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot -0.25\right)\right)}{\pi \cdot 0.5} + \left(\log f + \left(0.5416666666666666 \cdot \frac{f \cdot \left({\pi}^{4} \cdot \left(f \cdot 0.00390625\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(3.0517578125 \cdot 10^{-05} \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.25 \cdot \frac{f \cdot \left(f \cdot \left({\pi}^{3} \cdot -0.015625\right)\right)}{\pi \cdot 0.5} + 0.5 \cdot \left(\frac{{\pi}^{2} \cdot \left(f \cdot 0.0625\right)}{\pi \cdot 0.5} + \frac{f \cdot \left({\pi}^{3} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5\right)}^{2}}\right)\right)\right)\right)\right)\right)\right)\right) + 0.0078125 \cdot \left(\frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5\right)}^{2}} + \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right) \cdot \frac{-4}{\pi}\]

  9. Simplified2.2

    \[\leadsto \left(\left(0.0625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot 0.0625\right)\right)}{\pi \cdot 0.5} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot 0.0625\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.0078125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.000244140625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.03125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot -0.25\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.00390625 \cdot \frac{f \cdot \left(f \cdot {\pi}^{3}\right)}{\pi \cdot 0.5} + \left(0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.0026041666666666665 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.046875 \cdot \frac{f \cdot \left(0.0625 \cdot \left(f \cdot {\pi}^{4}\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(\left(2 \cdot \log \left(\sqrt[3]{\frac{4}{\pi}}\right) + \color{blue}{\log \left(\sqrt[3]{\frac{4}{\pi}}\right)}\right) + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\pi}^{3} \cdot 0.125} + \left(0.03125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5} + 0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.5 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{5} \cdot -0.0009765625\right)}{{\pi}^{3} \cdot 0.125} + \left(0.0021158854166666665 \cdot \frac{f \cdot \left(f \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(\left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.001953125 \cdot \frac{-0.25 \cdot \left(\left(f \cdot f\right) \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.015625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot -0.25\right)\right)}{\pi \cdot 0.5} + \left(\log f + \left(0.5416666666666666 \cdot \frac{f \cdot \left({\pi}^{4} \cdot \left(f \cdot 0.00390625\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(3.0517578125 \cdot 10^{-05} \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.25 \cdot \frac{f \cdot \left(f \cdot \left({\pi}^{3} \cdot -0.015625\right)\right)}{\pi \cdot 0.5} + 0.5 \cdot \left(\frac{{\pi}^{2} \cdot \left(f \cdot 0.0625\right)}{\pi \cdot 0.5} + \frac{f \cdot \left({\pi}^{3} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5\right)}^{2}}\right)\right)\right)\right)\right)\right)\right)\right) + 0.0078125 \cdot \left(\frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5\right)}^{2}} + \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right) \cdot \frac{-4}{\pi}\]
  10. Using strategy rm

  11. Applied div-inv_binary642.2

    \[\leadsto \left(\left(0.0625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot 0.0625\right)\right)}{\pi \cdot 0.5} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot 0.0625\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.0078125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.000244140625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.03125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot -0.25\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.00390625 \cdot \frac{f \cdot \left(f \cdot {\pi}^{3}\right)}{\pi \cdot 0.5} + \left(0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.0026041666666666665 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.046875 \cdot \frac{f \cdot \left(0.0625 \cdot \left(f \cdot {\pi}^{4}\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(\left(2 \cdot \log \left(\sqrt[3]{\color{blue}{4 \cdot \frac{1}{\pi}}}\right) + \log \left(\sqrt[3]{\frac{4}{\pi}}\right)\right) + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\pi}^{3} \cdot 0.125} + \left(0.03125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5} + 0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.5 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{5} \cdot -0.0009765625\right)}{{\pi}^{3} \cdot 0.125} + \left(0.0021158854166666665 \cdot \frac{f \cdot \left(f \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(\left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.001953125 \cdot \frac{-0.25 \cdot \left(\left(f \cdot f\right) \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.015625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot -0.25\right)\right)}{\pi \cdot 0.5} + \left(\log f + \left(0.5416666666666666 \cdot \frac{f \cdot \left({\pi}^{4} \cdot \left(f \cdot 0.00390625\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(3.0517578125 \cdot 10^{-05} \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.25 \cdot \frac{f \cdot \left(f \cdot \left({\pi}^{3} \cdot -0.015625\right)\right)}{\pi \cdot 0.5} + 0.5 \cdot \left(\frac{{\pi}^{2} \cdot \left(f \cdot 0.0625\right)}{\pi \cdot 0.5} + \frac{f \cdot \left({\pi}^{3} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5\right)}^{2}}\right)\right)\right)\right)\right)\right)\right)\right) + 0.0078125 \cdot \left(\frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5\right)}^{2}} + \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right) \cdot \frac{-4}{\pi}\]

  12. Applied cbrt-prod_binary642.2

    \[\leadsto \left(\left(0.0625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot 0.0625\right)\right)}{\pi \cdot 0.5} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot 0.0625\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.0078125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.000244140625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.03125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot -0.25\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.00390625 \cdot \frac{f \cdot \left(f \cdot {\pi}^{3}\right)}{\pi \cdot 0.5} + \left(0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.0026041666666666665 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.046875 \cdot \frac{f \cdot \left(0.0625 \cdot \left(f \cdot {\pi}^{4}\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(\left(2 \cdot \log \color{blue}{\left(\sqrt[3]{4} \cdot \sqrt[3]{\frac{1}{\pi}}\right)} + \log \left(\sqrt[3]{\frac{4}{\pi}}\right)\right) + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\pi}^{3} \cdot 0.125} + \left(0.03125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5} + 0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.5 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{5} \cdot -0.0009765625\right)}{{\pi}^{3} \cdot 0.125} + \left(0.0021158854166666665 \cdot \frac{f \cdot \left(f \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(\left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.001953125 \cdot \frac{-0.25 \cdot \left(\left(f \cdot f\right) \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.015625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot -0.25\right)\right)}{\pi \cdot 0.5} + \left(\log f + \left(0.5416666666666666 \cdot \frac{f \cdot \left({\pi}^{4} \cdot \left(f \cdot 0.00390625\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(3.0517578125 \cdot 10^{-05} \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.25 \cdot \frac{f \cdot \left(f \cdot \left({\pi}^{3} \cdot -0.015625\right)\right)}{\pi \cdot 0.5} + 0.5 \cdot \left(\frac{{\pi}^{2} \cdot \left(f \cdot 0.0625\right)}{\pi \cdot 0.5} + \frac{f \cdot \left({\pi}^{3} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5\right)}^{2}}\right)\right)\right)\right)\right)\right)\right)\right) + 0.0078125 \cdot \left(\frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5\right)}^{2}} + \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right) \cdot \frac{-4}{\pi}\]

  13. Applied log-prod_binary642.2

    \[\leadsto \left(\left(0.0625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot 0.0625\right)\right)}{\pi \cdot 0.5} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot 0.0625\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.0078125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.000244140625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.03125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot -0.25\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.00390625 \cdot \frac{f \cdot \left(f \cdot {\pi}^{3}\right)}{\pi \cdot 0.5} + \left(0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.0026041666666666665 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.046875 \cdot \frac{f \cdot \left(0.0625 \cdot \left(f \cdot {\pi}^{4}\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(\left(2 \cdot \color{blue}{\left(\log \left(\sqrt[3]{4}\right) + \log \left(\sqrt[3]{\frac{1}{\pi}}\right)\right)} + \log \left(\sqrt[3]{\frac{4}{\pi}}\right)\right) + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\pi}^{3} \cdot 0.125} + \left(0.03125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5} + 0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.5 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{5} \cdot -0.0009765625\right)}{{\pi}^{3} \cdot 0.125} + \left(0.0021158854166666665 \cdot \frac{f \cdot \left(f \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(\left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.001953125 \cdot \frac{-0.25 \cdot \left(\left(f \cdot f\right) \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.015625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot -0.25\right)\right)}{\pi \cdot 0.5} + \left(\log f + \left(0.5416666666666666 \cdot \frac{f \cdot \left({\pi}^{4} \cdot \left(f \cdot 0.00390625\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(3.0517578125 \cdot 10^{-05} \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.25 \cdot \frac{f \cdot \left(f \cdot \left({\pi}^{3} \cdot -0.015625\right)\right)}{\pi \cdot 0.5} + 0.5 \cdot \left(\frac{{\pi}^{2} \cdot \left(f \cdot 0.0625\right)}{\pi \cdot 0.5} + \frac{f \cdot \left({\pi}^{3} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5\right)}^{2}}\right)\right)\right)\right)\right)\right)\right)\right) + 0.0078125 \cdot \left(\frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5\right)}^{2}} + \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right) \cdot \frac{-4}{\pi}\]
  14. Using strategy rm

  15. Applied add-cube-cbrt_binary642.2

    \[\leadsto \left(\left(0.0625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot 0.0625\right)\right)}{\pi \cdot 0.5} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot 0.0625\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.0078125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.000244140625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.03125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot -0.25\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.00390625 \cdot \frac{f \cdot \left(f \cdot {\pi}^{3}\right)}{\pi \cdot 0.5} + \left(0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.0026041666666666665 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.046875 \cdot \frac{f \cdot \left(0.0625 \cdot \left(f \cdot {\pi}^{4}\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(\left(2 \cdot \left(\log \left(\sqrt[3]{4}\right) + \log \left(\sqrt[3]{\frac{1}{\pi}}\right)\right) + \log \left(\sqrt[3]{\frac{4}{\color{blue}{\left(\sqrt[3]{\pi} \cdot \sqrt[3]{\pi}\right) \cdot \sqrt[3]{\pi}}}}\right)\right) + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\pi}^{3} \cdot 0.125} + \left(0.03125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5} + 0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.5 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{5} \cdot -0.0009765625\right)}{{\pi}^{3} \cdot 0.125} + \left(0.0021158854166666665 \cdot \frac{f \cdot \left(f \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(\left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.001953125 \cdot \frac{-0.25 \cdot \left(\left(f \cdot f\right) \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.015625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot -0.25\right)\right)}{\pi \cdot 0.5} + \left(\log f + \left(0.5416666666666666 \cdot \frac{f \cdot \left({\pi}^{4} \cdot \left(f \cdot 0.00390625\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(3.0517578125 \cdot 10^{-05} \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.25 \cdot \frac{f \cdot \left(f \cdot \left({\pi}^{3} \cdot -0.015625\right)\right)}{\pi \cdot 0.5} + 0.5 \cdot \left(\frac{{\pi}^{2} \cdot \left(f \cdot 0.0625\right)}{\pi \cdot 0.5} + \frac{f \cdot \left({\pi}^{3} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5\right)}^{2}}\right)\right)\right)\right)\right)\right)\right)\right) + 0.0078125 \cdot \left(\frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5\right)}^{2}} + \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right) \cdot \frac{-4}{\pi}\]

  16. Applied *-un-lft-identity_binary642.2

    \[\leadsto \left(\left(0.0625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot 0.0625\right)\right)}{\pi \cdot 0.5} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot 0.0625\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.0078125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.000244140625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.03125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot -0.25\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.00390625 \cdot \frac{f \cdot \left(f \cdot {\pi}^{3}\right)}{\pi \cdot 0.5} + \left(0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.0026041666666666665 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.046875 \cdot \frac{f \cdot \left(0.0625 \cdot \left(f \cdot {\pi}^{4}\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(\left(2 \cdot \left(\log \left(\sqrt[3]{4}\right) + \log \left(\sqrt[3]{\frac{1}{\pi}}\right)\right) + \log \left(\sqrt[3]{\frac{\color{blue}{1 \cdot 4}}{\left(\sqrt[3]{\pi} \cdot \sqrt[3]{\pi}\right) \cdot \sqrt[3]{\pi}}}\right)\right) + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\pi}^{3} \cdot 0.125} + \left(0.03125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5} + 0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.5 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{5} \cdot -0.0009765625\right)}{{\pi}^{3} \cdot 0.125} + \left(0.0021158854166666665 \cdot \frac{f \cdot \left(f \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(\left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.001953125 \cdot \frac{-0.25 \cdot \left(\left(f \cdot f\right) \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.015625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot -0.25\right)\right)}{\pi \cdot 0.5} + \left(\log f + \left(0.5416666666666666 \cdot \frac{f \cdot \left({\pi}^{4} \cdot \left(f \cdot 0.00390625\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(3.0517578125 \cdot 10^{-05} \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.25 \cdot \frac{f \cdot \left(f \cdot \left({\pi}^{3} \cdot -0.015625\right)\right)}{\pi \cdot 0.5} + 0.5 \cdot \left(\frac{{\pi}^{2} \cdot \left(f \cdot 0.0625\right)}{\pi \cdot 0.5} + \frac{f \cdot \left({\pi}^{3} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5\right)}^{2}}\right)\right)\right)\right)\right)\right)\right)\right) + 0.0078125 \cdot \left(\frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5\right)}^{2}} + \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right) \cdot \frac{-4}{\pi}\]

  17. Applied times-frac_binary642.2

    \[\leadsto \left(\left(0.0625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot 0.0625\right)\right)}{\pi \cdot 0.5} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot 0.0625\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.0078125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.000244140625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.03125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot -0.25\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.00390625 \cdot \frac{f \cdot \left(f \cdot {\pi}^{3}\right)}{\pi \cdot 0.5} + \left(0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.0026041666666666665 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.046875 \cdot \frac{f \cdot \left(0.0625 \cdot \left(f \cdot {\pi}^{4}\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(\left(2 \cdot \left(\log \left(\sqrt[3]{4}\right) + \log \left(\sqrt[3]{\frac{1}{\pi}}\right)\right) + \log \left(\sqrt[3]{\color{blue}{\frac{1}{\sqrt[3]{\pi} \cdot \sqrt[3]{\pi}} \cdot \frac{4}{\sqrt[3]{\pi}}}}\right)\right) + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\pi}^{3} \cdot 0.125} + \left(0.03125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5} + 0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.5 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{5} \cdot -0.0009765625\right)}{{\pi}^{3} \cdot 0.125} + \left(0.0021158854166666665 \cdot \frac{f \cdot \left(f \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(\left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.001953125 \cdot \frac{-0.25 \cdot \left(\left(f \cdot f\right) \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.015625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot -0.25\right)\right)}{\pi \cdot 0.5} + \left(\log f + \left(0.5416666666666666 \cdot \frac{f \cdot \left({\pi}^{4} \cdot \left(f \cdot 0.00390625\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(3.0517578125 \cdot 10^{-05} \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.25 \cdot \frac{f \cdot \left(f \cdot \left({\pi}^{3} \cdot -0.015625\right)\right)}{\pi \cdot 0.5} + 0.5 \cdot \left(\frac{{\pi}^{2} \cdot \left(f \cdot 0.0625\right)}{\pi \cdot 0.5} + \frac{f \cdot \left({\pi}^{3} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5\right)}^{2}}\right)\right)\right)\right)\right)\right)\right)\right) + 0.0078125 \cdot \left(\frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5\right)}^{2}} + \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right) \cdot \frac{-4}{\pi}\]

  18. Applied cbrt-prod_binary642.2

    \[\leadsto \left(\left(0.0625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot 0.0625\right)\right)}{\pi \cdot 0.5} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot 0.0625\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.0078125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.000244140625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.03125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot -0.25\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.00390625 \cdot \frac{f \cdot \left(f \cdot {\pi}^{3}\right)}{\pi \cdot 0.5} + \left(0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.0026041666666666665 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.046875 \cdot \frac{f \cdot \left(0.0625 \cdot \left(f \cdot {\pi}^{4}\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(\left(2 \cdot \left(\log \left(\sqrt[3]{4}\right) + \log \left(\sqrt[3]{\frac{1}{\pi}}\right)\right) + \log \color{blue}{\left(\sqrt[3]{\frac{1}{\sqrt[3]{\pi} \cdot \sqrt[3]{\pi}}} \cdot \sqrt[3]{\frac{4}{\sqrt[3]{\pi}}}\right)}\right) + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\pi}^{3} \cdot 0.125} + \left(0.03125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5} + 0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.5 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{5} \cdot -0.0009765625\right)}{{\pi}^{3} \cdot 0.125} + \left(0.0021158854166666665 \cdot \frac{f \cdot \left(f \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(\left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.001953125 \cdot \frac{-0.25 \cdot \left(\left(f \cdot f\right) \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.015625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot -0.25\right)\right)}{\pi \cdot 0.5} + \left(\log f + \left(0.5416666666666666 \cdot \frac{f \cdot \left({\pi}^{4} \cdot \left(f \cdot 0.00390625\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(3.0517578125 \cdot 10^{-05} \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.25 \cdot \frac{f \cdot \left(f \cdot \left({\pi}^{3} \cdot -0.015625\right)\right)}{\pi \cdot 0.5} + 0.5 \cdot \left(\frac{{\pi}^{2} \cdot \left(f \cdot 0.0625\right)}{\pi \cdot 0.5} + \frac{f \cdot \left({\pi}^{3} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5\right)}^{2}}\right)\right)\right)\right)\right)\right)\right)\right) + 0.0078125 \cdot \left(\frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5\right)}^{2}} + \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right) \cdot \frac{-4}{\pi}\]

  19. Applied log-prod_binary642.2

    \[\leadsto \left(\left(0.0625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot 0.0625\right)\right)}{\pi \cdot 0.5} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot 0.0625\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.0078125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.000244140625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.03125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot -0.25\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.00390625 \cdot \frac{f \cdot \left(f \cdot {\pi}^{3}\right)}{\pi \cdot 0.5} + \left(0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.0026041666666666665 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.046875 \cdot \frac{f \cdot \left(0.0625 \cdot \left(f \cdot {\pi}^{4}\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(\left(2 \cdot \left(\log \left(\sqrt[3]{4}\right) + \log \left(\sqrt[3]{\frac{1}{\pi}}\right)\right) + \color{blue}{\left(\log \left(\sqrt[3]{\frac{1}{\sqrt[3]{\pi} \cdot \sqrt[3]{\pi}}}\right) + \log \left(\sqrt[3]{\frac{4}{\sqrt[3]{\pi}}}\right)\right)}\right) + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\pi}^{3} \cdot 0.125} + \left(0.03125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5} + 0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.5 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{5} \cdot -0.0009765625\right)}{{\pi}^{3} \cdot 0.125} + \left(0.0021158854166666665 \cdot \frac{f \cdot \left(f \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(\left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.001953125 \cdot \frac{-0.25 \cdot \left(\left(f \cdot f\right) \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.015625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot -0.25\right)\right)}{\pi \cdot 0.5} + \left(\log f + \left(0.5416666666666666 \cdot \frac{f \cdot \left({\pi}^{4} \cdot \left(f \cdot 0.00390625\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(3.0517578125 \cdot 10^{-05} \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.25 \cdot \frac{f \cdot \left(f \cdot \left({\pi}^{3} \cdot -0.015625\right)\right)}{\pi \cdot 0.5} + 0.5 \cdot \left(\frac{{\pi}^{2} \cdot \left(f \cdot 0.0625\right)}{\pi \cdot 0.5} + \frac{f \cdot \left({\pi}^{3} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5\right)}^{2}}\right)\right)\right)\right)\right)\right)\right)\right) + 0.0078125 \cdot \left(\frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5\right)}^{2}} + \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right) \cdot \frac{-4}{\pi}\]

  20. Final simplification2.2

    \[\leadsto \left(\left(0.0625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(0.0625 \cdot f\right)\right)}{\pi \cdot 0.5} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(0.0625 \cdot f\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.0078125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.000244140625 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot -0.25\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.03125 \cdot \frac{{\pi}^{3} \cdot \left(f \cdot -0.25\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.00390625 \cdot \frac{f \cdot \left(f \cdot {\pi}^{3}\right)}{\pi \cdot 0.5} + \left(0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{6}\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.0026041666666666665 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.046875 \cdot \frac{f \cdot \left(0.0625 \cdot \left(f \cdot {\pi}^{4}\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(\left(2 \cdot \left(\log \left(\sqrt[3]{4}\right) + \log \left(\sqrt[3]{\frac{1}{\pi}}\right)\right) + \left(\log \left(\sqrt[3]{\frac{1}{\sqrt[3]{\pi} \cdot \sqrt[3]{\pi}}}\right) + \log \left(\sqrt[3]{\frac{4}{\sqrt[3]{\pi}}}\right)\right)\right) + \left(0.00048828125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\pi}^{3} \cdot 0.125} + \left(0.03125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5} + 0.0625 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.5 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{5} \cdot -0.0009765625\right)}{{\pi}^{3} \cdot 0.125} + \left(0.0021158854166666665 \cdot \frac{f \cdot \left(f \cdot {\pi}^{4}\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(\left(0.125 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.001953125 \cdot \frac{-0.25 \cdot \left(\left(f \cdot f\right) \cdot {\pi}^{5}\right)}{{\pi}^{3} \cdot 0.125} + \left(0.015625 \cdot \frac{f \cdot \left({\pi}^{3} \cdot \left(f \cdot -0.25\right)\right)}{\pi \cdot 0.5} + \left(\log f + \left(0.5416666666666666 \cdot \frac{f \cdot \left({\pi}^{4} \cdot \left(f \cdot 0.00390625\right)\right)}{{\left(\pi \cdot 0.5\right)}^{2}} + \left(3.0517578125 \cdot 10^{-05} \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5\right)}^{4}} + \left(0.25 \cdot \frac{f \cdot \left(f \cdot \left({\pi}^{3} \cdot -0.015625\right)\right)}{\pi \cdot 0.5} + 0.5 \cdot \left(\frac{\left(0.0625 \cdot f\right) \cdot {\pi}^{2}}{\pi \cdot 0.5} + \frac{f \cdot \left({\pi}^{3} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5\right)}^{2}}\right)\right)\right)\right)\right)\right)\right)\right) + 0.0078125 \cdot \left(\frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5\right)}^{2}} + \frac{\left(f \cdot f\right) \cdot \left({\pi}^{6} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5\right)}^{4}}\right)\right)\right)\right)\right)\right) \cdot \frac{-4}{\pi}\]

Reproduce

herbie shell --seed 2020356 
(FPCore (f)
  :name "VandenBroeck and Keller, Equation (20)"
  :precision binary64
  (- (* (/ 1.0 (/ PI 4.0)) (log (/ (+ (exp (* (/ PI 4.0) f)) (exp (- (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (- (* (/ PI 4.0) f)))))))))