Average Error: 58.4 → 28.1
Time: 7.2m
Precision: 64
Internal Precision: 6976
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\sqrt[3]{\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 \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)} \cdot \sqrt[3]{\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 \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)}\right) \cdot \sqrt[3]{\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 \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)} = -\infty:\\ \;\;\;\;\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}\;\left(\sqrt[3]{\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 \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)} \cdot \sqrt[3]{\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 \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)}\right) \cdot \sqrt[3]{\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 \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)} \le +\infty:\\ \;\;\;\;\left(\frac{c0}{2 \cdot w} \cdot \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)}}}\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}}}\\ \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 3 regimes

  2. if (* (* (cbrt (* (/ c0 (* 2 w)) (* (/ (/ (fabs M) (cbrt (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) (sqrt (* (+ (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M) (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M)))))) (cbrt (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) (sqrt (* (+ (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M) (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M)))))) (/ (fabs M) (cbrt (- (* (* (/ d D) (/ d D)) (/ (/ c0 w) h)) (sqrt (- (* (* (* (/ d D) (/ d D)) (/ (/ c0 w) h)) (* (* (/ d D) (/ d D)) (/ (/ c0 w) h))) (* M M))))))))) (cbrt (* (/ c0 (* 2 w)) (* (/ (/ (fabs M) (cbrt (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) (sqrt (* (+ (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M) (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M)))))) (cbrt (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) (sqrt (* (+ (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M) (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M)))))) (/ (fabs M) (cbrt (- (* (* (/ d D) (/ d D)) (/ (/ c0 w) h)) (sqrt (- (* (* (* (/ d D) (/ d D)) (/ (/ c0 w) h)) (* (* (/ d D) (/ d D)) (/ (/ c0 w) h))) (* M M)))))))))) (cbrt (* (/ c0 (* 2 w)) (* (/ (/ (fabs M) (cbrt (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) (sqrt (* (+ (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M) (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M)))))) (cbrt (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) (sqrt (* (+ (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M) (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M)))))) (/ (fabs M) (cbrt (- (* (* (/ d D) (/ d D)) (/ (/ c0 w) h)) (sqrt (- (* (* (* (/ d D) (/ d D)) (/ (/ c0 w) h)) (* (* (/ d D) (/ d D)) (/ (/ c0 w) h))) (* M M)))))))))) < -inf.0

    1. Initial program 44.6

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

    3. Applied add-cbrt-cube49.7

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

    4. Applied simplify25.5

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

    if -inf.0 < (* (* (cbrt (* (/ c0 (* 2 w)) (* (/ (/ (fabs M) (cbrt (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) (sqrt (* (+ (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M) (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M)))))) (cbrt (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) (sqrt (* (+ (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M) (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M)))))) (/ (fabs M) (cbrt (- (* (* (/ d D) (/ d D)) (/ (/ c0 w) h)) (sqrt (- (* (* (* (/ d D) (/ d D)) (/ (/ c0 w) h)) (* (* (/ d D) (/ d D)) (/ (/ c0 w) h))) (* M M))))))))) (cbrt (* (/ c0 (* 2 w)) (* (/ (/ (fabs M) (cbrt (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) (sqrt (* (+ (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M) (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M)))))) (cbrt (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) (sqrt (* (+ (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M) (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M)))))) (/ (fabs M) (cbrt (- (* (* (/ d D) (/ d D)) (/ (/ c0 w) h)) (sqrt (- (* (* (* (/ d D) (/ d D)) (/ (/ c0 w) h)) (* (* (/ d D) (/ d D)) (/ (/ c0 w) h))) (* M M)))))))))) (cbrt (* (/ c0 (* 2 w)) (* (/ (/ (fabs M) (cbrt (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) (sqrt (* (+ (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M) (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M)))))) (cbrt (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) (sqrt (* (+ (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M) (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M)))))) (/ (fabs M) (cbrt (- (* (* (/ d D) (/ d D)) (/ (/ c0 w) h)) (sqrt (- (* (* (* (/ d D) (/ d D)) (/ (/ c0 w) h)) (* (* (/ d D) (/ d D)) (/ (/ c0 w) h))) (* M M)))))))))) < +inf.0

    1. Initial program 57.9

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

    3. Applied flip-+60.5

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

    4. Applied simplify32.9

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

    6. Applied add-cube-cbrt32.9

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

    7. Applied add-sqr-sqrt32.9

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

    8. Applied times-frac32.9

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

    9. Applied simplify33.0

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

    10. Applied simplify21.0

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

    12. Applied associate-*r*20.1

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

    if +inf.0 < (* (* (cbrt (* (/ c0 (* 2 w)) (* (/ (/ (fabs M) (cbrt (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) (sqrt (* (+ (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M) (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M)))))) (cbrt (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) (sqrt (* (+ (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M) (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M)))))) (/ (fabs M) (cbrt (- (* (* (/ d D) (/ d D)) (/ (/ c0 w) h)) (sqrt (- (* (* (* (/ d D) (/ d D)) (/ (/ c0 w) h)) (* (* (/ d D) (/ d D)) (/ (/ c0 w) h))) (* M M))))))))) (cbrt (* (/ c0 (* 2 w)) (* (/ (/ (fabs M) (cbrt (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) (sqrt (* (+ (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M) (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M)))))) (cbrt (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) (sqrt (* (+ (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M) (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M)))))) (/ (fabs M) (cbrt (- (* (* (/ d D) (/ d D)) (/ (/ c0 w) h)) (sqrt (- (* (* (* (/ d D) (/ d D)) (/ (/ c0 w) h)) (* (* (/ d D) (/ d D)) (/ (/ c0 w) h))) (* M M)))))))))) (cbrt (* (/ c0 (* 2 w)) (* (/ (/ (fabs M) (cbrt (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) (sqrt (* (+ (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M) (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M)))))) (cbrt (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) (sqrt (* (+ (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M) (- (* (/ (/ c0 w) h) (* (/ d D) (/ d D))) M)))))) (/ (fabs M) (cbrt (- (* (* (/ d D) (/ d D)) (/ (/ c0 w) h)) (sqrt (- (* (* (* (/ d D) (/ d D)) (/ (/ c0 w) h)) (* (* (/ d D) (/ d D)) (/ (/ c0 w) h))) (* M M))))))))))

    1. Initial program 60.4

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

    2. Taylor expanded around inf 48.4

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

    3. Applied simplify38.5

      \[\leadsto \color{blue}{0}\]
  3. Recombined 3 regimes into one program.

Runtime

Time bar (total: 7.2m)Debug logProfile

herbie shell --seed '#(1072330854 3074818769 591214268 3603999196 3863745332 3332387116)' 
(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))))))