Henrywood and Agarwal, Equation (13)

Average Error: 58.2 → 52.7

Time: 1.1m

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -1.2741829201065389e+272
  2. w = -5.813327964231231e-203
  3. h = -3.7321680490200443e+39
  4. D = 2.5381914025638748e+67
  5. d = -3.9176623746688055e+254
  6. M = -9.197303227536936e-144

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;h \le -8.264994368602302 \cdot 10^{+121}:\\ \;\;\;\;\frac{\sqrt[3]{\left(\sqrt{\left(M + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h} - M\right)} + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\left(\sqrt{\left(M + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h} - M\right)} + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\sqrt{\left(M + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h} - M\right)} + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right)\right)}}{w} \cdot \frac{c0}{2}\\ \mathbf{elif}\;h \le 1.4589782439453874 \cdot 10^{-111}:\\ \;\;\;\;\frac{\left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{c0}{w \cdot h}\right) \cdot 2}{w} \cdot \frac{c0}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{2} \cdot \frac{\sqrt[3]{\left(\sqrt[3]{\sqrt{\left(M + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h} - M\right)} + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}} \cdot \sqrt[3]{\sqrt{\left(M + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h} - M\right)} + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}}\right) \cdot \sqrt[3]{\sqrt{\left(M + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h} - M\right)} + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}}} \cdot \left(\sqrt[3]{\left(\sqrt[3]{\sqrt{\left(M + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h} - M\right)} + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}} \cdot \sqrt[3]{\sqrt{\left(M + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h} - M\right)} + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}}\right) \cdot \sqrt[3]{\sqrt{\left(M + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h} - M\right)} + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}}} \cdot \sqrt[3]{\sqrt{\left(M + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h} - M\right)} + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}}\right)}{w}\\ \end{array}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r6187116 = c0;
        double r6187117 = 2.0;
        double r6187118 = w;
        double r6187119 = r6187117 * r6187118;
        double r6187120 = r6187116 / r6187119;
        double r6187121 = d;
        double r6187122 = r6187121 * r6187121;
        double r6187123 = r6187116 * r6187122;
        double r6187124 = h;
        double r6187125 = r6187118 * r6187124;
        double r6187126 = D;
        double r6187127 = r6187126 * r6187126;
        double r6187128 = r6187125 * r6187127;
        double r6187129 = r6187123 / r6187128;
        double r6187130 = r6187129 * r6187129;
        double r6187131 = M;
        double r6187132 = r6187131 * r6187131;
        double r6187133 = r6187130 - r6187132;
        double r6187134 = sqrt(r6187133);
        double r6187135 = r6187129 + r6187134;
        double r6187136 = r6187120 * r6187135;
        return r6187136;
}

↓

double f(double c0, double w, double h, double D, double d, double M) {
        double r6187137 = h;
        double r6187138 = -8.264994368602302e+121;
        bool r6187139 = r6187137 <= r6187138;
        double r6187140 = M;
        double r6187141 = d;
        double r6187142 = D;
        double r6187143 = r6187141 / r6187142;
        double r6187144 = c0;
        double r6187145 = r6187144 * r6187143;
        double r6187146 = r6187143 * r6187145;
        double r6187147 = w;
        double r6187148 = r6187147 * r6187137;
        double r6187149 = r6187146 / r6187148;
        double r6187150 = r6187140 + r6187149;
        double r6187151 = r6187149 - r6187140;
        double r6187152 = r6187150 * r6187151;
        double r6187153 = sqrt(r6187152);
        double r6187154 = r6187153 + r6187149;
        double r6187155 = r6187154 * r6187154;
        double r6187156 = r6187154 * r6187155;
        double r6187157 = cbrt(r6187156);
        double r6187158 = r6187157 / r6187147;
        double r6187159 = 2.0;
        double r6187160 = r6187144 / r6187159;
        double r6187161 = r6187158 * r6187160;
        double r6187162 = 1.4589782439453874e-111;
        bool r6187163 = r6187137 <= r6187162;
        double r6187164 = r6187143 * r6187143;
        double r6187165 = r6187144 / r6187148;
        double r6187166 = r6187164 * r6187165;
        double r6187167 = r6187166 * r6187159;
        double r6187168 = r6187167 / r6187147;
        double r6187169 = r6187168 * r6187160;
        double r6187170 = cbrt(r6187154);
        double r6187171 = r6187170 * r6187170;
        double r6187172 = r6187171 * r6187170;
        double r6187173 = cbrt(r6187172);
        double r6187174 = r6187173 * r6187170;
        double r6187175 = r6187173 * r6187174;
        double r6187176 = r6187175 / r6187147;
        double r6187177 = r6187160 * r6187176;
        double r6187178 = r6187163 ? r6187169 : r6187177;
        double r6187179 = r6187139 ? r6187161 : r6187178;
        return r6187179;
}

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 h < -8.264994368602302e+121

   1. Initial program 59.4

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

   2. Simplified 52.8

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

   4. Applied add-cbrt-cube 53.9

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

   if -8.264994368602302e+121 < h < 1.4589782439453874e-111

   1. Initial program 58.3

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

   2. Simplified 51.9

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

   3. Taylor expanded around 0 58.3

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

   4. Simplified 53.6

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

   if 1.4589782439453874e-111 < h

   1. Initial program 57.6

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

   2. Simplified 50.5

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

   4. Applied add-cube-cbrt 50.5

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

   6. Applied add-cube-cbrt 50.5

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

   8. Applied add-cube-cbrt 50.5

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

4. Final simplification 52.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;h \le -8.264994368602302 \cdot 10^{+121}:\\ \;\;\;\;\frac{\sqrt[3]{\left(\sqrt{\left(M + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h} - M\right)} + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\left(\sqrt{\left(M + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h} - M\right)} + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\sqrt{\left(M + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h} - M\right)} + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right)\right)}}{w} \cdot \frac{c0}{2}\\ \mathbf{elif}\;h \le 1.4589782439453874 \cdot 10^{-111}:\\ \;\;\;\;\frac{\left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{c0}{w \cdot h}\right) \cdot 2}{w} \cdot \frac{c0}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{2} \cdot \frac{\sqrt[3]{\left(\sqrt[3]{\sqrt{\left(M + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h} - M\right)} + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}} \cdot \sqrt[3]{\sqrt{\left(M + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h} - M\right)} + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}}\right) \cdot \sqrt[3]{\sqrt{\left(M + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h} - M\right)} + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}}} \cdot \left(\sqrt[3]{\left(\sqrt[3]{\sqrt{\left(M + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h} - M\right)} + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}} \cdot \sqrt[3]{\sqrt{\left(M + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h} - M\right)} + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}}\right) \cdot \sqrt[3]{\sqrt{\left(M + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h} - M\right)} + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}}} \cdot \sqrt[3]{\sqrt{\left(M + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}\right) \cdot \left(\frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h} - M\right)} + \frac{\frac{d}{D} \cdot \left(c0 \cdot \frac{d}{D}\right)}{w \cdot h}}\right)}{w}\\ \end{array}\]

Reproduce

herbie shell --seed 2019139 
(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))))))