Average Error: 58.6 → 31.1
Time: 6.3m
Precision: 64
Internal Precision: 7296
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{-1}{M} \le -352698.84385416645:\\ \;\;\;\;0\\ \mathbf{if}\;\frac{-1}{M} \le -4.229474504364196 \cdot 10^{-111}:\\ \;\;\;\;\frac{\left(\frac{\left(c0 \cdot \frac{1}{2}\right) \cdot \frac{-1}{d}}{\frac{\frac{-1}{h}}{\frac{-1}{d}}} \cdot \frac{\frac{-\frac{-1}{2}}{c0}}{\frac{\frac{-1}{D}}{w}}\right) \cdot \left(\left(M \cdot M\right) \cdot D\right)}{w}\\ \mathbf{if}\;\frac{-1}{M} \le 1.8506234376954745 \cdot 10^{-299}:\\ \;\;\;\;0\\ \mathbf{if}\;\frac{-1}{M} \le 2.9496606837143694 \cdot 10^{-118}:\\ \;\;\;\;\frac{\left(\frac{\left(c0 \cdot \frac{1}{2}\right) \cdot \frac{-1}{d}}{\frac{\frac{-1}{h}}{\frac{-1}{d}}} \cdot \frac{-\frac{\frac{-1}{2}}{c0}}{\frac{\frac{\frac{-1}{M}}{w}}{D}}\right) \cdot \left(M \cdot D\right)}{w}\\ \mathbf{if}\;\frac{-1}{M} \le 4.7320346021865155 \cdot 10^{+224}:\\ \;\;\;\;0\\ \mathbf{if}\;\frac{-1}{M} \le 6.599920322578423 \cdot 10^{+251}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\sqrt{\left(\frac{c0}{w} \cdot \frac{d}{D}\right) \cdot \frac{\frac{d}{D}}{h} + \sqrt{(\left(\left(\frac{c0}{w} \cdot \frac{d}{D}\right) \cdot \frac{\frac{d}{D}}{h}\right) \cdot \left(\left(\frac{c0}{w} \cdot \frac{d}{D}\right) \cdot \frac{\frac{d}{D}}{h}\right) + \left(-M \cdot M\right))_*}} \cdot \sqrt{\left(\frac{c0}{w} \cdot \frac{d}{D}\right) \cdot \frac{\frac{d}{D}}{h} + \sqrt{(\left(\left(\frac{c0}{w} \cdot \frac{d}{D}\right) \cdot \frac{\frac{d}{D}}{h}\right) \cdot \left(\left(\frac{c0}{w} \cdot \frac{d}{D}\right) \cdot \frac{\frac{d}{D}}{h}\right) + \left(-M \cdot M\right))_*}}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Error

Bits error versus c0

Bits error versus w

Bits error versus h

Bits error versus D

Bits error versus d

Bits error versus M

Derivation

  1. Split input into 4 regimes

  2. if (/ -1 M) < -352698.84385416645 or -4.229474504364196e-111 < (/ -1 M) < 1.8506234376954745e-299 or 2.9496606837143694e-118 < (/ -1 M) < 4.7320346021865155e+224 or 6.599920322578423e+251 < (/ -1 M)

    1. Initial program 58.1

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]

    2. Taylor expanded around inf 33.9

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{0}\]

    3. Applied simplify29.8

      \[\leadsto \color{blue}{0}\]

    if -352698.84385416645 < (/ -1 M) < -4.229474504364196e-111

    1. Initial program 61.3

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
    2. Using strategy rm

    3. Applied add-cbrt-cube62.0

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\sqrt[3]{\left(\left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\right) \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)}}\]

    4. Applied simplify60.9

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \sqrt[3]{\color{blue}{{\left(\sqrt{(\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) \cdot \left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) + \left(-M \cdot M\right))_*} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)}^{3}}}\]

    5. Taylor expanded around -inf 62.8

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{e^{\left(\log \left(\frac{-1}{c0}\right) + \left(\log \frac{-1}{2} + 2 \cdot \log \left(\frac{-1}{d}\right)\right)\right) - \left(\log \left(\frac{-1}{h}\right) + \left(2 \cdot \log \left(\frac{-1}{D}\right) + \left(2 \cdot \log \left(\frac{-1}{M}\right) + \log \left(\frac{-1}{w}\right)\right)\right)\right)} \cdot c0}{w}}\]

    6. Applied simplify37.8

      \[\leadsto \color{blue}{\frac{\frac{\left(\frac{1}{2} \cdot c0\right) \cdot \left(\left(\frac{-1}{d} \cdot \frac{-1}{d}\right) \cdot \left(\frac{-1}{c0} \cdot \frac{-1}{2}\right)\right)}{\left(\frac{-1}{w} \cdot \left(\frac{-1}{M} \cdot \frac{-1}{M}\right)\right) \cdot \left(\left(\frac{-1}{D} \cdot \frac{-1}{D}\right) \cdot \frac{-1}{h}\right)}}{w}}\]
    7. Using strategy rm

    8. Applied associate-*r/37.8

      \[\leadsto \frac{\frac{\left(\frac{1}{2} \cdot c0\right) \cdot \left(\left(\frac{-1}{d} \cdot \frac{-1}{d}\right) \cdot \left(\frac{-1}{c0} \cdot \frac{-1}{2}\right)\right)}{\left(\frac{-1}{w} \cdot \left(\frac{-1}{M} \cdot \frac{-1}{M}\right)\right) \cdot \left(\color{blue}{\frac{\frac{-1}{D} \cdot -1}{D}} \cdot \frac{-1}{h}\right)}}{w}\]

    9. Applied associate-*l/36.5

      \[\leadsto \frac{\frac{\left(\frac{1}{2} \cdot c0\right) \cdot \left(\left(\frac{-1}{d} \cdot \frac{-1}{d}\right) \cdot \left(\frac{-1}{c0} \cdot \frac{-1}{2}\right)\right)}{\left(\frac{-1}{w} \cdot \left(\frac{-1}{M} \cdot \frac{-1}{M}\right)\right) \cdot \color{blue}{\frac{\left(\frac{-1}{D} \cdot -1\right) \cdot \frac{-1}{h}}{D}}}}{w}\]

    10. Applied frac-times36.5

      \[\leadsto \frac{\frac{\left(\frac{1}{2} \cdot c0\right) \cdot \left(\left(\frac{-1}{d} \cdot \frac{-1}{d}\right) \cdot \left(\frac{-1}{c0} \cdot \frac{-1}{2}\right)\right)}{\left(\frac{-1}{w} \cdot \color{blue}{\frac{-1 \cdot -1}{M \cdot M}}\right) \cdot \frac{\left(\frac{-1}{D} \cdot -1\right) \cdot \frac{-1}{h}}{D}}}{w}\]

    11. Applied associate-*r/36.5

      \[\leadsto \frac{\frac{\left(\frac{1}{2} \cdot c0\right) \cdot \left(\left(\frac{-1}{d} \cdot \frac{-1}{d}\right) \cdot \left(\frac{-1}{c0} \cdot \frac{-1}{2}\right)\right)}{\color{blue}{\frac{\frac{-1}{w} \cdot \left(-1 \cdot -1\right)}{M \cdot M}} \cdot \frac{\left(\frac{-1}{D} \cdot -1\right) \cdot \frac{-1}{h}}{D}}}{w}\]

    12. Applied frac-times33.2

      \[\leadsto \frac{\frac{\left(\frac{1}{2} \cdot c0\right) \cdot \left(\left(\frac{-1}{d} \cdot \frac{-1}{d}\right) \cdot \left(\frac{-1}{c0} \cdot \frac{-1}{2}\right)\right)}{\color{blue}{\frac{\left(\frac{-1}{w} \cdot \left(-1 \cdot -1\right)\right) \cdot \left(\left(\frac{-1}{D} \cdot -1\right) \cdot \frac{-1}{h}\right)}{\left(M \cdot M\right) \cdot D}}}}{w}\]

    13. Applied associate-/r/33.1

      \[\leadsto \frac{\color{blue}{\frac{\left(\frac{1}{2} \cdot c0\right) \cdot \left(\left(\frac{-1}{d} \cdot \frac{-1}{d}\right) \cdot \left(\frac{-1}{c0} \cdot \frac{-1}{2}\right)\right)}{\left(\frac{-1}{w} \cdot \left(-1 \cdot -1\right)\right) \cdot \left(\left(\frac{-1}{D} \cdot -1\right) \cdot \frac{-1}{h}\right)} \cdot \left(\left(M \cdot M\right) \cdot D\right)}}{w}\]

    14. Applied simplify31.9

      \[\leadsto \frac{\color{blue}{\left(\frac{\left(c0 \cdot \frac{1}{2}\right) \cdot \frac{-1}{d}}{\frac{\frac{-1}{h}}{\frac{-1}{d}}} \cdot \frac{\frac{-\frac{-1}{2}}{c0}}{\frac{\frac{-1}{D}}{w}}\right)} \cdot \left(\left(M \cdot M\right) \cdot D\right)}{w}\]

    if 1.8506234376954745e-299 < (/ -1 M) < 2.9496606837143694e-118

    1. Initial program 62.5

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
    2. Using strategy rm

    3. Applied add-cbrt-cube62.6

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\sqrt[3]{\left(\left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\right) \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)}}\]

    4. Applied simplify62.6

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \sqrt[3]{\color{blue}{{\left(\sqrt{(\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) \cdot \left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) + \left(-M \cdot M\right))_*} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)}^{3}}}\]

    5. Taylor expanded around -inf 62.6

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{e^{\left(\log \left(\frac{-1}{c0}\right) + \left(\log \frac{-1}{2} + 2 \cdot \log \left(\frac{-1}{d}\right)\right)\right) - \left(\log \left(\frac{-1}{h}\right) + \left(2 \cdot \log \left(\frac{-1}{D}\right) + \left(2 \cdot \log \left(\frac{-1}{M}\right) + \log \left(\frac{-1}{w}\right)\right)\right)\right)} \cdot c0}{w}}\]

    6. Applied simplify57.5

      \[\leadsto \color{blue}{\frac{\frac{\left(\frac{1}{2} \cdot c0\right) \cdot \left(\left(\frac{-1}{d} \cdot \frac{-1}{d}\right) \cdot \left(\frac{-1}{c0} \cdot \frac{-1}{2}\right)\right)}{\left(\frac{-1}{w} \cdot \left(\frac{-1}{M} \cdot \frac{-1}{M}\right)\right) \cdot \left(\left(\frac{-1}{D} \cdot \frac{-1}{D}\right) \cdot \frac{-1}{h}\right)}}{w}}\]
    7. Using strategy rm

    8. Applied associate-*r/57.5

      \[\leadsto \frac{\frac{\left(\frac{1}{2} \cdot c0\right) \cdot \left(\left(\frac{-1}{d} \cdot \frac{-1}{d}\right) \cdot \left(\frac{-1}{c0} \cdot \frac{-1}{2}\right)\right)}{\left(\frac{-1}{w} \cdot \left(\frac{-1}{M} \cdot \frac{-1}{M}\right)\right) \cdot \left(\color{blue}{\frac{\frac{-1}{D} \cdot -1}{D}} \cdot \frac{-1}{h}\right)}}{w}\]

    9. Applied associate-*l/57.1

      \[\leadsto \frac{\frac{\left(\frac{1}{2} \cdot c0\right) \cdot \left(\left(\frac{-1}{d} \cdot \frac{-1}{d}\right) \cdot \left(\frac{-1}{c0} \cdot \frac{-1}{2}\right)\right)}{\left(\frac{-1}{w} \cdot \left(\frac{-1}{M} \cdot \frac{-1}{M}\right)\right) \cdot \color{blue}{\frac{\left(\frac{-1}{D} \cdot -1\right) \cdot \frac{-1}{h}}{D}}}}{w}\]

    10. Applied associate-*r/57.1

      \[\leadsto \frac{\frac{\left(\frac{1}{2} \cdot c0\right) \cdot \left(\left(\frac{-1}{d} \cdot \frac{-1}{d}\right) \cdot \left(\frac{-1}{c0} \cdot \frac{-1}{2}\right)\right)}{\left(\frac{-1}{w} \cdot \color{blue}{\frac{\frac{-1}{M} \cdot -1}{M}}\right) \cdot \frac{\left(\frac{-1}{D} \cdot -1\right) \cdot \frac{-1}{h}}{D}}}{w}\]

    11. Applied associate-*r/53.0

      \[\leadsto \frac{\frac{\left(\frac{1}{2} \cdot c0\right) \cdot \left(\left(\frac{-1}{d} \cdot \frac{-1}{d}\right) \cdot \left(\frac{-1}{c0} \cdot \frac{-1}{2}\right)\right)}{\color{blue}{\frac{\frac{-1}{w} \cdot \left(\frac{-1}{M} \cdot -1\right)}{M}} \cdot \frac{\left(\frac{-1}{D} \cdot -1\right) \cdot \frac{-1}{h}}{D}}}{w}\]

    12. Applied frac-times42.1

      \[\leadsto \frac{\frac{\left(\frac{1}{2} \cdot c0\right) \cdot \left(\left(\frac{-1}{d} \cdot \frac{-1}{d}\right) \cdot \left(\frac{-1}{c0} \cdot \frac{-1}{2}\right)\right)}{\color{blue}{\frac{\left(\frac{-1}{w} \cdot \left(\frac{-1}{M} \cdot -1\right)\right) \cdot \left(\left(\frac{-1}{D} \cdot -1\right) \cdot \frac{-1}{h}\right)}{M \cdot D}}}}{w}\]

    13. Applied associate-/r/42.5

      \[\leadsto \frac{\color{blue}{\frac{\left(\frac{1}{2} \cdot c0\right) \cdot \left(\left(\frac{-1}{d} \cdot \frac{-1}{d}\right) \cdot \left(\frac{-1}{c0} \cdot \frac{-1}{2}\right)\right)}{\left(\frac{-1}{w} \cdot \left(\frac{-1}{M} \cdot -1\right)\right) \cdot \left(\left(\frac{-1}{D} \cdot -1\right) \cdot \frac{-1}{h}\right)} \cdot \left(M \cdot D\right)}}{w}\]

    14. Applied simplify39.1

      \[\leadsto \frac{\color{blue}{\left(\frac{\left(c0 \cdot \frac{1}{2}\right) \cdot \frac{-1}{d}}{\frac{\frac{-1}{h}}{\frac{-1}{d}}} \cdot \frac{-\frac{\frac{-1}{2}}{c0}}{\frac{\frac{\frac{-1}{M}}{w}}{D}}\right)} \cdot \left(M \cdot D\right)}{w}\]

    if 4.7320346021865155e+224 < (/ -1 M) < 6.599920322578423e+251

    1. Initial program 52.6

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
    2. Using strategy rm

    3. Applied add-cbrt-cube53.4

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\sqrt[3]{\left(\left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\right) \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)}}\]

    4. Applied simplify45.5

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \sqrt[3]{\color{blue}{{\left(\sqrt{(\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) \cdot \left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) + \left(-M \cdot M\right))_*} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)}^{3}}}\]
    5. Using strategy rm

    6. Applied add-sqr-sqrt45.6

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\left(\sqrt{\sqrt[3]{{\left(\sqrt{(\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) \cdot \left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) + \left(-M \cdot M\right))_*} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)}^{3}}} \cdot \sqrt{\sqrt[3]{{\left(\sqrt{(\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) \cdot \left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) + \left(-M \cdot M\right))_*} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)}^{3}}}\right)}\]

    7. Applied simplify46.8

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\sqrt{\left(\frac{c0}{w} \cdot \frac{d}{D}\right) \cdot \frac{\frac{d}{D}}{h} + \sqrt{(\left(\left(\frac{c0}{w} \cdot \frac{d}{D}\right) \cdot \frac{\frac{d}{D}}{h}\right) \cdot \left(\left(\frac{c0}{w} \cdot \frac{d}{D}\right) \cdot \frac{\frac{d}{D}}{h}\right) + \left(-M \cdot M\right))_*}}} \cdot \sqrt{\sqrt[3]{{\left(\sqrt{(\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) \cdot \left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) + \left(-M \cdot M\right))_*} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)}^{3}}}\right)\]

    8. Applied simplify39.2

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\sqrt{\left(\frac{c0}{w} \cdot \frac{d}{D}\right) \cdot \frac{\frac{d}{D}}{h} + \sqrt{(\left(\left(\frac{c0}{w} \cdot \frac{d}{D}\right) \cdot \frac{\frac{d}{D}}{h}\right) \cdot \left(\left(\frac{c0}{w} \cdot \frac{d}{D}\right) \cdot \frac{\frac{d}{D}}{h}\right) + \left(-M \cdot M\right))_*}} \cdot \color{blue}{\sqrt{\left(\frac{c0}{w} \cdot \frac{d}{D}\right) \cdot \frac{\frac{d}{D}}{h} + \sqrt{(\left(\left(\frac{c0}{w} \cdot \frac{d}{D}\right) \cdot \frac{\frac{d}{D}}{h}\right) \cdot \left(\left(\frac{c0}{w} \cdot \frac{d}{D}\right) \cdot \frac{\frac{d}{D}}{h}\right) + \left(-M \cdot M\right))_*}}}\right)\]
  3. Recombined 4 regimes into one program.

Runtime

Time bar (total: 6.3m)Debug logProfile

herbie shell --seed '#(1064397287 3527694221 3797617954 1138343853 2854031332 1153838279)' +o rules:numerics
(FPCore (c0 w h D d M)
  :name "Henrywood and Agarwal, Equation (13)"
  (* (/ c0 (* 2 w)) (+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))))