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nonlinear-expr-rewrite's Introduction

Step 1

Identify all non-linear variable expressions, and replace each with a new symbolic variable. Each time an expression is killed (i.e. one of its operands is redefined), reassign the symbolic variable.

For example,

a = b*b;
b = b+1;
a = b*b;

is rewritten as

int x0 = Debug.makeSymbolicInteger("x0");
a = x0;
b = b+1;
x0 = Debug.makeSymbolicInteger("x0");
a = x0;

Step 2

Use reaching definitions analysis to remove definitions that are not used.
For example, we can remove the re-assignment of x0 after b = b+1, since it is not used before it is reassigned.

a = b*c;
b = b+1;
c = c+1;
a = b*c;

int x0 = Debug.makeSymbolicInteger("x0");
a = x0;
b = b+1;
x0 = Debug.makeSymbolicInteger("x0");
c = c+1;
x0 = Debug.makeSymbolicInteger("x0");
a = x0;

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