Average Error: 61.5 → 2.3
Time: 29.3s
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(8 \cdot \frac{\left(f \cdot f\right) \cdot {\left(\pi \cdot 0.25\right)}^{5}}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(16 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{4}\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(16 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{5} \cdot \left(\left(f \cdot f\right) \cdot \left(\pi \cdot -0.25\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{4}} + \left(0.046875 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot {\pi}^{2}\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(12 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{2} \cdot \left(\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{3}\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(2 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{4} \cdot \left(\left(f \cdot f\right) \cdot \pi\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(16 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left(-0.0009765625 \cdot {\pi}^{5}\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{4}} + \left(4 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{2} \cdot \left(f \cdot \left(\pi \cdot -0.25\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(0.25 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{3}\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(0.75 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left({\pi}^{2} \cdot 0.0625\right)\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(0.125 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left({\pi}^{2} \cdot \left(\left(f \cdot f\right) \cdot -0.25\right)\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(8 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{4} \cdot \left(\left(f \cdot f\right) \cdot \left({\pi}^{2} \cdot 0.0625\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{4}} + \left(8 \cdot \frac{\left(\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{4}\right)\right) \cdot {\left(\pi \cdot 0.25\right)}^{2}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{4}} + \left(4 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{2} \cdot \left(\left(f \cdot f\right) \cdot \left({\pi}^{2} \cdot 0.0625\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(4 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left({\pi}^{4} \cdot -0.015625\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(\frac{\left(\pi \cdot 0.25\right) \cdot \left(f \cdot \left(\pi \cdot -0.25\right)\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(4 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{2} \cdot \left(\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{3}\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(10.666666666666666 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{3}\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(8 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{4}\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(0.25 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(f \cdot \pi\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(\frac{\left(\pi \cdot 0.25\right) \cdot \left({\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(2.6666666666666665 \cdot \frac{\left(\left(f \cdot f\right) \cdot \left(\pi \cdot -0.25\right)\right) \cdot {\left(\pi \cdot 0.25\right)}^{3}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(2 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left({\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(\log \left(\frac{4}{\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2}\right) + 4 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(f \cdot \left({\pi}^{2} \cdot 0.0625\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(32 \cdot \frac{\left(\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{3}\right)\right) \cdot {\left(\pi \cdot 0.25\right)}^{3}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{4}} + \left(16 \cdot \frac{\left(\left(f \cdot f\right) \cdot \left({\pi}^{2} \cdot 0.0625\right)\right) \cdot {\left(\pi \cdot 0.25\right)}^{3}}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(4 \cdot \frac{f \cdot {\left(\pi \cdot 0.25\right)}^{3}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(\frac{f \cdot \left({\pi}^{2} \cdot 0.0625\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(8 \cdot \frac{\left(f \cdot f\right) \cdot {\left(\pi \cdot 0.25\right)}^{6}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{4}} + \left(4 \cdot \frac{\left(\left(f \cdot f\right) \cdot \left(\pi \cdot -0.25\right)\right) \cdot {\left(\pi \cdot 0.25\right)}^{3}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(0.046875 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{3}\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(0.75 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{3}\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(8 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot 0.000244140625\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{4}} + \left(2.6666666666666665 \cdot \frac{\left(f \cdot f\right) \cdot {\left(\pi \cdot 0.25\right)}^{4}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(\log f + \left(0.25 \cdot \frac{f \cdot \left(-0.25 \cdot {\pi}^{2}\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(8.666666666666666 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{4}\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(2 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{4} \cdot -0.015625\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(4 \cdot \frac{\left({\pi}^{2} \cdot \left(\left(f \cdot f\right) \cdot -0.25\right)\right) \cdot {\left(\pi \cdot 0.25\right)}^{3}}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(16 \cdot \frac{\left(\left(f \cdot f\right) \cdot \left({\pi}^{2} \cdot 0.0625\right)\right) \cdot {\left(\pi \cdot 0.25\right)}^{3}}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(\frac{\left(\left(f \cdot f\right) \cdot \pi\right) \cdot {\left(\pi \cdot 0.25\right)}^{3}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(2 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot 0.00390625\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(0.125 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(0.125 \cdot \frac{\left(\left(f \cdot f\right) \cdot {\pi}^{2}\right) \cdot {\left(\pi \cdot 0.25\right)}^{2}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(4 \cdot \frac{f \cdot \left(-0.015625 \cdot {\pi}^{3}\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(2 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{2} \cdot \left(\left(f \cdot f\right) \cdot \left({\pi}^{2} \cdot 0.0625\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + 16 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.0009765625 \cdot {\pi}^{5}\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\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(8 \cdot \frac{\left(f \cdot f\right) \cdot {\left(\pi \cdot 0.25\right)}^{5}}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(16 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{4}\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(16 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{5} \cdot \left(\left(f \cdot f\right) \cdot \left(\pi \cdot -0.25\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{4}} + \left(0.046875 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot {\pi}^{2}\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(12 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{2} \cdot \left(\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{3}\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(2 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{4} \cdot \left(\left(f \cdot f\right) \cdot \pi\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(16 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left(-0.0009765625 \cdot {\pi}^{5}\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{4}} + \left(4 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{2} \cdot \left(f \cdot \left(\pi \cdot -0.25\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(0.25 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{3}\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(0.75 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left({\pi}^{2} \cdot 0.0625\right)\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(0.125 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left({\pi}^{2} \cdot \left(\left(f \cdot f\right) \cdot -0.25\right)\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(8 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{4} \cdot \left(\left(f \cdot f\right) \cdot \left({\pi}^{2} \cdot 0.0625\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{4}} + \left(8 \cdot \frac{\left(\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{4}\right)\right) \cdot {\left(\pi \cdot 0.25\right)}^{2}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{4}} + \left(4 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{2} \cdot \left(\left(f \cdot f\right) \cdot \left({\pi}^{2} \cdot 0.0625\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(4 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left({\pi}^{4} \cdot -0.015625\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(\frac{\left(\pi \cdot 0.25\right) \cdot \left(f \cdot \left(\pi \cdot -0.25\right)\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(4 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{2} \cdot \left(\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{3}\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(10.666666666666666 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{3}\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(8 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{4}\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(0.25 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(f \cdot \pi\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(\frac{\left(\pi \cdot 0.25\right) \cdot \left({\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(2.6666666666666665 \cdot \frac{\left(\left(f \cdot f\right) \cdot \left(\pi \cdot -0.25\right)\right) \cdot {\left(\pi \cdot 0.25\right)}^{3}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(2 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left({\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(\log \left(\frac{4}{\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2}\right) + 4 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(f \cdot \left({\pi}^{2} \cdot 0.0625\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(32 \cdot \frac{\left(\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{3}\right)\right) \cdot {\left(\pi \cdot 0.25\right)}^{3}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{4}} + \left(16 \cdot \frac{\left(\left(f \cdot f\right) \cdot \left({\pi}^{2} \cdot 0.0625\right)\right) \cdot {\left(\pi \cdot 0.25\right)}^{3}}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(4 \cdot \frac{f \cdot {\left(\pi \cdot 0.25\right)}^{3}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(\frac{f \cdot \left({\pi}^{2} \cdot 0.0625\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(8 \cdot \frac{\left(f \cdot f\right) \cdot {\left(\pi \cdot 0.25\right)}^{6}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{4}} + \left(4 \cdot \frac{\left(\left(f \cdot f\right) \cdot \left(\pi \cdot -0.25\right)\right) \cdot {\left(\pi \cdot 0.25\right)}^{3}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(0.046875 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{3}\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(0.75 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{3}\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(8 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot 0.000244140625\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{4}} + \left(2.6666666666666665 \cdot \frac{\left(f \cdot f\right) \cdot {\left(\pi \cdot 0.25\right)}^{4}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(\log f + \left(0.25 \cdot \frac{f \cdot \left(-0.25 \cdot {\pi}^{2}\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(8.666666666666666 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{4}\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(2 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{4} \cdot -0.015625\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(4 \cdot \frac{\left({\pi}^{2} \cdot \left(\left(f \cdot f\right) \cdot -0.25\right)\right) \cdot {\left(\pi \cdot 0.25\right)}^{3}}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(16 \cdot \frac{\left(\left(f \cdot f\right) \cdot \left({\pi}^{2} \cdot 0.0625\right)\right) \cdot {\left(\pi \cdot 0.25\right)}^{3}}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(\frac{\left(\left(f \cdot f\right) \cdot \pi\right) \cdot {\left(\pi \cdot 0.25\right)}^{3}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(2 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot 0.00390625\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(0.125 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(0.125 \cdot \frac{\left(\left(f \cdot f\right) \cdot {\pi}^{2}\right) \cdot {\left(\pi \cdot 0.25\right)}^{2}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(4 \cdot \frac{f \cdot \left(-0.015625 \cdot {\pi}^{3}\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(2 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{2} \cdot \left(\left(f \cdot f\right) \cdot \left({\pi}^{2} \cdot 0.0625\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + 16 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.0009765625 \cdot {\pi}^{5}\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\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
 (*
  (-
   (+
    (*
     8.0
     (/
      (* (* f f) (pow (* PI 0.25) 5.0))
      (* 8.0 (pow (- (* PI 0.25) (* PI -0.25)) 3.0))))
    (+
     (*
      16.0
      (/
       (* (* PI 0.25) (* (* f f) (* 0.00390625 (pow PI 4.0))))
       (* 8.0 (pow (- (* PI 0.25) (* PI -0.25)) 3.0))))
     (+
      (*
       16.0
       (/
        (* (pow (* PI 0.25) 5.0) (* (* f f) (* PI -0.25)))
        (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 4.0)))
      (+
       (*
        0.046875
        (/
         (* (* PI 0.25) (* (* f f) (pow PI 2.0)))
         (- (* PI 0.25) (* PI -0.25))))
       (+
        (*
         12.0
         (/
          (* (pow (* PI 0.25) 2.0) (* (* f f) (* -0.015625 (pow PI 3.0))))
          (* 8.0 (pow (- (* PI 0.25) (* PI -0.25)) 3.0))))
        (+
         (*
          2.0
          (/
           (* (pow (* PI 0.25) 4.0) (* (* f f) PI))
           (* 8.0 (pow (- (* PI 0.25) (* PI -0.25)) 3.0))))
         (+
          (*
           16.0
           (/
            (* (* PI 0.25) (* (* f f) (* -0.0009765625 (pow PI 5.0))))
            (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 4.0)))
          (+
           (*
            4.0
            (/
             (* (pow (* PI 0.25) 2.0) (* f (* PI -0.25)))
             (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 2.0)))
           (+
            (*
             0.25
             (/
              (* (* PI 0.25) (* (* f f) (* -0.25 (pow PI 3.0))))
              (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 2.0)))
            (+
             (*
              0.75
              (/
               (* (* PI 0.25) (* (* f f) (* (pow PI 2.0) 0.0625)))
               (- (* PI 0.25) (* PI -0.25))))
             (+
              (*
               0.125
               (/
                (* (* PI 0.25) (* (pow PI 2.0) (* (* f f) -0.25)))
                (- (* PI 0.25) (* PI -0.25))))
              (+
               (*
                8.0
                (/
                 (* (pow (* PI 0.25) 4.0) (* (* f f) (* (pow PI 2.0) 0.0625)))
                 (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 4.0)))
               (+
                (*
                 8.0
                 (/
                  (*
                   (* (* f f) (* 0.00390625 (pow PI 4.0)))
                   (pow (* PI 0.25) 2.0))
                  (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 4.0)))
                (+
                 (*
                  4.0
                  (/
                   (*
                    (pow (* PI 0.25) 2.0)
                    (* (* f f) (* (pow PI 2.0) 0.0625)))
                   (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 2.0)))
                 (+
                  (*
                   4.0
                   (/
                    (* (* PI 0.25) (* (* f f) (* (pow PI 4.0) -0.015625)))
                    (* 8.0 (pow (- (* PI 0.25) (* PI -0.25)) 3.0))))
                  (+
                   (/
                    (* (* PI 0.25) (* f (* PI -0.25)))
                    (- (* PI 0.25) (* PI -0.25)))
                   (+
                    (*
                     4.0
                     (/
                      (*
                       (pow (* PI 0.25) 2.0)
                       (* (* f f) (* -0.015625 (pow PI 3.0))))
                      (* 8.0 (pow (- (* PI 0.25) (* PI -0.25)) 3.0))))
                    (+
                     (*
                      10.666666666666666
                      (/
                       (* (* PI 0.25) (* (* f f) (* -0.015625 (pow PI 3.0))))
                       (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 2.0)))
                     (+
                      (*
                       8.0
                       (/
                        (* (* PI 0.25) (* (* f f) (* 0.00390625 (pow PI 4.0))))
                        (* 8.0 (pow (- (* PI 0.25) (* PI -0.25)) 3.0))))
                      (+
                       (*
                        0.25
                        (/
                         (* (* PI 0.25) (* f PI))
                         (- (* PI 0.25) (* PI -0.25))))
                       (+
                        (/
                         (* (* PI 0.25) (* (pow PI 3.0) (* (* f f) 0.0625)))
                         (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 2.0))
                        (+
                         (*
                          2.6666666666666665
                          (/
                           (* (* (* f f) (* PI -0.25)) (pow (* PI 0.25) 3.0))
                           (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 2.0)))
                         (+
                          (*
                           2.0
                           (/
                            (* (* PI 0.25) (* (pow PI 3.0) (* (* f f) 0.0625)))
                            (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 2.0)))
                          (+
                           (log (/ 4.0 (* (- (* PI 0.25) (* PI -0.25)) 2.0)))
                           (*
                            4.0
                            (/
                             (* (* PI 0.25) (* f (* (pow PI 2.0) 0.0625)))
                             (pow
                              (* (- (* PI 0.25) (* PI -0.25)) 2.0)
                              2.0)))))))))))))))))))))))))))
   (+
    (*
     32.0
     (/
      (* (* (* f f) (* -0.015625 (pow PI 3.0))) (pow (* PI 0.25) 3.0))
      (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 4.0)))
    (+
     (*
      16.0
      (/
       (* (* (* f f) (* (pow PI 2.0) 0.0625)) (pow (* PI 0.25) 3.0))
       (* 8.0 (pow (- (* PI 0.25) (* PI -0.25)) 3.0))))
     (+
      (*
       4.0
       (/
        (* f (pow (* PI 0.25) 3.0))
        (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 2.0)))
      (+
       (/ (* f (* (pow PI 2.0) 0.0625)) (- (* PI 0.25) (* PI -0.25)))
       (+
        (*
         8.0
         (/
          (* (* f f) (pow (* PI 0.25) 6.0))
          (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 4.0)))
        (+
         (*
          4.0
          (/
           (* (* (* f f) (* PI -0.25)) (pow (* PI 0.25) 3.0))
           (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 2.0)))
         (+
          (*
           0.046875
           (/ (* (* f f) (* -0.25 (pow PI 3.0))) (- (* PI 0.25) (* PI -0.25))))
          (+
           (*
            0.125
            (/
             (* (pow PI 3.0) (* (* f f) 0.0625))
             (- (* PI 0.25) (* PI -0.25))))
           (+
            (*
             0.75
             (/
              (* (* f f) (* -0.015625 (pow PI 3.0)))
              (- (* PI 0.25) (* PI -0.25))))
            (+
             (*
              8.0
              (/
               (* (pow PI 6.0) (* (* f f) 0.000244140625))
               (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 4.0)))
             (+
              (*
               2.6666666666666665
               (/
                (* (* f f) (pow (* PI 0.25) 4.0))
                (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 2.0)))
              (+
               (log f)
               (+
                (*
                 0.25
                 (/ (* f (* -0.25 (pow PI 2.0))) (- (* PI 0.25) (* PI -0.25))))
                (+
                 (*
                  8.666666666666666
                  (/
                   (* (* f f) (* 0.00390625 (pow PI 4.0)))
                   (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 2.0)))
                 (+
                  (*
                   2.0
                   (/
                    (* (* f f) (* (pow PI 4.0) -0.015625))
                    (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 2.0)))
                  (+
                   (*
                    4.0
                    (/
                     (*
                      (* (pow PI 2.0) (* (* f f) -0.25))
                      (pow (* PI 0.25) 3.0))
                     (* 8.0 (pow (- (* PI 0.25) (* PI -0.25)) 3.0))))
                   (+
                    (*
                     16.0
                     (/
                      (*
                       (* (* f f) (* (pow PI 2.0) 0.0625))
                       (pow (* PI 0.25) 3.0))
                      (* 8.0 (pow (- (* PI 0.25) (* PI -0.25)) 3.0))))
                    (+
                     (/
                      (* (* (* f f) PI) (pow (* PI 0.25) 3.0))
                      (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 2.0))
                     (+
                      (*
                       2.0
                       (/
                        (* (pow PI 5.0) (* (* f f) 0.00390625))
                        (* 8.0 (pow (- (* PI 0.25) (* PI -0.25)) 3.0))))
                      (+
                       (*
                        0.125
                        (/
                         (* (pow PI 4.0) (* (* f f) 0.0625))
                         (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 2.0)))
                       (+
                        (*
                         0.125
                         (/
                          (* (* (* f f) (pow PI 2.0)) (pow (* PI 0.25) 2.0))
                          (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 2.0)))
                        (+
                         (*
                          4.0
                          (/
                           (* f (* -0.015625 (pow PI 3.0)))
                           (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 2.0)))
                         (+
                          (*
                           2.0
                           (/
                            (*
                             (pow (* PI 0.25) 2.0)
                             (* (* f f) (* (pow PI 2.0) 0.0625)))
                            (pow (* (- (* PI 0.25) (* PI -0.25)) 2.0) 2.0)))
                          (*
                           16.0
                           (/
                            (* (* f f) (* -0.0009765625 (pow PI 5.0)))
                            (*
                             8.0
                             (pow
                              (- (* PI 0.25) (* PI -0.25))
                              3.0))))))))))))))))))))))))))))
  (/ -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 (((8.0 * (((f * f) * pow((((double) M_PI) * 0.25), 5.0)) / (8.0 * pow(((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)), 3.0)))) + ((16.0 * (((((double) M_PI) * 0.25) * ((f * f) * (0.00390625 * pow(((double) M_PI), 4.0)))) / (8.0 * pow(((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)), 3.0)))) + ((16.0 * ((pow((((double) M_PI) * 0.25), 5.0) * ((f * f) * (((double) M_PI) * -0.25))) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 4.0))) + ((0.046875 * (((((double) M_PI) * 0.25) * ((f * f) * pow(((double) M_PI), 2.0))) / ((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)))) + ((12.0 * ((pow((((double) M_PI) * 0.25), 2.0) * ((f * f) * (-0.015625 * pow(((double) M_PI), 3.0)))) / (8.0 * pow(((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)), 3.0)))) + ((2.0 * ((pow((((double) M_PI) * 0.25), 4.0) * ((f * f) * ((double) M_PI))) / (8.0 * pow(((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)), 3.0)))) + ((16.0 * (((((double) M_PI) * 0.25) * ((f * f) * (-0.0009765625 * pow(((double) M_PI), 5.0)))) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 4.0))) + ((4.0 * ((pow((((double) M_PI) * 0.25), 2.0) * (f * (((double) M_PI) * -0.25))) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 2.0))) + ((0.25 * (((((double) M_PI) * 0.25) * ((f * f) * (-0.25 * pow(((double) M_PI), 3.0)))) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 2.0))) + ((0.75 * (((((double) M_PI) * 0.25) * ((f * f) * (pow(((double) M_PI), 2.0) * 0.0625))) / ((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)))) + ((0.125 * (((((double) M_PI) * 0.25) * (pow(((double) M_PI), 2.0) * ((f * f) * -0.25))) / ((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)))) + ((8.0 * ((pow((((double) M_PI) * 0.25), 4.0) * ((f * f) * (pow(((double) M_PI), 2.0) * 0.0625))) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 4.0))) + ((8.0 * ((((f * f) * (0.00390625 * pow(((double) M_PI), 4.0))) * pow((((double) M_PI) * 0.25), 2.0)) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 4.0))) + ((4.0 * ((pow((((double) M_PI) * 0.25), 2.0) * ((f * f) * (pow(((double) M_PI), 2.0) * 0.0625))) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 2.0))) + ((4.0 * (((((double) M_PI) * 0.25) * ((f * f) * (pow(((double) M_PI), 4.0) * -0.015625))) / (8.0 * pow(((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)), 3.0)))) + ((((((double) M_PI) * 0.25) * (f * (((double) M_PI) * -0.25))) / ((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25))) + ((4.0 * ((pow((((double) M_PI) * 0.25), 2.0) * ((f * f) * (-0.015625 * pow(((double) M_PI), 3.0)))) / (8.0 * pow(((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)), 3.0)))) + ((10.666666666666666 * (((((double) M_PI) * 0.25) * ((f * f) * (-0.015625 * pow(((double) M_PI), 3.0)))) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 2.0))) + ((8.0 * (((((double) M_PI) * 0.25) * ((f * f) * (0.00390625 * pow(((double) M_PI), 4.0)))) / (8.0 * pow(((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)), 3.0)))) + ((0.25 * (((((double) M_PI) * 0.25) * (f * ((double) M_PI))) / ((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)))) + ((((((double) M_PI) * 0.25) * (pow(((double) M_PI), 3.0) * ((f * f) * 0.0625))) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 2.0)) + ((2.6666666666666665 * ((((f * f) * (((double) M_PI) * -0.25)) * pow((((double) M_PI) * 0.25), 3.0)) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 2.0))) + ((2.0 * (((((double) M_PI) * 0.25) * (pow(((double) M_PI), 3.0) * ((f * f) * 0.0625))) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 2.0))) + (log(4.0 / (((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0)) + (4.0 * (((((double) M_PI) * 0.25) * (f * (pow(((double) M_PI), 2.0) * 0.0625))) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 2.0))))))))))))))))))))))))))) - ((32.0 * ((((f * f) * (-0.015625 * pow(((double) M_PI), 3.0))) * pow((((double) M_PI) * 0.25), 3.0)) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 4.0))) + ((16.0 * ((((f * f) * (pow(((double) M_PI), 2.0) * 0.0625)) * pow((((double) M_PI) * 0.25), 3.0)) / (8.0 * pow(((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)), 3.0)))) + ((4.0 * ((f * pow((((double) M_PI) * 0.25), 3.0)) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 2.0))) + (((f * (pow(((double) M_PI), 2.0) * 0.0625)) / ((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25))) + ((8.0 * (((f * f) * pow((((double) M_PI) * 0.25), 6.0)) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 4.0))) + ((4.0 * ((((f * f) * (((double) M_PI) * -0.25)) * pow((((double) M_PI) * 0.25), 3.0)) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 2.0))) + ((0.046875 * (((f * f) * (-0.25 * pow(((double) M_PI), 3.0))) / ((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)))) + ((0.125 * ((pow(((double) M_PI), 3.0) * ((f * f) * 0.0625)) / ((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)))) + ((0.75 * (((f * f) * (-0.015625 * pow(((double) M_PI), 3.0))) / ((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)))) + ((8.0 * ((pow(((double) M_PI), 6.0) * ((f * f) * 0.000244140625)) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 4.0))) + ((2.6666666666666665 * (((f * f) * pow((((double) M_PI) * 0.25), 4.0)) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 2.0))) + (log(f) + ((0.25 * ((f * (-0.25 * pow(((double) M_PI), 2.0))) / ((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)))) + ((8.666666666666666 * (((f * f) * (0.00390625 * pow(((double) M_PI), 4.0))) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 2.0))) + ((2.0 * (((f * f) * (pow(((double) M_PI), 4.0) * -0.015625)) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 2.0))) + ((4.0 * (((pow(((double) M_PI), 2.0) * ((f * f) * -0.25)) * pow((((double) M_PI) * 0.25), 3.0)) / (8.0 * pow(((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)), 3.0)))) + ((16.0 * ((((f * f) * (pow(((double) M_PI), 2.0) * 0.0625)) * pow((((double) M_PI) * 0.25), 3.0)) / (8.0 * pow(((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)), 3.0)))) + (((((f * f) * ((double) M_PI)) * pow((((double) M_PI) * 0.25), 3.0)) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 2.0)) + ((2.0 * ((pow(((double) M_PI), 5.0) * ((f * f) * 0.00390625)) / (8.0 * pow(((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)), 3.0)))) + ((0.125 * ((pow(((double) M_PI), 4.0) * ((f * f) * 0.0625)) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 2.0))) + ((0.125 * ((((f * f) * pow(((double) M_PI), 2.0)) * pow((((double) M_PI) * 0.25), 2.0)) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 2.0))) + ((4.0 * ((f * (-0.015625 * pow(((double) M_PI), 3.0))) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 2.0))) + ((2.0 * ((pow((((double) M_PI) * 0.25), 2.0) * ((f * f) * (pow(((double) M_PI), 2.0) * 0.0625))) / pow((((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)) * 2.0), 2.0))) + (16.0 * (((f * f) * (-0.0009765625 * pow(((double) M_PI), 5.0))) / (8.0 * pow(((((double) M_PI) * 0.25) - (((double) M_PI) * -0.25)), 3.0)))))))))))))))))))))))))))) * (-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 61.5

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

  2. Simplified61.5

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

  4. Applied flip--_binary6461.6

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

  5. Simplified61.6

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

  6. Taylor expanded around 0 2.3

    \[\leadsto \color{blue}{\left(\left(8 \cdot \frac{{\log \left(e^{0.25 \cdot \pi}\right)}^{5} \cdot {f}^{2}}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{3}} + \left(16 \cdot \frac{\log \left(e^{0.25 \cdot \pi}\right) \cdot \left({f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{4} \cdot {\pi}^{4}\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{3}} + \left(16 \cdot \frac{{\log \left(e^{0.25 \cdot \pi}\right)}^{5} \cdot \left({f}^{2} \cdot \left(\log \left(e^{-0.25}\right) \cdot \pi\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{4}} + \left(0.09375 \cdot \frac{\log \left(e^{0.25 \cdot \pi}\right) \cdot \left({\pi}^{2} \cdot {f}^{2}\right)}{2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)} + \left(12 \cdot \frac{{\log \left(e^{0.25 \cdot \pi}\right)}^{2} \cdot \left({\pi}^{3} \cdot \left({\log \left(e^{-0.25}\right)}^{3} \cdot {f}^{2}\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{3}} + \left(2 \cdot \frac{{\log \left(e^{0.25 \cdot \pi}\right)}^{4} \cdot \left(\pi \cdot {f}^{2}\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{3}} + \left(16 \cdot \frac{\log \left(e^{0.25 \cdot \pi}\right) \cdot \left({f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{5} \cdot {\pi}^{5}\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{4}} + \left(4 \cdot \frac{{\log \left(e^{0.25 \cdot \pi}\right)}^{2} \cdot \left(f \cdot \left(\log \left(e^{-0.25}\right) \cdot \pi\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(0.25 \cdot \frac{\log \left(e^{0.25 \cdot \pi}\right) \cdot \left({f}^{2} \cdot \left(\log \left(e^{-0.25}\right) \cdot {\pi}^{3}\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(1.5 \cdot \frac{\log \left(e^{0.25 \cdot \pi}\right) \cdot \left({f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot {\pi}^{2}\right)\right)}{2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)} + \left(0.25 \cdot \frac{\log \left(e^{0.25 \cdot \pi}\right) \cdot \left({\pi}^{2} \cdot \left(\log \left(e^{-0.25}\right) \cdot {f}^{2}\right)\right)}{2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)} + \left(8 \cdot \frac{{\log \left(e^{0.25 \cdot \pi}\right)}^{4} \cdot \left({f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot {\pi}^{2}\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{4}} + \left(8 \cdot \frac{{\log \left(e^{0.25 \cdot \pi}\right)}^{2} \cdot \left({f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{4} \cdot {\pi}^{4}\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{4}} + \left(4 \cdot \frac{{\log \left(e^{0.25 \cdot \pi}\right)}^{2} \cdot \left({f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot {\pi}^{2}\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(4 \cdot \frac{\log \left(e^{0.25 \cdot \pi}\right) \cdot \left({f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{3} \cdot {\pi}^{4}\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{3}} + \left(2 \cdot \frac{\log \left(e^{0.25 \cdot \pi}\right) \cdot \left(\pi \cdot \left(\log \left(e^{-0.25}\right) \cdot f\right)\right)}{2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)} + \left(4 \cdot \frac{{\log \left(e^{0.25 \cdot \pi}\right)}^{2} \cdot \left({f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{3} \cdot {\pi}^{3}\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{3}} + \left(10.666666666666666 \cdot \frac{\log \left(e^{0.25 \cdot \pi}\right) \cdot \left({f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{3} \cdot {\pi}^{3}\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(8 \cdot \frac{\log \left(e^{0.25 \cdot \pi}\right) \cdot \left({\pi}^{4} \cdot \left({\log \left(e^{-0.25}\right)}^{4} \cdot {f}^{2}\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{3}} + \left(0.5 \cdot \frac{\log \left(e^{0.25 \cdot \pi}\right) \cdot \left(f \cdot \pi\right)}{2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)} + \left(\frac{\log \left(e^{0.25 \cdot \pi}\right) \cdot \left({\pi}^{3} \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot {f}^{2}\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(2.6666666666666665 \cdot \frac{{\log \left(e^{0.25 \cdot \pi}\right)}^{3} \cdot \left(\pi \cdot \left(\log \left(e^{-0.25}\right) \cdot {f}^{2}\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(2 \cdot \frac{\log \left(e^{0.25 \cdot \pi}\right) \cdot \left({f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot {\pi}^{3}\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(\log \left(\frac{4}{2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)}\right) + 4 \cdot \frac{\log \left(e^{0.25 \cdot \pi}\right) \cdot \left(f \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot {\pi}^{2}\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(32 \cdot \frac{{\log \left(e^{0.25 \cdot \pi}\right)}^{3} \cdot \left({f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{3} \cdot {\pi}^{3}\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{4}} + \left(16 \cdot \frac{{\log \left(e^{0.25 \cdot \pi}\right)}^{3} \cdot \left({f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot {\pi}^{2}\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{3}} + \left(4 \cdot \frac{{\log \left(e^{0.25 \cdot \pi}\right)}^{3} \cdot f}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(2 \cdot \frac{f \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot {\pi}^{2}\right)}{2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)} + \left(8 \cdot \frac{{\log \left(e^{0.25 \cdot \pi}\right)}^{6} \cdot {f}^{2}}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{4}} + \left(4 \cdot \frac{{\log \left(e^{0.25 \cdot \pi}\right)}^{3} \cdot \left({f}^{2} \cdot \left(\log \left(e^{-0.25}\right) \cdot \pi\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(0.09375 \cdot \frac{{\pi}^{3} \cdot \left(\log \left(e^{-0.25}\right) \cdot {f}^{2}\right)}{2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)} + \left(0.25 \cdot \frac{{\pi}^{3} \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot {f}^{2}\right)}{2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)} + \left(1.5 \cdot \frac{{f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{3} \cdot {\pi}^{3}\right)}{2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)} + \left(8 \cdot \frac{{\pi}^{6} \cdot \left({\log \left(e^{-0.25}\right)}^{6} \cdot {f}^{2}\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{4}} + \left(2.6666666666666665 \cdot \frac{{\log \left(e^{0.25 \cdot \pi}\right)}^{4} \cdot {f}^{2}}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(\log f + \left(0.5 \cdot \frac{f \cdot \left(\log \left(e^{-0.25}\right) \cdot {\pi}^{2}\right)}{2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)} + \left(8.666666666666666 \cdot \frac{{f}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{4} \cdot {\pi}^{4}\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(2 \cdot \frac{{\pi}^{4} \cdot \left({\log \left(e^{-0.25}\right)}^{3} \cdot {f}^{2}\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(4 \cdot \frac{{\log \left(e^{0.25 \cdot \pi}\right)}^{3} \cdot \left({f}^{2} \cdot \left(\log \left(e^{-0.25}\right) \cdot {\pi}^{2}\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{3}} + \left(16 \cdot \frac{{\log \left(e^{0.25 \cdot \pi}\right)}^{3} \cdot \left({\pi}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot {f}^{2}\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{3}} + \left(\frac{{\log \left(e^{0.25 \cdot \pi}\right)}^{3} \cdot \left(\pi \cdot {f}^{2}\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(2 \cdot \frac{{\pi}^{5} \cdot \left({\log \left(e^{-0.25}\right)}^{4} \cdot {f}^{2}\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{3}} + \left(0.125 \cdot \frac{{\pi}^{4} \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot {f}^{2}\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(0.125 \cdot \frac{{\log \left(e^{0.25 \cdot \pi}\right)}^{2} \cdot \left({\pi}^{2} \cdot {f}^{2}\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 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(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + \left(2 \cdot \frac{{\log \left(e^{0.25 \cdot \pi}\right)}^{2} \cdot \left({\pi}^{2} \cdot \left({\log \left(e^{-0.25}\right)}^{2} \cdot {f}^{2}\right)\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{2}} + 16 \cdot \frac{{\pi}^{5} \cdot \left({\log \left(e^{-0.25}\right)}^{5} \cdot {f}^{2}\right)}{{\left(2 \cdot \log \left(e^{0.25 \cdot \pi}\right) - 2 \cdot \left(\pi \cdot \log \left(e^{-0.25}\right)\right)\right)}^{3}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)} \cdot \frac{-4}{\pi}\]

  7. Simplified2.3

    \[\leadsto \color{blue}{\left(\left(8 \cdot \frac{\left(f \cdot f\right) \cdot {\left(\pi \cdot 0.25\right)}^{5}}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(16 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{4}\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(16 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{5} \cdot \left(\left(f \cdot f\right) \cdot \left(\pi \cdot -0.25\right)\right)}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{4}} + \left(0.046875 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot {\pi}^{2}\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(12 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{2} \cdot \left(\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{3}\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(2 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{4} \cdot \left(\pi \cdot \left(f \cdot f\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(16 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left(-0.0009765625 \cdot {\pi}^{5}\right)\right)}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{4}} + \left(4 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{2} \cdot \left(f \cdot \left(\pi \cdot -0.25\right)\right)}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{2}} + \left(0.25 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{3}\right)\right)}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{2}} + \left(0.75 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{2}\right)\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(0.125 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left({\pi}^{2} \cdot \left(-0.25 \cdot \left(f \cdot f\right)\right)\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(8 \cdot \frac{\left(\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{2}\right)\right) \cdot {\left(\pi \cdot 0.25\right)}^{4}}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{4}} + \left(8 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{2} \cdot \left(\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{4}\right)\right)}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{4}} + \left(4 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{2} \cdot \left(\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{2}\right)\right)}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{2}} + \left(4 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{4}\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(1 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(f \cdot \left(\pi \cdot -0.25\right)\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(4 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{2} \cdot \left(\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{3}\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(10.666666666666666 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{3}\right)\right)}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{2}} + \left(8 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{4}\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(0.25 \cdot \frac{\left(\pi \cdot f\right) \cdot \left(\pi \cdot 0.25\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(\frac{\left(\pi \cdot 0.25\right) \cdot \left({\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)\right)}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{2}} + \left(2.6666666666666665 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{3} \cdot \left(\left(f \cdot f\right) \cdot \left(\pi \cdot -0.25\right)\right)}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{2}} + \left(2 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left({\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)\right)}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{2}} + \left(\log \left(\frac{4}{2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}\right) + 4 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(f \cdot \left(0.0625 \cdot {\pi}^{2}\right)\right)}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{2}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(32 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{3} \cdot \left(\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{3}\right)\right)}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{4}} + \left(16 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{3} \cdot \left(\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{2}\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(4 \cdot \frac{f \cdot {\left(\pi \cdot 0.25\right)}^{3}}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{2}} + \left(1 \cdot \frac{f \cdot \left(0.0625 \cdot {\pi}^{2}\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(8 \cdot \frac{\left(f \cdot f\right) \cdot {\left(\pi \cdot 0.25\right)}^{6}}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{4}} + \left(4 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{3} \cdot \left(\left(f \cdot f\right) \cdot \left(\pi \cdot -0.25\right)\right)}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{2}} + \left(0.046875 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{3}\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(0.75 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{3}\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(8 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot 0.000244140625\right)}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{4}} + \left(2.6666666666666665 \cdot \frac{\left(f \cdot f\right) \cdot {\left(\pi \cdot 0.25\right)}^{4}}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{2}} + \left(\log f + \left(0.25 \cdot \frac{f \cdot \left(-0.25 \cdot {\pi}^{2}\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(8.666666666666666 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{4}\right)}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{2}} + \left(2 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{4}\right)}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{2}} + \left(4 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{3} \cdot \left({\pi}^{2} \cdot \left(-0.25 \cdot \left(f \cdot f\right)\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(16 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{3} \cdot \left(\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{2}\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(\frac{{\left(\pi \cdot 0.25\right)}^{3} \cdot \left(\pi \cdot \left(f \cdot f\right)\right)}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{2}} + \left(2 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot 0.00390625\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(0.125 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{2}} + \left(0.125 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{2} \cdot \left(\left(f \cdot f\right) \cdot {\pi}^{2}\right)}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{2}} + \left(4 \cdot \frac{f \cdot \left(-0.015625 \cdot {\pi}^{3}\right)}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{2}} + \left(2 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{2} \cdot \left(\left(f \cdot f\right) \cdot \left(0.0625 \cdot {\pi}^{2}\right)\right)}{{\left(2 \cdot \left(\pi \cdot 0.25 - \pi \cdot -0.25\right)\right)}^{2}} + 16 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.0009765625 \cdot {\pi}^{5}\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)} \cdot \frac{-4}{\pi}\]

  8. Final simplification2.3

    \[\leadsto \left(\left(8 \cdot \frac{\left(f \cdot f\right) \cdot {\left(\pi \cdot 0.25\right)}^{5}}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(16 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{4}\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(16 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{5} \cdot \left(\left(f \cdot f\right) \cdot \left(\pi \cdot -0.25\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{4}} + \left(0.046875 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot {\pi}^{2}\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(12 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{2} \cdot \left(\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{3}\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(2 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{4} \cdot \left(\left(f \cdot f\right) \cdot \pi\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(16 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left(-0.0009765625 \cdot {\pi}^{5}\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{4}} + \left(4 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{2} \cdot \left(f \cdot \left(\pi \cdot -0.25\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(0.25 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{3}\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(0.75 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left({\pi}^{2} \cdot 0.0625\right)\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(0.125 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left({\pi}^{2} \cdot \left(\left(f \cdot f\right) \cdot -0.25\right)\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(8 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{4} \cdot \left(\left(f \cdot f\right) \cdot \left({\pi}^{2} \cdot 0.0625\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{4}} + \left(8 \cdot \frac{\left(\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{4}\right)\right) \cdot {\left(\pi \cdot 0.25\right)}^{2}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{4}} + \left(4 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{2} \cdot \left(\left(f \cdot f\right) \cdot \left({\pi}^{2} \cdot 0.0625\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(4 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left({\pi}^{4} \cdot -0.015625\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(\frac{\left(\pi \cdot 0.25\right) \cdot \left(f \cdot \left(\pi \cdot -0.25\right)\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(4 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{2} \cdot \left(\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{3}\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(10.666666666666666 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{3}\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(8 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{4}\right)\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(0.25 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(f \cdot \pi\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(\frac{\left(\pi \cdot 0.25\right) \cdot \left({\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(2.6666666666666665 \cdot \frac{\left(\left(f \cdot f\right) \cdot \left(\pi \cdot -0.25\right)\right) \cdot {\left(\pi \cdot 0.25\right)}^{3}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(2 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left({\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(\log \left(\frac{4}{\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2}\right) + 4 \cdot \frac{\left(\pi \cdot 0.25\right) \cdot \left(f \cdot \left({\pi}^{2} \cdot 0.0625\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) - \left(32 \cdot \frac{\left(\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{3}\right)\right) \cdot {\left(\pi \cdot 0.25\right)}^{3}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{4}} + \left(16 \cdot \frac{\left(\left(f \cdot f\right) \cdot \left({\pi}^{2} \cdot 0.0625\right)\right) \cdot {\left(\pi \cdot 0.25\right)}^{3}}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(4 \cdot \frac{f \cdot {\left(\pi \cdot 0.25\right)}^{3}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(\frac{f \cdot \left({\pi}^{2} \cdot 0.0625\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(8 \cdot \frac{\left(f \cdot f\right) \cdot {\left(\pi \cdot 0.25\right)}^{6}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{4}} + \left(4 \cdot \frac{\left(\left(f \cdot f\right) \cdot \left(\pi \cdot -0.25\right)\right) \cdot {\left(\pi \cdot 0.25\right)}^{3}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(0.046875 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.25 \cdot {\pi}^{3}\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(0.125 \cdot \frac{{\pi}^{3} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(0.75 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.015625 \cdot {\pi}^{3}\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(8 \cdot \frac{{\pi}^{6} \cdot \left(\left(f \cdot f\right) \cdot 0.000244140625\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{4}} + \left(2.6666666666666665 \cdot \frac{\left(f \cdot f\right) \cdot {\left(\pi \cdot 0.25\right)}^{4}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(\log f + \left(0.25 \cdot \frac{f \cdot \left(-0.25 \cdot {\pi}^{2}\right)}{\pi \cdot 0.25 - \pi \cdot -0.25} + \left(8.666666666666666 \cdot \frac{\left(f \cdot f\right) \cdot \left(0.00390625 \cdot {\pi}^{4}\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(2 \cdot \frac{\left(f \cdot f\right) \cdot \left({\pi}^{4} \cdot -0.015625\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(4 \cdot \frac{\left({\pi}^{2} \cdot \left(\left(f \cdot f\right) \cdot -0.25\right)\right) \cdot {\left(\pi \cdot 0.25\right)}^{3}}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(16 \cdot \frac{\left(\left(f \cdot f\right) \cdot \left({\pi}^{2} \cdot 0.0625\right)\right) \cdot {\left(\pi \cdot 0.25\right)}^{3}}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(\frac{\left(\left(f \cdot f\right) \cdot \pi\right) \cdot {\left(\pi \cdot 0.25\right)}^{3}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(2 \cdot \frac{{\pi}^{5} \cdot \left(\left(f \cdot f\right) \cdot 0.00390625\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}} + \left(0.125 \cdot \frac{{\pi}^{4} \cdot \left(\left(f \cdot f\right) \cdot 0.0625\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(0.125 \cdot \frac{\left(\left(f \cdot f\right) \cdot {\pi}^{2}\right) \cdot {\left(\pi \cdot 0.25\right)}^{2}}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(4 \cdot \frac{f \cdot \left(-0.015625 \cdot {\pi}^{3}\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + \left(2 \cdot \frac{{\left(\pi \cdot 0.25\right)}^{2} \cdot \left(\left(f \cdot f\right) \cdot \left({\pi}^{2} \cdot 0.0625\right)\right)}{{\left(\left(\pi \cdot 0.25 - \pi \cdot -0.25\right) \cdot 2\right)}^{2}} + 16 \cdot \frac{\left(f \cdot f\right) \cdot \left(-0.0009765625 \cdot {\pi}^{5}\right)}{8 \cdot {\left(\pi \cdot 0.25 - \pi \cdot -0.25\right)}^{3}}\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \frac{-4}{\pi}\]

Reproduce

herbie shell --seed 2020342 
(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)))))))))