Average Error: 61.4 → 2.2
Time: 28.3s
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(0.6666666666666666 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot -0.015625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(4 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot 0.00390625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.5 \cdot \frac{\left(\left(f \cdot f\right) \cdot 0.00390625\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(2 \cdot \frac{\left(\left(f \cdot f\right) \cdot -0.015625\right) \cdot {\pi}^{5}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(\frac{f \cdot \left(-0.25 \cdot {\pi}^{3}\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} \cdot 0.25 + \left(0.125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.75 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot -0.25\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.015625 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot -0.25\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.0234375 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{3}}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(\frac{f \cdot \left({\pi}^{3} \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(\left(\log \left(\sqrt[3]{\frac{4}{\pi}}\right) + 2 \cdot \log \left(\sqrt[3]{\frac{4}{\pi}}\right)\right) + \left(0.03125 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + 4 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.0625 \cdot \frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.5 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.0625 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot -0.25\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.001953125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(2 \cdot \frac{f \cdot \left({\pi}^{2} \cdot 0.0625\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.033854166666666664 \cdot \frac{{\pi}^{4} \cdot \left(f \cdot f\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(4 \cdot \frac{f \cdot \left(-0.015625 \cdot {\pi}^{3}\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(8.666666666666666 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot 0.00390625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(\log f + \left(8 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.5 \cdot \frac{\left(\left(f \cdot f\right) \cdot -0.015625\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(16 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(1.5 \cdot \frac{\left(\left(f \cdot f\right) \cdot -0.015625\right) \cdot {\pi}^{3}}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + 0.03125 \cdot \frac{{\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot -0.25\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)}\right)\right)\right)\right)\right)\right)\right)\right)\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(0.6666666666666666 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot -0.015625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(4 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot 0.00390625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.5 \cdot \frac{\left(\left(f \cdot f\right) \cdot 0.00390625\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(2 \cdot \frac{\left(\left(f \cdot f\right) \cdot -0.015625\right) \cdot {\pi}^{5}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(\frac{f \cdot \left(-0.25 \cdot {\pi}^{3}\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} \cdot 0.25 + \left(0.125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.75 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot -0.25\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.015625 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot -0.25\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.0234375 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{3}}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(\frac{f \cdot \left({\pi}^{3} \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(\left(\log \left(\sqrt[3]{\frac{4}{\pi}}\right) + 2 \cdot \log \left(\sqrt[3]{\frac{4}{\pi}}\right)\right) + \left(0.03125 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + 4 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.0625 \cdot \frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.5 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.0625 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot -0.25\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.001953125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(2 \cdot \frac{f \cdot \left({\pi}^{2} \cdot 0.0625\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.033854166666666664 \cdot \frac{{\pi}^{4} \cdot \left(f \cdot f\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(4 \cdot \frac{f \cdot \left(-0.015625 \cdot {\pi}^{3}\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(8.666666666666666 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot 0.00390625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(\log f + \left(8 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.5 \cdot \frac{\left(\left(f \cdot f\right) \cdot -0.015625\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(16 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(1.5 \cdot \frac{\left(\left(f \cdot f\right) \cdot -0.015625\right) \cdot {\pi}^{3}}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + 0.03125 \cdot \frac{{\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot -0.25\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)}\right)\right)\right)\right)\right)\right)\right)\right)\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
 (*
  (-
   (+
    (*
     0.6666666666666666
     (/
      (* (pow PI 4.0) (* (* f f) -0.015625))
      (pow (- (* PI 0.5) (* 2.0 (* PI -0.25))) 2.0)))
    (+
     (*
      4.0
      (/
       (* (pow PI 5.0) (* (* f f) 0.00390625))
       (pow (- (* PI 0.5) (* 2.0 (* PI -0.25))) 3.0)))
     (+
      (*
       0.5
       (/
        (* (* (* f f) 0.00390625) (pow PI 6.0))
        (pow (- (* PI 0.5) (* 2.0 (* PI -0.25))) 4.0)))
      (+
       (*
        2.0
        (/
         (* (* (* f f) -0.015625) (pow PI 5.0))
         (pow (- (* PI 0.5) (* 2.0 (* PI -0.25))) 3.0)))
       (+
        (*
         (/
          (* f (* -0.25 (pow PI 3.0)))
          (pow (- (* PI 0.5) (* 2.0 (* PI -0.25))) 2.0))
         0.25)
        (+
         (* 0.125 (/ (* f (pow PI 2.0)) (- (* PI 0.5) (* 2.0 (* PI -0.25)))))
         (+
          (*
           0.75
           (/
            (* (pow PI 4.0) (* (* f f) 0.0625))
            (pow (- (* PI 0.5) (* 2.0 (* PI -0.25))) 2.0)))
          (+
           (*
            0.041666666666666664
            (/
             (* (pow PI 4.0) (* (* f f) -0.25))
             (pow (- (* PI 0.5) (* 2.0 (* PI -0.25))) 2.0)))
           (+
            (*
             0.015625
             (/
              (* (pow PI 6.0) (* (* f f) -0.25))
              (pow (- (* PI 0.5) (* 2.0 (* PI -0.25))) 4.0)))
            (+
             (*
              0.0234375
              (/ (* (* f f) (pow PI 3.0)) (- (* PI 0.5) (* 2.0 (* PI -0.25)))))
             (+
              (/
               (* f (* (pow PI 3.0) 0.0625))
               (pow (- (* PI 0.5) (* 2.0 (* PI -0.25))) 2.0))
              (+
               (+ (log (cbrt (/ 4.0 PI))) (* 2.0 (log (cbrt (/ 4.0 PI)))))
               (+
                (*
                 0.03125
                 (/
                  (* (pow PI 6.0) (* (* f f) 0.0625))
                  (pow (- (* PI 0.5) (* 2.0 (* PI -0.25))) 4.0)))
                (+
                 (*
                  0.125
                  (/
                   (* (pow PI 3.0) (* (* f f) 0.0625))
                   (- (* PI 0.5) (* 2.0 (* PI -0.25)))))
                 (+
                  (*
                   0.015625
                   (/
                    (* (* f f) (pow PI 5.0))
                    (pow (- (* PI 0.5) (* 2.0 (* PI -0.25))) 3.0)))
                  (*
                   4.0
                   (/
                    (* (pow PI 6.0) (* (* f f) -0.0009765625))
                    (pow
                     (- (* PI 0.5) (* 2.0 (* PI -0.25)))
                     4.0))))))))))))))))))
   (+
    (*
     0.0625
     (/ (* f (pow PI 3.0)) (pow (- (* PI 0.5) (* 2.0 (* PI -0.25))) 2.0)))
    (+
     (*
      0.5
      (/
       (* (pow PI 5.0) (* (* f f) 0.0625))
       (pow (- (* PI 0.5) (* 2.0 (* PI -0.25))) 3.0)))
     (+
      (*
       0.0625
       (/
        (* (pow PI 5.0) (* (* f f) -0.25))
        (pow (- (* PI 0.5) (* 2.0 (* PI -0.25))) 3.0)))
      (+
       (*
        0.001953125
        (/
         (* (* f f) (pow PI 6.0))
         (pow (- (* PI 0.5) (* 2.0 (* PI -0.25))) 4.0)))
       (+
        (*
         2.0
         (/ (* f (* (pow PI 2.0) 0.0625)) (- (* PI 0.5) (* 2.0 (* PI -0.25)))))
        (+
         (*
          0.033854166666666664
          (/
           (* (pow PI 4.0) (* f f))
           (pow (- (* PI 0.5) (* 2.0 (* PI -0.25))) 2.0)))
         (+
          (*
           4.0
           (/
            (* f (* -0.015625 (pow PI 3.0)))
            (pow (- (* PI 0.5) (* 2.0 (* PI -0.25))) 2.0)))
          (+
           (*
            8.666666666666666
            (/
             (* (pow PI 4.0) (* (* f f) 0.00390625))
             (pow (- (* PI 0.5) (* 2.0 (* PI -0.25))) 2.0)))
           (+
            (log f)
            (+
             (*
              8.0
              (/
               (* (pow PI 6.0) (* (* f f) 0.000244140625))
               (pow (- (* PI 0.5) (* 2.0 (* PI -0.25))) 4.0)))
             (+
              (*
               0.5
               (/
                (* (* (* f f) -0.015625) (pow PI 6.0))
                (pow (- (* PI 0.5) (* 2.0 (* PI -0.25))) 4.0)))
              (+
               (*
                16.0
                (/
                 (* (pow PI 5.0) (* (* f f) -0.0009765625))
                 (pow (- (* PI 0.5) (* 2.0 (* PI -0.25))) 3.0)))
               (+
                (*
                 1.5
                 (/
                  (* (* (* f f) -0.015625) (pow PI 3.0))
                  (- (* PI 0.5) (* 2.0 (* PI -0.25)))))
                (*
                 0.03125
                 (/
                  (* (pow PI 3.0) (* (* f f) -0.25))
                  (- (* PI 0.5) (* 2.0 (* PI -0.25)))))))))))))))))))
  (/ -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 (((0.6666666666666666 * ((pow(((double) M_PI), 4.0) * ((f * f) * -0.015625)) / pow(((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))), 2.0))) + ((4.0 * ((pow(((double) M_PI), 5.0) * ((f * f) * 0.00390625)) / pow(((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))), 3.0))) + ((0.5 * ((((f * f) * 0.00390625) * pow(((double) M_PI), 6.0)) / pow(((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))), 4.0))) + ((2.0 * ((((f * f) * -0.015625) * pow(((double) M_PI), 5.0)) / pow(((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))), 3.0))) + ((((f * (-0.25 * pow(((double) M_PI), 3.0))) / pow(((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))), 2.0)) * 0.25) + ((0.125 * ((f * pow(((double) M_PI), 2.0)) / ((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))))) + ((0.75 * ((pow(((double) M_PI), 4.0) * ((f * f) * 0.0625)) / pow(((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))), 2.0))) + ((0.041666666666666664 * ((pow(((double) M_PI), 4.0) * ((f * f) * -0.25)) / pow(((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))), 2.0))) + ((0.015625 * ((pow(((double) M_PI), 6.0) * ((f * f) * -0.25)) / pow(((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))), 4.0))) + ((0.0234375 * (((f * f) * pow(((double) M_PI), 3.0)) / ((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))))) + (((f * (pow(((double) M_PI), 3.0) * 0.0625)) / pow(((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))), 2.0)) + ((log(cbrt(4.0 / ((double) M_PI))) + (2.0 * log(cbrt(4.0 / ((double) M_PI))))) + ((0.03125 * ((pow(((double) M_PI), 6.0) * ((f * f) * 0.0625)) / pow(((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))), 4.0))) + ((0.125 * ((pow(((double) M_PI), 3.0) * ((f * f) * 0.0625)) / ((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))))) + ((0.015625 * (((f * f) * pow(((double) M_PI), 5.0)) / pow(((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))), 3.0))) + (4.0 * ((pow(((double) M_PI), 6.0) * ((f * f) * -0.0009765625)) / pow(((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))), 4.0)))))))))))))))))) - ((0.0625 * ((f * pow(((double) M_PI), 3.0)) / pow(((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))), 2.0))) + ((0.5 * ((pow(((double) M_PI), 5.0) * ((f * f) * 0.0625)) / pow(((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))), 3.0))) + ((0.0625 * ((pow(((double) M_PI), 5.0) * ((f * f) * -0.25)) / pow(((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))), 3.0))) + ((0.001953125 * (((f * f) * pow(((double) M_PI), 6.0)) / pow(((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))), 4.0))) + ((2.0 * ((f * (pow(((double) M_PI), 2.0) * 0.0625)) / ((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))))) + ((0.033854166666666664 * ((pow(((double) M_PI), 4.0) * (f * f)) / pow(((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))), 2.0))) + ((4.0 * ((f * (-0.015625 * pow(((double) M_PI), 3.0))) / pow(((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))), 2.0))) + ((8.666666666666666 * ((pow(((double) M_PI), 4.0) * ((f * f) * 0.00390625)) / pow(((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))), 2.0))) + (log(f) + ((8.0 * ((pow(((double) M_PI), 6.0) * ((f * f) * 0.000244140625)) / pow(((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))), 4.0))) + ((0.5 * ((((f * f) * -0.015625) * pow(((double) M_PI), 6.0)) / pow(((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))), 4.0))) + ((16.0 * ((pow(((double) M_PI), 5.0) * ((f * f) * -0.0009765625)) / pow(((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))), 3.0))) + ((1.5 * ((((f * f) * -0.015625) * pow(((double) M_PI), 3.0)) / ((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))))) + (0.03125 * ((pow(((double) M_PI), 3.0) * ((f * f) * -0.25)) / ((((double) M_PI) * 0.5) - (2.0 * (((double) M_PI) * -0.25))))))))))))))))))) * (-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 61.4

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

  2. Simplified61.4

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

  4. Applied flip--_binary6461.4

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

  5. Simplified61.4

    \[\leadsto \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + {\left(e^{-0.25}\right)}^{\left(\pi \cdot f\right)}}{\frac{\color{blue}{\sqrt{e^{\pi \cdot f}} - {\left(e^{-0.25}\right)}^{\left(\left(\pi \cdot f\right) \cdot 2\right)}}}{e^{\frac{\pi}{4} \cdot f} + {\left(e^{-0.25}\right)}^{\left(\pi \cdot f\right)}}}\right) \cdot \frac{-4}{\pi}\]

  6. Taylor expanded around 0 2.2

    \[\leadsto \color{blue}{\left(\left(0.6666666666666666 \cdot \frac{{\pi}^{4} \cdot \left({\log \left(e^{-0.25}\right)}^{3} \cdot {f}^{2}\right)}{{\left(0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(4 \cdot \frac{{\pi}^{5} \cdot \left({\log \left(e^{-0.25}\right)}^{4} \cdot {f}^{2}\right)}{{\left(0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{3}} + \left(0.5 \cdot \frac{{\pi}^{6} \cdot \left({\log \left(e^{-0.25}\right)}^{4} \cdot {f}^{2}\right)}{{\left(0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{4}} + \left(2 \cdot \frac{{\pi}^{5} \cdot \left({\log \left(e^{-0.25}\right)}^{3} \cdot {f}^{2}\right)}{{\left(0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{3}} + \left(0.25 \cdot \frac{f \cdot \left(\log \left(e^{-0.25}\right) \cdot {\pi}^{3}\right)}{{\left(0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(0.125 \cdot \frac{f \cdot {\pi}^{2}}{0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)} + \left(0.75 \cdot \frac{{\pi}^{4} \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot {f}^{2}\right)}{{\left(0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{{\pi}^{4} \cdot \left(\log \left(e^{-0.25}\right) \cdot {f}^{2}\right)}{{\left(0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(0.015625 \cdot \frac{{\pi}^{6} \cdot \left(\log \left(e^{-0.25}\right) \cdot {f}^{2}\right)}{{\left(0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{4}} + \left(0.0234375 \cdot \frac{{\pi}^{3} \cdot {f}^{2}}{0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)} + \left(\frac{{\pi}^{3} \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot f\right)}{{\left(0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(\log \left(\frac{4}{0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)}\right) + \left(0.03125 \cdot \frac{{\pi}^{6} \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot {f}^{2}\right)}{{\left(0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{4}} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot {f}^{2}\right)}{0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)} + \left(0.015625 \cdot \frac{{\pi}^{5} \cdot {f}^{2}}{{\left(0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{3}} + 4 \cdot \frac{{\pi}^{6} \cdot \left({\log \left(e^{-0.25}\right)}^{5} \cdot {f}^{2}\right)}{{\left(0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.0625 \cdot \frac{f \cdot {\pi}^{3}}{{\left(0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(0.5 \cdot \frac{{\pi}^{5} \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot {f}^{2}\right)}{{\left(0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{3}} + \left(0.0625 \cdot \frac{{\pi}^{5} \cdot \left(\log \left(e^{-0.25}\right) \cdot {f}^{2}\right)}{{\left(0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{3}} + \left(0.001953125 \cdot \frac{{\pi}^{6} \cdot {f}^{2}}{{\left(0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{4}} + \left(2 \cdot \frac{f \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot {\pi}^{2}\right)}{0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)} + \left(0.033854166666666664 \cdot \frac{{\pi}^{4} \cdot {f}^{2}}{{\left(0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(4 \cdot \frac{f \cdot \left({\log \left(e^{-0.25}\right)}^{3} \cdot {\pi}^{3}\right)}{{\left(0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(8.666666666666666 \cdot \frac{{\pi}^{4} \cdot \left({\log \left(e^{-0.25}\right)}^{4} \cdot {f}^{2}\right)}{{\left(0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(\log f + \left(8 \cdot \frac{{\pi}^{6} \cdot \left({\log \left(e^{-0.25}\right)}^{6} \cdot {f}^{2}\right)}{{\left(0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{4}} + \left(0.5 \cdot \frac{{\pi}^{6} \cdot \left({\log \left(e^{-0.25}\right)}^{3} \cdot {f}^{2}\right)}{{\left(0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{4}} + \left(16 \cdot \frac{{\pi}^{5} \cdot \left({\log \left(e^{-0.25}\right)}^{5} \cdot {f}^{2}\right)}{{\left(0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{3}} + \left(1.5 \cdot \frac{{\pi}^{3} \cdot \left({\log \left(e^{-0.25}\right)}^{3} \cdot {f}^{2}\right)}{0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)} + 0.03125 \cdot \frac{{\pi}^{3} \cdot \left(\log \left(e^{-0.25}\right) \cdot {f}^{2}\right)}{0.5 \cdot \pi - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)} \cdot \frac{-4}{\pi}\]

  7. Simplified2.2

    \[\leadsto \color{blue}{\left(\left(0.6666666666666666 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot -0.015625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(4 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot 0.00390625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.5 \cdot \frac{\left(\left(f \cdot f\right) \cdot 0.00390625\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(2 \cdot \frac{\left(\left(f \cdot f\right) \cdot -0.015625\right) \cdot {\pi}^{5}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(\frac{f \cdot \left(-0.25 \cdot {\pi}^{3}\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} \cdot 0.25 + \left(0.125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.75 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{{\pi}^{4} \cdot \left(-0.25 \cdot \left(f \cdot f\right)\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.015625 \cdot \frac{{\pi}^{6} \cdot \left(-0.25 \cdot \left(f \cdot f\right)\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.0234375 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{3}}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(\frac{f \cdot \left({\pi}^{3} \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(\log \left(\frac{4}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)}\right) + \left(0.03125 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + 4 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.0625 \cdot \frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.5 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.0625 \cdot \frac{{\pi}^{5} \cdot \left(-0.25 \cdot \left(f \cdot f\right)\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.001953125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(2 \cdot \frac{f \cdot \left({\pi}^{2} \cdot 0.0625\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.033854166666666664 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{4}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(4 \cdot \frac{f \cdot \left({\pi}^{3} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(8.666666666666666 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot 0.00390625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(\log f + \left(8 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.5 \cdot \frac{\left(\left(f \cdot f\right) \cdot -0.015625\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(16 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(1.5 \cdot \frac{{\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot -0.015625\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + 0.03125 \cdot \frac{{\pi}^{3} \cdot \left(-0.25 \cdot \left(f \cdot f\right)\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)} \cdot \frac{-4}{\pi}\]
  8. Using strategy rm

  9. Applied add-cube-cbrt_binary642.2

    \[\leadsto \left(\left(0.6666666666666666 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot -0.015625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(4 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot 0.00390625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.5 \cdot \frac{\left(\left(f \cdot f\right) \cdot 0.00390625\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(2 \cdot \frac{\left(\left(f \cdot f\right) \cdot -0.015625\right) \cdot {\pi}^{5}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(\frac{f \cdot \left(-0.25 \cdot {\pi}^{3}\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} \cdot 0.25 + \left(0.125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.75 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{{\pi}^{4} \cdot \left(-0.25 \cdot \left(f \cdot f\right)\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.015625 \cdot \frac{{\pi}^{6} \cdot \left(-0.25 \cdot \left(f \cdot f\right)\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.0234375 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{3}}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(\frac{f \cdot \left({\pi}^{3} \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(\log \color{blue}{\left(\left(\sqrt[3]{\frac{4}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)}} \cdot \sqrt[3]{\frac{4}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)}}\right) \cdot \sqrt[3]{\frac{4}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)}}\right)} + \left(0.03125 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + 4 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.0625 \cdot \frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.5 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.0625 \cdot \frac{{\pi}^{5} \cdot \left(-0.25 \cdot \left(f \cdot f\right)\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.001953125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(2 \cdot \frac{f \cdot \left({\pi}^{2} \cdot 0.0625\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.033854166666666664 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{4}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(4 \cdot \frac{f \cdot \left({\pi}^{3} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(8.666666666666666 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot 0.00390625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(\log f + \left(8 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.5 \cdot \frac{\left(\left(f \cdot f\right) \cdot -0.015625\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(16 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(1.5 \cdot \frac{{\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot -0.015625\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + 0.03125 \cdot \frac{{\pi}^{3} \cdot \left(-0.25 \cdot \left(f \cdot f\right)\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \frac{-4}{\pi}\]

  10. Applied log-prod_binary642.2

    \[\leadsto \left(\left(0.6666666666666666 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot -0.015625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(4 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot 0.00390625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.5 \cdot \frac{\left(\left(f \cdot f\right) \cdot 0.00390625\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(2 \cdot \frac{\left(\left(f \cdot f\right) \cdot -0.015625\right) \cdot {\pi}^{5}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(\frac{f \cdot \left(-0.25 \cdot {\pi}^{3}\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} \cdot 0.25 + \left(0.125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.75 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{{\pi}^{4} \cdot \left(-0.25 \cdot \left(f \cdot f\right)\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.015625 \cdot \frac{{\pi}^{6} \cdot \left(-0.25 \cdot \left(f \cdot f\right)\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.0234375 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{3}}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(\frac{f \cdot \left({\pi}^{3} \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(\color{blue}{\left(\log \left(\sqrt[3]{\frac{4}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)}} \cdot \sqrt[3]{\frac{4}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)}}\right) + \log \left(\sqrt[3]{\frac{4}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)}}\right)\right)} + \left(0.03125 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + 4 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.0625 \cdot \frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.5 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.0625 \cdot \frac{{\pi}^{5} \cdot \left(-0.25 \cdot \left(f \cdot f\right)\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.001953125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(2 \cdot \frac{f \cdot \left({\pi}^{2} \cdot 0.0625\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.033854166666666664 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{4}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(4 \cdot \frac{f \cdot \left({\pi}^{3} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(8.666666666666666 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot 0.00390625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(\log f + \left(8 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.5 \cdot \frac{\left(\left(f \cdot f\right) \cdot -0.015625\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(16 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(1.5 \cdot \frac{{\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot -0.015625\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + 0.03125 \cdot \frac{{\pi}^{3} \cdot \left(-0.25 \cdot \left(f \cdot f\right)\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \frac{-4}{\pi}\]

  11. Simplified2.2

    \[\leadsto \left(\left(0.6666666666666666 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot -0.015625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(4 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot 0.00390625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.5 \cdot \frac{\left(\left(f \cdot f\right) \cdot 0.00390625\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(2 \cdot \frac{\left(\left(f \cdot f\right) \cdot -0.015625\right) \cdot {\pi}^{5}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(\frac{f \cdot \left(-0.25 \cdot {\pi}^{3}\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} \cdot 0.25 + \left(0.125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.75 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{{\pi}^{4} \cdot \left(-0.25 \cdot \left(f \cdot f\right)\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.015625 \cdot \frac{{\pi}^{6} \cdot \left(-0.25 \cdot \left(f \cdot f\right)\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.0234375 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{3}}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(\frac{f \cdot \left({\pi}^{3} \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(\left(\color{blue}{2 \cdot \log \left(\sqrt[3]{\frac{4}{\pi}}\right)} + \log \left(\sqrt[3]{\frac{4}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)}}\right)\right) + \left(0.03125 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + 4 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.0625 \cdot \frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.5 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.0625 \cdot \frac{{\pi}^{5} \cdot \left(-0.25 \cdot \left(f \cdot f\right)\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.001953125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(2 \cdot \frac{f \cdot \left({\pi}^{2} \cdot 0.0625\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.033854166666666664 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{4}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(4 \cdot \frac{f \cdot \left({\pi}^{3} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(8.666666666666666 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot 0.00390625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(\log f + \left(8 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.5 \cdot \frac{\left(\left(f \cdot f\right) \cdot -0.015625\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(16 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(1.5 \cdot \frac{{\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot -0.015625\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + 0.03125 \cdot \frac{{\pi}^{3} \cdot \left(-0.25 \cdot \left(f \cdot f\right)\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \frac{-4}{\pi}\]

  12. Simplified2.2

    \[\leadsto \left(\left(0.6666666666666666 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot -0.015625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(4 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot 0.00390625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.5 \cdot \frac{\left(\left(f \cdot f\right) \cdot 0.00390625\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(2 \cdot \frac{\left(\left(f \cdot f\right) \cdot -0.015625\right) \cdot {\pi}^{5}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(\frac{f \cdot \left(-0.25 \cdot {\pi}^{3}\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} \cdot 0.25 + \left(0.125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.75 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{{\pi}^{4} \cdot \left(-0.25 \cdot \left(f \cdot f\right)\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.015625 \cdot \frac{{\pi}^{6} \cdot \left(-0.25 \cdot \left(f \cdot f\right)\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.0234375 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{3}}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(\frac{f \cdot \left({\pi}^{3} \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\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(0.03125 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + 4 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.0625 \cdot \frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.5 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.0625 \cdot \frac{{\pi}^{5} \cdot \left(-0.25 \cdot \left(f \cdot f\right)\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.001953125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(2 \cdot \frac{f \cdot \left({\pi}^{2} \cdot 0.0625\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.033854166666666664 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{4}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(4 \cdot \frac{f \cdot \left({\pi}^{3} \cdot -0.015625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(8.666666666666666 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot 0.00390625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(\log f + \left(8 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.5 \cdot \frac{\left(\left(f \cdot f\right) \cdot -0.015625\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(16 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(1.5 \cdot \frac{{\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot -0.015625\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + 0.03125 \cdot \frac{{\pi}^{3} \cdot \left(-0.25 \cdot \left(f \cdot f\right)\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \frac{-4}{\pi}\]

  13. Final simplification2.2

    \[\leadsto \left(\left(0.6666666666666666 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot -0.015625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(4 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot 0.00390625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.5 \cdot \frac{\left(\left(f \cdot f\right) \cdot 0.00390625\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(2 \cdot \frac{\left(\left(f \cdot f\right) \cdot -0.015625\right) \cdot {\pi}^{5}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(\frac{f \cdot \left(-0.25 \cdot {\pi}^{3}\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} \cdot 0.25 + \left(0.125 \cdot \frac{f \cdot {\pi}^{2}}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.75 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.041666666666666664 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot -0.25\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.015625 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot -0.25\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.0234375 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{3}}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(\frac{f \cdot \left({\pi}^{3} \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(\left(\log \left(\sqrt[3]{\frac{4}{\pi}}\right) + 2 \cdot \log \left(\sqrt[3]{\frac{4}{\pi}}\right)\right) + \left(0.03125 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.015625 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{5}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + 4 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(0.0625 \cdot \frac{f \cdot {\pi}^{3}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(0.5 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.0625 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot -0.25\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(0.001953125 \cdot \frac{\left(f \cdot f\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(2 \cdot \frac{f \cdot \left({\pi}^{2} \cdot 0.0625\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + \left(0.033854166666666664 \cdot \frac{{\pi}^{4} \cdot \left(f \cdot f\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(4 \cdot \frac{f \cdot \left(-0.015625 \cdot {\pi}^{3}\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(8.666666666666666 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot 0.00390625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{2}} + \left(\log f + \left(8 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot 0.000244140625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(0.5 \cdot \frac{\left(\left(f \cdot f\right) \cdot -0.015625\right) \cdot {\pi}^{6}}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{4}} + \left(16 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot -0.0009765625\right)}{{\left(\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)\right)}^{3}} + \left(1.5 \cdot \frac{\left(\left(f \cdot f\right) \cdot -0.015625\right) \cdot {\pi}^{3}}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)} + 0.03125 \cdot \frac{{\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot -0.25\right)}{\pi \cdot 0.5 - 2 \cdot \left(\pi \cdot -0.25\right)}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \frac{-4}{\pi}\]

Reproduce

herbie shell --seed 2020343 
(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)))))))))