Average Error: 58.6 → 28.7
Time: 8.1m
Precision: 64
Internal Precision: 7232
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \sqrt[3]{{\left(\sqrt{\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right) \cdot \left(M + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)}^{3}} \le -7.519876729503522 \cdot 10^{+193}:\\ \;\;\;\;0\\ \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \sqrt[3]{{\left(\sqrt{\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right) \cdot \left(M + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)}^{3}} \le -8.500207144237293 \cdot 10^{-288}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \sqrt[3]{{\left(\sqrt{\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right) \cdot \left(M + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)}^{3}}\\ \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \sqrt[3]{{\left(\sqrt{\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right) \cdot \left(M + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)}^{3}} \le 1.2719154583505496 \cdot 10^{-234}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\frac{\frac{\left|M\right|}{\sqrt[3]{\frac{\frac{c0}{w}}{h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - \sqrt{\left(\frac{\frac{c0}{w}}{h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) + M\right) \cdot \left(\frac{\frac{c0}{w}}{h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right)}}}}{\sqrt[3]{\sqrt[3]{\frac{\frac{c0}{w}}{h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - \sqrt{\left(\frac{\frac{c0}{w}}{h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) + M\right) \cdot \left(\frac{\frac{c0}{w}}{h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right)}} \cdot \sqrt[3]{\frac{\frac{c0}{w}}{h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - \sqrt{\left(\frac{\frac{c0}{w}}{h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) + M\right) \cdot \left(\frac{\frac{c0}{w}}{h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right)}}} \cdot \sqrt[3]{\sqrt[3]{\frac{\frac{c0}{w}}{h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - \sqrt{\left(\frac{\frac{c0}{w}}{h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) + M\right) \cdot \left(\frac{\frac{c0}{w}}{h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right)}}}} \cdot \frac{\left|M\right|}{\sqrt[3]{\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{w}}{h} - \sqrt{\left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{w}}{h}\right) \cdot \left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{w}}{h}\right) - M \cdot M}}}\right)\\ \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \sqrt[3]{{\left(\sqrt{\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right) \cdot \left(M + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)}^{3}} \le 1.5341797079646859 \cdot 10^{+94}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \sqrt[3]{{\left(\sqrt{\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right) \cdot \left(M + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)}^{3}}\\ \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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if (* (/ c0 (* 2 w)) (cbrt (pow (+ (sqrt (* (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M) (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) 3))) < -7.519876729503522e+193 or 1.5341797079646859e+94 < (* (/ c0 (* 2 w)) (cbrt (pow (+ (sqrt (* (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M) (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) 3)))

    1. Initial program 60.9

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

    2. Taylor expanded around inf 35.5

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

    3. Applied simplify30.7

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

    if -7.519876729503522e+193 < (* (/ c0 (* 2 w)) (cbrt (pow (+ (sqrt (* (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M) (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) 3))) < -8.500207144237293e-288 or 1.2719154583505496e-234 < (* (/ c0 (* 2 w)) (cbrt (pow (+ (sqrt (* (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M) (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) 3))) < 1.5341797079646859e+94

    1. Initial program 44.9

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

    3. Applied add-cbrt-cube45.0

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

    4. Applied simplify2.7

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

    if -8.500207144237293e-288 < (* (/ c0 (* 2 w)) (cbrt (pow (+ (sqrt (* (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M) (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) 3))) < 1.2719154583505496e-234

    1. Initial program 49.1

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

    3. Applied flip-+54.0

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

    4. Applied simplify46.6

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\color{blue}{0 + M \cdot M}}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}\]
    5. Using strategy rm

    6. Applied add-cube-cbrt46.6

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{0 + M \cdot M}{\color{blue}{\left(\sqrt[3]{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}} \cdot \sqrt[3]{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}\right) \cdot \sqrt[3]{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}}}\]

    7. Applied add-sqr-sqrt46.6

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{\color{blue}{\sqrt{0 + M \cdot M} \cdot \sqrt{0 + M \cdot M}}}{\left(\sqrt[3]{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}} \cdot \sqrt[3]{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}\right) \cdot \sqrt[3]{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}}\]

    8. Applied times-frac46.6

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\left(\frac{\sqrt{0 + M \cdot M}}{\sqrt[3]{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}} \cdot \sqrt[3]{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}} \cdot \frac{\sqrt{0 + M \cdot M}}{\sqrt[3]{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}}\right)}\]

    9. Applied simplify49.4

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{\frac{\left|M\right|}{\sqrt[3]{\frac{\frac{c0}{w}}{h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - \sqrt{\left(\frac{\frac{c0}{w}}{h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) + M\right) \cdot \left(\frac{\frac{c0}{w}}{h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right)}}}}{\sqrt[3]{\frac{\frac{c0}{w}}{h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - \sqrt{\left(\frac{\frac{c0}{w}}{h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) + M\right) \cdot \left(\frac{\frac{c0}{w}}{h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right)}}}} \cdot \frac{\sqrt{0 + M \cdot M}}{\sqrt[3]{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}}}\right)\]

    10. Applied simplify24.7

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

    12. Applied add-cube-cbrt24.8

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

    13. Applied cbrt-prod24.8

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

Runtime

Time bar (total: 8.1m)Debug logProfile

herbie shell --seed 2018193 
(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))))))