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using Random: shuffle, seed! | ||
using SymbolicUtils: getdepth, Rewriters, Term | ||
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@testset "Chain, Postwalk and Fixpoint" begin | ||
@syms w z α::Real β::Real | ||
# @testset "Chain, Postwalk and Fixpoint" begin | ||
# @syms w z α::Real β::Real | ||
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# r1 = @rule ~x + ~x => 2 * (~x) | ||
# r2 = @acrule ~x * +(~~ys) => sum(map(y -> ~x * y, ~~ys)) | ||
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# rset = Rewriters.Postwalk(Rewriters.Chain([r2])) | ||
# @test getdepth(rset) == typemax(Int) | ||
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# ex = 2 * (w + w + α + β) | ||
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# @eqtest rset(ex) == (((2 * w) + (2 * w)) + (2 * α)) + (2 * β) | ||
# @eqtest Rewriters.Fixpoint(rset)(ex) == ((2 * (2 * w)) + (2 * α)) + (2 * β) | ||
# end | ||
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# @testset "Numeric" begin | ||
# @syms a::Integer b c d x::Real y::Number | ||
# @eqtest simplify(Term{Real}(conj, [x])) == x | ||
# @eqtest simplify(Term{Real}(real, [x])) == x | ||
# @eqtest simplify(Term{Real}(imag, [x])) == 0 | ||
# @eqtest simplify(Term{Real}(imag, [y])) == imag(y) | ||
# @eqtest simplify(x - y) == x + -1 * y | ||
# @eqtest simplify(x - sin(y)) == x + -1 * sin(y) | ||
# @eqtest simplify(-sin(x)) == -1 * sin(x) | ||
# @eqtest simplify(1 * x * 2) == 2 * x | ||
# @eqtest simplify(1 + x + 2) == 3 + x | ||
# @eqtest simplify(b * b) == b^2 # tests merge_repeats | ||
# @eqtest simplify((a * b)^2) == a^2 * b^2 | ||
# @eqtest simplify((a * b)^c) == (a * b)^c | ||
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# @eqtest simplify(1x + 2x) == 3x | ||
# @eqtest simplify(3x + 2x) == 5x | ||
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# @eqtest simplify(a + b + (x * y) + c + 2 * (x * y) + d) == simplify((3 * x * y) + a + b + c + d) | ||
# @eqtest simplify(a + b + 2 * (x * y) + c + 2 * (x * y) + d) == simplify((4 * x * y) + a + b + c + d) | ||
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# @eqtest simplify(a * x^y * b * x^d) == simplify(a * b * (x^(d + y))) | ||
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# @eqtest simplify(a + b + 0 * c + d) == simplify(a + b + d) | ||
# @eqtest simplify(a * b * c^0 * d) == simplify(a * b * d) | ||
# @eqtest simplify(a * b * 1 * c * d) == simplify(a * b * c * d) | ||
# @eqtest simplify_fractions(x^2.0 / (x * y)^2.0) == simplify_fractions(1 / (y^2.0)) | ||
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# @test simplify(Term(one, [a])) == 1 | ||
# @test simplify(Term(one, [b + 1])) == 1 | ||
# @test simplify(Term(one, [x + 2])) == 1 | ||
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# @test simplify(Term(zero, [a])) == 0 | ||
# @test simplify(Term(zero, [b + 1])) == 0 | ||
# @test simplify(Term(zero, [x + 2])) == 0 | ||
# end | ||
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# @testset "LiteralReal" begin | ||
# @syms x1::LiteralReal x2::LiteralReal | ||
# s = cos(x1 * 3.2) - x2 * 5.8 + x2 * 1.2 | ||
# @eqtest s == cos(x1 * 3.2) - x2 * 5.8 + x2 * 1.2 | ||
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# # Prevents automatic simplification: | ||
# @eqtest s != cos(3.2(x1^1)) - 4.6x2 | ||
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# # However, manual simplification should still work: | ||
# @eqtest simplify(s) == simplify(cos(3.2x1) - 4.6x2) | ||
# end | ||
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# @testset "boolean" begin | ||
# @syms a::Real b c | ||
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# @eqtest simplify(a < 0) == (a < 0) | ||
# @eqtest simplify(0 < a) == (0 < a) | ||
# @eqtest simplify((0 < a) | true) == true | ||
# @eqtest simplify(true | (0 < a)) == true | ||
# @eqtest simplify((0 < a) & true) == (0 < a) | ||
# @eqtest simplify(true & (0 < a)) == (0 < a) | ||
# @eqtest simplify(false & (0 < a)) == false | ||
# @eqtest simplify((0 < a) & false) == false | ||
# @eqtest simplify(Term{Bool}(!, [true])) == false | ||
# @eqtest simplify(Term{Bool}(|, [false, true])) == true | ||
# @eqtest simplify(ifelse(true, a, b)) == a | ||
# @eqtest simplify(ifelse(false, a, b)) == b | ||
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# # abs | ||
# @test simplify(substitute(ifelse(!(a < 0), a, -a), Dict(a => -1))) == 1 | ||
# @test simplify(substitute(ifelse(!(a < 0), a, -a), Dict(a => 1))) == 1 | ||
# @test simplify(substitute(ifelse(a < 0, -a, a), Dict(a => -1))) == 1 | ||
# @test simplify(substitute(ifelse(a < 0, -a, a), Dict(a => 1))) == 1 | ||
# end | ||
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# @testset "Pythagorean Identities" begin | ||
# @syms a::Integer x::Real y::Number | ||
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# @test simplify(cos(x)^2 + 1 + sin(x)^2) == 2 | ||
# @test simplify(cos(y)^2 + 1 + sin(y)^2) == 2 | ||
# @test simplify(sin(y)^2 + cos(y)^2 + 1) == 2 | ||
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# @eqtest simplify(1 + y + tan(x)^2) == sec(x)^2 + y | ||
# @eqtest simplify(1 + y + cot(x)^2) == csc(x)^2 + y | ||
# @eqtest simplify(cos(x)^2 - 1) == -sin(x)^2 | ||
# @eqtest simplify(sin(x)^2 - 1) == -cos(x)^2 | ||
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# @eqtest simplify(cosh(x)^2 + 1 - sinh(x)^2) == 2 | ||
# @eqtest simplify(cosh(y)^2 + 1 - sinh(y)^2) == 2 | ||
# @eqtest simplify(-sinh(y)^2 + cosh(y)^2 + 1) == 2 | ||
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# @eqtest simplify(cosh(x)^2 - 1) == sinh(x)^2 | ||
# @eqtest simplify(sinh(x)^2 + 1) == cosh(x)^2 | ||
# end | ||
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# @testset "Double angle formulas" begin | ||
# @syms r x | ||
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# @eqtest simplify(r * cos(x / 2)^2 - r * sin(x / 2)^2) == r * cos(x) | ||
# @eqtest simplify(r * sin(x / 2)^2 - r * cos(x / 2)^2) == -r * cos(x) | ||
# @eqtest simplify(2cos(x) * sin(x)) == sin(2x) | ||
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# @eqtest simplify(r * cosh(x / 2)^2 + r * sinh(x / 2)^2) == r * cosh(x) | ||
# @eqtest simplify(r * sinh(x / 2)^2 + r * cosh(x / 2)^2) == r * cosh(x) | ||
# @eqtest simplify(2cosh(x) * sinh(x)) == sinh(2x) | ||
# end | ||
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# @testset "Exponentials" begin | ||
# @syms a::Real b::Real | ||
# @eqtest simplify(exp(a) * exp(b)) == simplify(exp(a + b)) | ||
# @eqtest simplify(exp(a) * exp(a)) == simplify(exp(2a)) | ||
# @test simplify(exp(a) * exp(-a)) == 1 | ||
# @eqtest simplify(exp(a)^2) == simplify(exp(2a)) | ||
# @eqtest simplify(exp(a) * a * exp(b)) == simplify(a * exp(a + b)) | ||
# @eqtest simplify(one(Int)^a) == 1 | ||
# @eqtest simplify(one(Complex{Float64})^a) == 1 | ||
# @eqtest simplify(a^b * 1^a) == a^b | ||
# end | ||
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# @testset "simplify_fractions" begin | ||
# @syms x y z | ||
# @eqtest simplify(2 * ((y + z) / x) - 2 * y / x - z / x * 2) == 0 | ||
# end | ||
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# @testset "Depth" begin | ||
# @syms x | ||
# R = Rewriters.Postwalk(Rewriters.Chain([@rule(sin(~x) => cos(~x)), | ||
# @rule(1 + ~x => ~x - 1)])) | ||
# @eqtest R(sin(sin(sin(x + 1)))) == cos(cos(cos(x - 1))) | ||
# #@eqtest R(sin(sin(sin(x + 1))), depth=2) == cos(cos(sin(x + 1))) | ||
# end | ||
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# pred(x) = error("Fail") | ||
# @testset "RuleRewriteError" begin | ||
# @syms a b | ||
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# rs = Rewriters.Postwalk(Rewriters.Chain(([@rule ~x + ~y::pred => ~x]))) | ||
# @test_throws SymbolicUtils.RuleRewriteError rs(a + b) | ||
# err = try | ||
# rs(a + b) | ||
# catch err | ||
# err | ||
# end | ||
# @test sprint(io -> Base.showerror(io, err)) == "Failed to apply rule ~x + ~(y::pred) => ~x on expression a + b" | ||
# end | ||
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# @testset "Threading" begin | ||
# @syms a b c d | ||
# ex = (((0.6666666666666666 / (c / 1)) + ((1 * a) / (c / 1))) + | ||
# (1.0 / (((1 * d) / (1 + b)) * (1 / b)))) + | ||
# ((((1 * a) + (1 * a)) / ((2.0 * (d + 1)) / 1.0)) + | ||
# ((((d * 1) / (1 + c)) * 2.0) / ((1 / d) + (1 / c)))) | ||
# @eqtest simplify(ex) == simplify(ex, threaded=true, thread_subtree_cutoff=3) | ||
# @test SymbolicUtils.node_count(a + b * c / d) == 7 | ||
# end | ||
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# @testset "timerwrite" begin | ||
# @syms a b c d | ||
# expr1 = foldr((x, y) -> rand([*, /])(x, y), rand([a, b, c, d], 100)) | ||
# SymbolicUtils.@timerewrite simplify(expr1) | ||
# end | ||
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# _g(y) = sin | ||
# @testset "interpolation" begin | ||
# @syms a | ||
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# @test isnothing(@rule(_g(1)(a) => 2)(sin(a))) | ||
# @test @rule($(_g(1))(a) => 2)(sin(a)) == 2 | ||
# end | ||
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r1 = @rule ~x + ~x => 2 * (~x) | ||
r2 = @acrule ~x * +(~~ys) => sum(map(y -> ~x * y, ~~ys)) | ||
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rset = Rewriters.Postwalk(Rewriters.Chain([r2])) | ||
@test getdepth(rset) == typemax(Int) | ||
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ex = 2 * (w + w + α + β) | ||
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@eqtest rset(ex) == (((2 * w) + (2 * w)) + (2 * α)) + (2 * β) | ||
@eqtest Rewriters.Fixpoint(rset)(ex) == ((2 * (2 * w)) + (2 * α)) + (2 * β) | ||
end | ||
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@testset "Numeric" begin | ||
@syms a::Integer b c d x::Real y::Number | ||
@eqtest simplify(Term{Real}(conj, [x])) == x | ||
@eqtest simplify(Term{Real}(real, [x])) == x | ||
@eqtest simplify(Term{Real}(imag, [x])) == 0 | ||
@eqtest simplify(Term{Real}(imag, [y])) == imag(y) | ||
@eqtest simplify(x - y) == x + -1 * y | ||
@eqtest simplify(x - sin(y)) == x + -1 * sin(y) | ||
@eqtest simplify(-sin(x)) == -1 * sin(x) | ||
@eqtest simplify(1 * x * 2) == 2 * x | ||
@eqtest simplify(1 + x + 2) == 3 + x | ||
@eqtest simplify(b * b) == b^2 # tests merge_repeats | ||
@eqtest simplify((a * b)^2) == a^2 * b^2 | ||
@eqtest simplify((a * b)^c) == (a * b)^c | ||
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@eqtest simplify(1x + 2x) == 3x | ||
@eqtest simplify(3x + 2x) == 5x | ||
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@eqtest simplify(a + b + (x * y) + c + 2 * (x * y) + d) == simplify((3 * x * y) + a + b + c + d) | ||
@eqtest simplify(a + b + 2 * (x * y) + c + 2 * (x * y) + d) == simplify((4 * x * y) + a + b + c + d) | ||
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@eqtest simplify(a * x^y * b * x^d) == simplify(a * b * (x^(d + y))) | ||
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@eqtest simplify(a + b + 0 * c + d) == simplify(a + b + d) | ||
@eqtest simplify(a * b * c^0 * d) == simplify(a * b * d) | ||
@eqtest simplify(a * b * 1 * c * d) == simplify(a * b * c * d) | ||
@eqtest simplify_fractions(x^2.0 / (x * y)^2.0) == simplify_fractions(1 / (y^2.0)) | ||
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@test simplify(Term(one, [a])) == 1 | ||
@test simplify(Term(one, [b + 1])) == 1 | ||
@test simplify(Term(one, [x + 2])) == 1 | ||
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@test simplify(Term(zero, [a])) == 0 | ||
@test simplify(Term(zero, [b + 1])) == 0 | ||
@test simplify(Term(zero, [x + 2])) == 0 | ||
end | ||
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@testset "LiteralReal" begin | ||
@syms x1::LiteralReal x2::LiteralReal | ||
s = cos(x1 * 3.2) - x2 * 5.8 + x2 * 1.2 | ||
@eqtest s == cos(x1 * 3.2) - x2 * 5.8 + x2 * 1.2 | ||
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# Prevents automatic simplification: | ||
@eqtest s != cos(3.2(x1^1)) - 4.6x2 | ||
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# However, manual simplification should still work: | ||
@eqtest simplify(s) == simplify(cos(3.2x1) - 4.6x2) | ||
end | ||
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@testset "boolean" begin | ||
@syms a::Real b c | ||
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@eqtest simplify(a < 0) == (a < 0) | ||
@eqtest simplify(0 < a) == (0 < a) | ||
@eqtest simplify((0 < a) | true) == true | ||
@eqtest simplify(true | (0 < a)) == true | ||
@eqtest simplify((0 < a) & true) == (0 < a) | ||
@eqtest simplify(true & (0 < a)) == (0 < a) | ||
@eqtest simplify(false & (0 < a)) == false | ||
@eqtest simplify((0 < a) & false) == false | ||
@eqtest simplify(Term{Bool}(!, [true])) == false | ||
@eqtest simplify(Term{Bool}(|, [false, true])) == true | ||
@eqtest simplify(ifelse(true, a, b)) == a | ||
@eqtest simplify(ifelse(false, a, b)) == b | ||
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# abs | ||
@test simplify(substitute(ifelse(!(a < 0), a, -a), Dict(a => -1))) == 1 | ||
@test simplify(substitute(ifelse(!(a < 0), a, -a), Dict(a => 1))) == 1 | ||
@test simplify(substitute(ifelse(a < 0, -a, a), Dict(a => -1))) == 1 | ||
@test simplify(substitute(ifelse(a < 0, -a, a), Dict(a => 1))) == 1 | ||
end | ||
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@testset "Pythagorean Identities" begin | ||
@syms a::Integer x::Real y::Number | ||
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@test simplify(cos(x)^2 + 1 + sin(x)^2) == 2 | ||
@test simplify(cos(y)^2 + 1 + sin(y)^2) == 2 | ||
@test simplify(sin(y)^2 + cos(y)^2 + 1) == 2 | ||
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@eqtest simplify(1 + y + tan(x)^2) == sec(x)^2 + y | ||
@eqtest simplify(1 + y + cot(x)^2) == csc(x)^2 + y | ||
@eqtest simplify(cos(x)^2 - 1) == -sin(x)^2 | ||
@eqtest simplify(sin(x)^2 - 1) == -cos(x)^2 | ||
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@eqtest simplify(cosh(x)^2 + 1 - sinh(x)^2) == 2 | ||
@eqtest simplify(cosh(y)^2 + 1 - sinh(y)^2) == 2 | ||
@eqtest simplify(-sinh(y)^2 + cosh(y)^2 + 1) == 2 | ||
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@eqtest simplify(cosh(x)^2 - 1) == sinh(x)^2 | ||
@eqtest simplify(sinh(x)^2 + 1) == cosh(x)^2 | ||
end | ||
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@testset "Double angle formulas" begin | ||
@syms r x | ||
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@eqtest simplify(r * cos(x / 2)^2 - r * sin(x / 2)^2) == r * cos(x) | ||
@eqtest simplify(r * sin(x / 2)^2 - r * cos(x / 2)^2) == -r * cos(x) | ||
@eqtest simplify(2cos(x) * sin(x)) == sin(2x) | ||
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@eqtest simplify(r * cosh(x / 2)^2 + r * sinh(x / 2)^2) == r * cosh(x) | ||
@eqtest simplify(r * sinh(x / 2)^2 + r * cosh(x / 2)^2) == r * cosh(x) | ||
@eqtest simplify(2cosh(x) * sinh(x)) == sinh(2x) | ||
end | ||
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@testset "Exponentials" begin | ||
@syms a::Real b::Real | ||
@eqtest simplify(exp(a) * exp(b)) == simplify(exp(a + b)) | ||
@eqtest simplify(exp(a) * exp(a)) == simplify(exp(2a)) | ||
@test simplify(exp(a) * exp(-a)) == 1 | ||
@eqtest simplify(exp(a)^2) == simplify(exp(2a)) | ||
@eqtest simplify(exp(a) * a * exp(b)) == simplify(a * exp(a + b)) | ||
@eqtest simplify(one(Int)^a) == 1 | ||
@eqtest simplify(one(Complex{Float64})^a) == 1 | ||
@eqtest simplify(a^b * 1^a) == a^b | ||
end | ||
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@testset "simplify_fractions" begin | ||
@syms x y z | ||
@eqtest simplify(2 * ((y + z) / x) - 2 * y / x - z / x * 2) == 0 | ||
end | ||
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@testset "Depth" begin | ||
@syms x | ||
R = Rewriters.Postwalk(Rewriters.Chain([@rule(sin(~x) => cos(~x)), | ||
@rule(1 + ~x => ~x - 1)])) | ||
@eqtest R(sin(sin(sin(x + 1)))) == cos(cos(cos(x - 1))) | ||
#@eqtest R(sin(sin(sin(x + 1))), depth=2) == cos(cos(sin(x + 1))) | ||
end | ||
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pred(x) = error("Fail") | ||
@testset "RuleRewriteError" begin | ||
@syms a | ||
_f(x) = x === a | ||
@testset "where1" begin | ||
@syms a b | ||
r = @rule ~x => ~x where {_f(~x)} | ||
@eqtest r(a) == a | ||
@test isnothing(r(b)) | ||
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rs = Rewriters.Postwalk(Rewriters.Chain(([@rule ~x + ~y::pred => ~x]))) | ||
@test_throws SymbolicUtils.RuleRewriteError rs(a + b) | ||
err = try | ||
rs(a + b) | ||
catch err | ||
err | ||
end | ||
@test sprint(io -> Base.showerror(io, err)) == "Failed to apply rule ~x + ~(y::pred) => ~x on expression a + b" | ||
end | ||
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@testset "Threading" begin | ||
@syms a b c d | ||
ex = (((0.6666666666666666 / (c / 1)) + ((1 * a) / (c / 1))) + | ||
(1.0 / (((1 * d) / (1 + b)) * (1 / b)))) + | ||
((((1 * a) + (1 * a)) / ((2.0 * (d + 1)) / 1.0)) + | ||
((((d * 1) / (1 + c)) * 2.0) / ((1 / d) + (1 / c)))) | ||
@eqtest simplify(ex) == simplify(ex, threaded=true, thread_subtree_cutoff=3) | ||
@test SymbolicUtils.node_count(a + b * c / d) == 7 | ||
end | ||
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@testset "timerwrite" begin | ||
@syms a b c d | ||
expr1 = foldr((x, y) -> rand([*, /])(x, y), rand([a, b, c, d], 100)) | ||
SymbolicUtils.@timerewrite simplify(expr1) | ||
end | ||
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_g(y) = sin | ||
@testset "interpolation" begin | ||
@syms a | ||
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@test isnothing(@rule(_g(1)(a) => 2)(sin(a))) | ||
@test @rule($(_g(1))(a) => 2)(sin(a)) == 2 | ||
r = @acrule ~x => ~x where {_f(~x)} | ||
@eqtest r(a) == a | ||
@test r(b) === nothing | ||
end | ||
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@syms a | ||
_f(x) = x === a | ||
@testset "where" begin | ||
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@testset "where2" begin | ||
@syms a b | ||
r = @rule ~x => ~x where {_f(~x)} | ||
@eqtest r(a) == a | ||
@test isnothing(r(b)) | ||
end | ||
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@testset "where3" begin | ||
@syms a b | ||
r = @acrule ~x => ~x where {_f(~x)} | ||
@eqtest r(a) == a | ||
@test r(b) === nothing | ||
end | ||
end |
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