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Table 1 Developed equations using gene expression programming for predicting explant growth parameters

From: Combining gene expression programming and genetic algorithm as a powerful hybrid modeling approach for pear rootstocks tissue culture media formulation

Pear rootstock

Equation

Pyrodwarf

\(PR = \left[ {\exp \left( {\left( {F - B} \right) \times c} \right) - D} \right] + \left[ {\left( {\ln \left( {\frac{{\sqrt {\frac{E - 2.1016}{2}} + E}}{2}} \right)} \right)^{ - 1} + D} \right] + \left[ {\left( {\sqrt[3]{3.1775 - C}} \right)^{2} + \sqrt[3]{{\frac{\exp \left( A \right)}{C + 0.11065}}}} \right]\)

 

\(SL = \left[ {\sqrt[3]{{{ \ln }\left( {D^{3} } \right)}} + \left( {F \times \left( {\frac{C + A}{2} \times E} \right)} \right)} \right] + \left[ {2.4011 \times \left( {\frac{{\left( {\frac{E + 1.7251}{2} \times 2.7057} \right) + \left( {1.7251 - B} \right)}}{2} - E} \right)^{2} } \right] + \left[ {\sqrt[3]{{2.3488 \times \left( {\left( {E^{ - 1} - 7.0907} \right) + \left( {E - D} \right)} \right)}}} \right]\)

 

\(STN = \left[ {\frac{{D + \left( {\sqrt C \times \left( {F - E} \right)} \right)}}{2} + exp\left( {A - C} \right)} \right] + \left[ {\left( {B - \frac{{\frac{6.1753}{E} + E}}{2}} \right) + \left( {9.3446A \times { \ln }\left( B \right)} \right)} \right] + \left[ {\frac{{\left( {\left( {\ln \left( F \right) + \frac{11.3038}{A}} \right) - E + 1.0814} \right) + 15.0404A^{2} }}{2}} \right]\)

 

\(VITRI = \left[ {\frac{{\left( {{ \exp }\left( B \right) \times B} \right) \times {\text{C}}^{ - 1} }}{2} - \left( {D - B} \right) - 1.5069} \right] + \left[ {\frac{{\exp \left( {2.988 - D} \right) + \frac{A - 9.0917}{2}}}{2} \times \left( {2B - \left( {B \times D} \right)} \right)} \right] + \left[ {\frac{{\frac{{\frac{E + B}{2} + B}}{2} + F + 8.8145}}{2} \times \left( {\frac{A + B}{2} + 2B} \right)} \right]\)

 

\(QL = \left[ {\sqrt[9]{{\frac{D \times A}{\sqrt C \times B}}}} \right] + \left[ {\sqrt[3]{{\left( {\frac{{\frac{E}{30.7869} + B}}{2}} \right)^{ - 1} + \left( {0.9692 - A - B} \right)}}} \right] + \left[ {\sqrt[6]{{\left( {\exp \left( C \right) \times \left( {10.3785 + F} \right)} \right) + F^{ - 1} - A}}} \right]\)

OHF

 
 

\(PR = \left[ {\sqrt {\left( {0.0894D \times B} \right) + \left( {A + E} \right)^{ - 1} } } \right] + \left[ {\left( {\sqrt[3]{{\frac{ - 8.5762}{A} - 6.8234}}} \right) \times \left( {3.2661 - E} \right)^{ - 1} } \right] + \left[ {\frac{{\frac{C + 0.1838}{2} + 6.8196}}{2} + C^{ - 1} + \left( {\left( {B \times F} \right) - B} \right)} \right]\)

 

\(SL = \left[ {\frac{{\ln \left( {\frac{B + 4.8333}{2}} \right) + \left( {\frac{D + 4.7651}{2} - \left( {A + B} \right)} \right)}}{2}} \right] + \left[ {C + \left( {{ \exp }\left( {\left( { - 2.8335A} \right) \times \left( {\frac{{\left( {D - 6.4679} \right) + \left( {9.3060C} \right)}}{2}} \right)} \right)} \right)} \right] + \left[ {{ \exp }\left( {\frac{{\left( {\left( {3.8362F} \right) - A} \right) + \left( {\frac{E + 3.1237}{2}} \right)}}{2} - \left( {3.4882 - E} \right)^{ - 1} } \right)} \right]\)

 

\(STN = \left[ {B^{2} - \left( {\sqrt[3]{{\frac{{\frac{C}{E} + 8.1303}}{{{ \ln }\left( A \right)}}}}} \right)} \right] + \left[ {\exp \left( A \right) + C^{3} - C} \right] + \left[ {F + \frac{{D + \left( {\left( {\frac{ - 4.4380}{C}} \right)^{2} - \frac{6.1907}{B}} \right)}}{2}} \right]\)

 

\(VITRI = \left[ {E \times \left( {A + \frac{{\left( {\frac{E - 0.8805}{2}} \right) \times B}}{F + A}} \right)} \right] + \left[ {\frac{{A - \left( {\sqrt[3]{A} - 6.8169} \right)}}{{D^{2} }}} \right] + \left[ {\left( {\frac{A + 2D - 6.8579}{2}} \right) \times \left( {\frac{{D^{2} + \frac{B}{A}}}{2}} \right)} \right]\)

 

\(QL = \left[ {\sqrt {\left( {\sqrt[4]{{\left( {\frac{{E^{ - 1} + 8.3712}}{2}} \right) \times \left( {C - F} \right)}}} \right)^{3} } } \right] + \left[ {\left( {\left( {C - 5.1079} \right) \times \sqrt D } \right) \times \left( {\left( {C \times A} \right) - 5.0292} \right)} \right]^{ - 1} + \left[ {\frac{{B^{ - 1} + ln\left( {\left( {ln\frac{C}{0.3661}} \right) \times \left( {D + F} \right)} \right)}}{2}} \right]\)

  1. A: NH4NO3, B: KNO3, C: mesos, D: minor, E: 6-benzylaminopurine (BA), F: indole-3-butyric acid (IBA)