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Review mass of the Earth

abstract:
reference:

step	inference rule	input	feed	output	validity (as per SymPy)
6	ID: 111715; replace constant with value number of inputs: 1; feeds: 3; outputs: 1 Replace constant $#1$ with value $#2$ and units $#3$ in Eq.~\\ref{eq:#4}; yields Eq.~\\ref{eq:#5}	9440616166 $m_{\rm Earth}=\frac{g_{\rm Earth} r_{\rm Earth}^2}{G}$	9590696981 $9.80665$ 7816982139 $m/s^2$ 2091584724 $g_{\rm Earth}$	7846240076 $m_{\rm Earth}=\frac{(9.80665 m/s^2) r_{\rm Earth}^2}{G}$	recognized infrule but not yet supported
4	ID: 111975; divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	9407192813 $G \frac{m_{\rm Earth} m}{r_{\rm Earth}^2}=m g_{\rm Earth}$	3246378279 $m$	2308660627 $G \frac{m_{\rm Earth}}{r_{\rm Earth}^2}=g_{\rm Earth}$	valid
8	ID: 111715; replace constant with value number of inputs: 1; feeds: 3; outputs: 1 Replace constant $#1$ with value $#2$ and units $#3$ in Eq.~\\ref{eq:#4}; yields Eq.~\\ref{eq:#5}	7112613117 $m_{\rm Earth}=\frac{(9.80665 m/s^2) r_{\rm Earth}^2}{6.67430*10^{-11}m^3 kg^{-1} s^{-2}}$	3723096423 $6.3781*10^6$ 7935917166 $r_{\rm Earth}$ 7560908617 $m$	1132941271 $m_{\rm Earth}=\frac{(9.80665 m/s^2) (6.378110^6 m)^2}{6.6743010^{-11}m^3 kg^{-1} s^{-2}}$	recognized infrule but not yet supported
1	ID: 111886; change variable X to Y number of inputs: 1; feeds: 2; outputs: 1 Change variable $#1$ to $#2$ in Eq.~\\ref{eq:#3}; yields Eq.~\\ref{eq:#4}.	5345738321 $F=m a$	9881106100 $a$ 5781435087 $g$	2484824786 $F=m g$	valid
2	ID: 111236; change three variables in expression number of inputs: 1; feeds: 6; outputs: 1 Change of variable $#1$ to $#2$ and $#3$ to $#4$ and $#5$ to $#6$ in Eq.~\\ref{eq:#7}; yields Eq.~\\ref{eq:#8}.	6935745841 $F=G \frac{m_1 m_2}{x^2}$	6535639720 $r_{\rm Earth}$ 4651061153 $m_2$ 3921072591 $m_1$ 3353418803 $x$ 9903988330 $m$ 1193980495 $m_{\rm Earth}$	8661803554 $F=G \frac{m_{\rm Earth} m}{r_{\rm Earth}^2}$	list index out of range
9	ID: 111457; simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	1132941271 $m_{\rm Earth}=\frac{(9.80665 m/s^2) (6.378110^6 m)^2}{6.6743010^{-11}m^3 kg^{-1} s^{-2}}$		3364286646 $m_{\rm Earth}=5.972*10^{24} kg$	LHS diff is 0 RHS diff is 6.3781 - 5.972e+24*kg
7	ID: 111715; replace constant with value number of inputs: 1; feeds: 3; outputs: 1 Replace constant $#1$ with value $#2$ and units $#3$ in Eq.~\\ref{eq:#4}; yields Eq.~\\ref{eq:#5}	7846240076 $m_{\rm Earth}=\frac{(9.80665 m/s^2) r_{\rm Earth}^2}{G}$	2957211007 $m^3 kg^{-1} s^{-2}$ 9956609318 $6.67430*10^{-11}$ 7326066466 $G$	7112613117 $m_{\rm Earth}=\frac{(9.80665 m/s^2) r_{\rm Earth}^2}{6.67430*10^{-11}m^3 kg^{-1} s^{-2}}$	recognized infrule but not yet supported
0.5	ID: 111981; declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			5345738321 $F=m a$	no validation is available for declarations
3	ID: 111355; LHS of expr 1 equals LHS of expr 2 number of inputs: 2; feeds: 0; outputs: 1 LHS of Eq.~\\ref{eq:#1} is equal to LHS of Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	4800170179 $F=m g_{\rm Earth}$ 8661803554 $F=G \frac{m_{\rm Earth} m}{r_{\rm Earth}^2}$		9407192813 $G \frac{m_{\rm Earth} m}{r_{\rm Earth}^2}=m g_{\rm Earth}$	input diff is 0 diff is pdg0005156pdg0007557 - pdg0005156pdg0005458pdg0006277/pdg00032362 diff is -pdg0005156pdg0007557 + pdg0005156pdg0005458pdg0006277/pdg0003236**2
1.5	ID: 111981; declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			6935745841 $F=G \frac{m_1 m_2}{x^2}$	no validation is available for declarations
5	ID: 111182; multiply both sides by number of inputs: 1; feeds: 1; outputs: 1 Multiply both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	2308660627 $G \frac{m_{\rm Earth}}{r_{\rm Earth}^2}=g_{\rm Earth}$	2685587762 $\frac{r_{\rm Earth}^2}{G}$	9440616166 $m_{\rm Earth}=\frac{g_{\rm Earth} r_{\rm Earth}^2}{G}$	valid
1.25	ID: 111886; change variable X to Y number of inputs: 1; feeds: 2; outputs: 1 Change variable $#1$ to $#2$ in Eq.~\\ref{eq:#3}; yields Eq.~\\ref{eq:#4}.	2484824786 $F=m g$	2232825726 $g_{\rm Earth}$ 9355039511 $g$	4800170179 $F=m g_{\rm Earth}$	LHS diff is 0 RHS diff is pdg0005156*(pdg0001649 - pdg0007557)

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timing of Neo4j queries:

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step	inference rule	input	feed	output	validity (as per SymPy)
6	ID: 111715; replace constant with value number of inputs: 1; feeds: 3; outputs: 1 Replace constant $#1$ with value $#2$ and units $#3$ in Eq.~\\ref{eq:#4}; yields Eq.~\\ref{eq:#5}	9440616166 \(m_{\rm Earth}=\frac{g_{\rm Earth} r_{\rm Earth}^2}{G}\)	9590696981 \(9.80665\) 7816982139 \(m/s^2\) 2091584724 \(g_{\rm Earth}\)	7846240076 \(m_{\rm Earth}=\frac{(9.80665 m/s^2) r_{\rm Earth}^2}{G}\)	recognized infrule but not yet supported
4	ID: 111975; divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	9407192813 \(G \frac{m_{\rm Earth} m}{r_{\rm Earth}^2}=m g_{\rm Earth}\)	3246378279 \(m\)	2308660627 \(G \frac{m_{\rm Earth}}{r_{\rm Earth}^2}=g_{\rm Earth}\)	valid
8	ID: 111715; replace constant with value number of inputs: 1; feeds: 3; outputs: 1 Replace constant $#1$ with value $#2$ and units $#3$ in Eq.~\\ref{eq:#4}; yields Eq.~\\ref{eq:#5}	7112613117 \(m_{\rm Earth}=\frac{(9.80665 m/s^2) r_{\rm Earth}^2}{6.67430*10^{-11}m^3 kg^{-1} s^{-2}}\)	3723096423 \(6.3781*10^6\) 7935917166 \(r_{\rm Earth}\) 7560908617 \(m\)	1132941271 \(m_{\rm Earth}=\frac{(9.80665 m/s^2) (6.378110^6 m)^2}{6.6743010^{-11}m^3 kg^{-1} s^{-2}}\)	recognized infrule but not yet supported
1	ID: 111886; change variable X to Y number of inputs: 1; feeds: 2; outputs: 1 Change variable $#1$ to $#2$ in Eq.~\\ref{eq:#3}; yields Eq.~\\ref{eq:#4}.	5345738321 \(F=m a\)	9881106100 \(a\) 5781435087 \(g\)	2484824786 \(F=m g\)	valid
2	ID: 111236; change three variables in expression number of inputs: 1; feeds: 6; outputs: 1 Change of variable $#1$ to $#2$ and $#3$ to $#4$ and $#5$ to $#6$ in Eq.~\\ref{eq:#7}; yields Eq.~\\ref{eq:#8}.	6935745841 \(F=G \frac{m_1 m_2}{x^2}\)	6535639720 \(r_{\rm Earth}\) 4651061153 \(m_2\) 3921072591 \(m_1\) 3353418803 \(x\) 9903988330 \(m\) 1193980495 \(m_{\rm Earth}\)	8661803554 \(F=G \frac{m_{\rm Earth} m}{r_{\rm Earth}^2}\)	list index out of range
9	ID: 111457; simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	1132941271 \(m_{\rm Earth}=\frac{(9.80665 m/s^2) (6.378110^6 m)^2}{6.6743010^{-11}m^3 kg^{-1} s^{-2}}\)		3364286646 \(m_{\rm Earth}=5.972*10^{24} kg\)	LHS diff is 0 RHS diff is 6.3781 - 5.972e+24*kg
7	ID: 111715; replace constant with value number of inputs: 1; feeds: 3; outputs: 1 Replace constant $#1$ with value $#2$ and units $#3$ in Eq.~\\ref{eq:#4}; yields Eq.~\\ref{eq:#5}	7846240076 \(m_{\rm Earth}=\frac{(9.80665 m/s^2) r_{\rm Earth}^2}{G}\)	2957211007 \(m^3 kg^{-1} s^{-2}\) 9956609318 \(6.67430*10^{-11}\) 7326066466 \(G\)	7112613117 \(m_{\rm Earth}=\frac{(9.80665 m/s^2) r_{\rm Earth}^2}{6.67430*10^{-11}m^3 kg^{-1} s^{-2}}\)	recognized infrule but not yet supported
0.5	ID: 111981; declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			5345738321 \(F=m a\)	no validation is available for declarations
3	ID: 111355; LHS of expr 1 equals LHS of expr 2 number of inputs: 2; feeds: 0; outputs: 1 LHS of Eq.~\\ref{eq:#1} is equal to LHS of Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	4800170179 \(F=m g_{\rm Earth}\) 8661803554 \(F=G \frac{m_{\rm Earth} m}{r_{\rm Earth}^2}\)		9407192813 \(G \frac{m_{\rm Earth} m}{r_{\rm Earth}^2}=m g_{\rm Earth}\)	input diff is 0 diff is pdg0005156pdg0007557 - pdg0005156pdg0005458pdg0006277/pdg00032362 diff is -pdg0005156pdg0007557 + pdg0005156pdg0005458pdg0006277/pdg0003236**2
1.5	ID: 111981; declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			6935745841 \(F=G \frac{m_1 m_2}{x^2}\)	no validation is available for declarations
5	ID: 111182; multiply both sides by number of inputs: 1; feeds: 1; outputs: 1 Multiply both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	2308660627 \(G \frac{m_{\rm Earth}}{r_{\rm Earth}^2}=g_{\rm Earth}\)	2685587762 \(\frac{r_{\rm Earth}^2}{G}\)	9440616166 \(m_{\rm Earth}=\frac{g_{\rm Earth} r_{\rm Earth}^2}{G}\)	valid
1.25	ID: 111886; change variable X to Y number of inputs: 1; feeds: 2; outputs: 1 Change variable $#1$ to $#2$ in Eq.~\\ref{eq:#3}; yields Eq.~\\ref{eq:#4}.	2484824786 \(F=m g\)	2232825726 \(g_{\rm Earth}\) 9355039511 \(g\)	4800170179 \(F=m g_{\rm Earth}\)	LHS diff is 0 RHS diff is pdg0005156*(pdg0001649 - pdg0007557)