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simplify_rules.jl
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simplify_rules.jl
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using .Rewriters
"""
is_operation(f)
Returns a single argument anonymous function predicate, that returns `true` if and only if
the argument to the predicate satisfies `iscall` and `operation(x) == f`
"""
is_operation(f) = @nospecialize(x) -> iscall(x) && (operation(x) == f)
let
CANONICALIZE_PLUS = [
@rule(~x::isnotflat(+) => flatten_term(+, ~x))
@rule(~x::needs_sorting(+) => sort_args(+, ~x))
@ordered_acrule(~a::is_literal_number + ~b::is_literal_number => ~a + ~b)
@acrule(*(~~x) + *(~β, ~~x) => *(1 + ~β, (~~x)...))
@acrule(~x + *(~β, ~x) => *(1 + ~β, ~x))
@acrule(*(~α::is_literal_number, ~x) + ~x => *(~α + 1, ~x))
@rule(+(~~x::hasrepeats) => +(merge_repeats(*, ~~x)...))
@ordered_acrule((~z::_iszero + ~x) => ~x)
@rule(+(~x) => ~x)
]
PLUS_DISTRIBUTE = [
@acrule(*(~α, ~~x) + *(~β, ~~x) => *(~α + ~β, (~~x)...))
@acrule(*(~~x, ~α) + *(~~x, ~β) => *(~α + ~β, (~~x)...))
]
CANONICALIZE_TIMES = [
@rule(~x::isnotflat(*) => flatten_term(*, ~x))
@rule(~x::needs_sorting(*) => sort_args(*, ~x))
@ordered_acrule(~a::is_literal_number * ~b::is_literal_number => ~a * ~b)
@rule(*(~~x::hasrepeats) => *(merge_repeats(^, ~~x)...))
@acrule((~y)^(~n) * ~y => (~y)^(~n+1))
@ordered_acrule((~z::_isone * ~x) => ~x)
@ordered_acrule((~z::_iszero * ~x) => ~z)
@rule(*(~x) => ~x)
]
MUL_DISTRIBUTE = @ordered_acrule((~x)^(~n) * (~x)^(~m) => (~x)^(~n + ~m))
CANONICALIZE_POW = [
@rule(^(*(~~x), ~y::_isinteger) => *(map(a->pow(a, ~y), ~~x)...))
@rule((((~x)^(~p::_isinteger))^(~q::_isinteger)) => (~x)^((~p)*(~q)))
@rule(^(~x, ~z::_iszero) => 1)
@rule(^(~x, ~z::_isone) => ~x)
@rule(inv(~x) => 1/(~x))
]
POW_RULES = [
@rule(^(~x::_isone, ~z) => 1)
]
ASSORTED_RULES = [
@rule(identity(~x) => ~x)
@rule(-(~x) => -1*~x)
@rule(-(~x, ~y) => ~x + -1(~y))
@rule(~x::_isone \ ~y => ~y)
@rule(~x \ ~y => ~y / (~x))
@rule(one(~x) => one(symtype(~x)))
@rule(zero(~x) => zero(symtype(~x)))
@rule(conj(~x::_isreal) => ~x)
@rule(real(~x::_isreal) => ~x)
@rule(imag(~x::_isreal) => zero(symtype(~x)))
@rule(ifelse(~x::is_literal_number, ~y, ~z) => ~x ? ~y : ~z)
@rule(ifelse(~x, ~y, ~y) => ~y)
]
TRIG_EXP_RULES = [
@acrule(~r*~x::has_trig_exp + ~r*~y => ~r*(~x + ~y))
@acrule(~r*~x::has_trig_exp + -1*~r*~y => ~r*(~x - ~y))
@acrule(sin(~x)^2 + cos(~x)^2 => one(~x))
@acrule(sin(~x)^2 + -1 => -1*cos(~x)^2)
@acrule(cos(~x)^2 + -1 => -1*sin(~x)^2)
@acrule(cos(~x)^2 + -1*sin(~x)^2 => cos(2 * ~x))
@acrule(sin(~x)^2 + -1*cos(~x)^2 => -cos(2 * ~x))
@acrule(cos(~x) * sin(~x) => sin(2 * ~x)/2)
@acrule(tan(~x)^2 + -1*sec(~x)^2 => one(~x))
@acrule(-1*tan(~x)^2 + sec(~x)^2 => one(~x))
@acrule(tan(~x)^2 + 1 => sec(~x)^2)
@acrule(sec(~x)^2 + -1 => tan(~x)^2)
@acrule(cot(~x)^2 + -1*csc(~x)^2 => one(~x))
@acrule(cot(~x)^2 + 1 => csc(~x)^2)
@acrule(csc(~x)^2 + -1 => cot(~x)^2)
@acrule(cosh(~x)^2 + -1*sinh(~x)^2 => one(~x))
@acrule(cosh(~x)^2 + -1 => sinh(~x)^2)
@acrule(sinh(~x)^2 + 1 => cosh(~x)^2)
@acrule(cosh(~x)^2 + sinh(~x)^2 => cosh(2 * ~x))
@acrule(cosh(~x) * sinh(~x) => sinh(2 * ~x)/2)
@acrule(exp(~x) * exp(~y) => _iszero(~x + ~y) ? 1 : exp(~x + ~y))
@rule(exp(~x)^(~y) => exp(~x * ~y))
]
BOOLEAN_RULES = [
@rule((true | (~x)) => true)
@rule(((~x) | true) => true)
@rule((false | (~x)) => ~x)
@rule(((~x) | false) => ~x)
@rule((true & (~x)) => ~x)
@rule(((~x) & true) => ~x)
@rule((false & (~x)) => false)
@rule(((~x) & false) => false)
@rule(!(~x) & ~x => false)
@rule(~x & !(~x) => false)
@rule(!(~x) | ~x => true)
@rule(~x | !(~x) => true)
@rule(xor(~x, !(~x)) => true)
@rule(xor(~x, ~x) => false)
@rule(~x == ~x => true)
@rule(~x != ~x => false)
@rule(~x < ~x => false)
@rule(~x > ~x => false)
# simplify terms with no symbolic arguments
# e.g. this simplifies term(isodd, 3, type=Bool)
# or term(!, false)
@rule((~f)(~x::is_literal_number) => (~f)(~x))
# and this simplifies any binary comparison operator
@rule((~f)(~x::is_literal_number, ~y::is_literal_number) => (~f)(~x, ~y))
]
function number_simplifier()
rule_tree = [If(iscall, Chain(ASSORTED_RULES)),
If(x -> !isadd(x) && is_operation(+)(x),
Chain(CANONICALIZE_PLUS)),
If(is_operation(+), Chain(PLUS_DISTRIBUTE)), # This would be useful even if isadd
If(x -> !ismul(x) && is_operation(*)(x),
Chain(CANONICALIZE_TIMES)),
If(is_operation(*), MUL_DISTRIBUTE),
If(x -> !ispow(x) && is_operation(^)(x),
Chain(CANONICALIZE_POW)),
If(is_operation(^), Chain(POW_RULES)),
] |> RestartedChain
rule_tree
end
trig_exp_simplifier(;kw...) = Chain(TRIG_EXP_RULES)
bool_simplifier() = Chain(BOOLEAN_RULES)
global default_simplifier
global serial_simplifier
global threaded_simplifier
global serial_simplifier
global serial_expand_simplifier
function default_simplifier(; kw...)
IfElse(has_trig_exp,
Postwalk(IfElse(x->symtype(x) <: Number,
Chain((number_simplifier(),
trig_exp_simplifier())),
If(x->symtype(x) <: Bool,
bool_simplifier()))
; kw...),
Postwalk(Chain((If(x->symtype(x) <: Number,
number_simplifier()),
If(x->symtype(x) <: Bool,
bool_simplifier())))
; kw...))
end
# reduce overhead of simplify by defining these as constant
serial_simplifier = If(iscall, Fixpoint(default_simplifier()))
threaded_simplifier(cutoff) = Fixpoint(default_simplifier(threaded=true,
thread_cutoff=cutoff))
serial_expand_simplifier = If(iscall,
Fixpoint(Chain((expand,
Fixpoint(default_simplifier())))))
end