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Review Euler equation to e^(i pi) + 1 = 0

abstract:
reference:

step	inference rule	input	feed	output	validity (as per SymPy)
3	ID: 111457; simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	8332931442 $\exp(i \pi)=\cos(\pi)+i \sin(\pi)$		6885625907 $\exp(i \pi)=-1 + i 0$	LHS diff is 0 RHS diff is pdg0004621*sin(pdg0003141) + cos(pdg0003141) + 1
2	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}.	4938429483 $\exp(i x)=\cos(x)+i \sin(x)$	3268645065 $x$ 9350663581 $\pi$	8332931442 $\exp(i \pi)=\cos(\pi)+i \sin(\pi)$	valid
1	ID: 111981; declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			4938429483 $\exp(i x)=\cos(x)+i \sin(x)$	no validation is available for declarations
5	ID: 111530; add X to both sides number of inputs: 1; feeds: 1; outputs: 1 Add $#1$ to both sides of Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	3331824625 $\exp(i \pi)=-1$	4901237716 $1$	2501591100 $\exp(i \pi) + 1=0$	valid
4	ID: 111457; simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	6885625907 $\exp(i \pi)=-1 + i 0$		3331824625 $\exp(i \pi)=-1$	valid
6	ID: 111341; declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\\ref{eq:#1} is one of the final equations.	2501591100 $\exp(i \pi) + 1=0$			no validation is available for declarations

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timing of Neo4j queries:

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step	inference rule	input	feed	output	validity (as per SymPy)
3	ID: 111457; simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	8332931442 \(\exp(i \pi)=\cos(\pi)+i \sin(\pi)\)		6885625907 \(\exp(i \pi)=-1 + i 0\)	LHS diff is 0 RHS diff is pdg0004621*sin(pdg0003141) + cos(pdg0003141) + 1
2	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}.	4938429483 \(\exp(i x)=\cos(x)+i \sin(x)\)	3268645065 \(x\) 9350663581 \(\pi\)	8332931442 \(\exp(i \pi)=\cos(\pi)+i \sin(\pi)\)	valid
1	ID: 111981; declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			4938429483 \(\exp(i x)=\cos(x)+i \sin(x)\)	no validation is available for declarations
5	ID: 111530; add X to both sides number of inputs: 1; feeds: 1; outputs: 1 Add $#1$ to both sides of Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	3331824625 \(\exp(i \pi)=-1\)	4901237716 \(1\)	2501591100 \(\exp(i \pi) + 1=0\)	valid
4	ID: 111457; simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	6885625907 \(\exp(i \pi)=-1 + i 0\)		3331824625 \(\exp(i \pi)=-1\)	valid
6	ID: 111341; declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\\ref{eq:#1} is one of the final equations.	2501591100 \(\exp(i \pi) + 1=0\)			no validation is available for declarations