Simplifying acos(0/1), asin(0,1) and anything + 0

ext/SymbolicsGroebnerExt.jl

@@ -320,13 +320,9 @@ end
 # Helps with precompilation time
 PrecompileTools.@setup_workload begin
     @variables a b c x y z
-    equation1 = a*log(x)^b + c ~ 0
-    equation_actually_polynomial = sin(x^2 +1)^2 + sin(x^2 + 1) + 3
     simple_linear_equations = [x - y, y + 2z]
     equations_intersect_sphere_line = [x^2 + y^2 + z^2 - 9, x - 2y + 3, y - z]
     PrecompileTools.@compile_workload begin
-        symbolic_solve(equation1, x)
-        symbolic_solve(equation_actually_polynomial)
         symbolic_solve(simple_linear_equations, [x, y], warns=false)
         symbolic_solve(equations_intersect_sphere_line, [x, y, z], warns=false)
     end

ext/SymbolicsNemoExt.jl

@@ -61,7 +61,13 @@ end
 PrecompileTools.@setup_workload begin
     @variables a b c x y z
     expr_with_params = expand((x + b)*(x^2 + 2x + 1)*(x^2 - a))
+    equation1 = a*log(x)^b + c ~ 0
+    equation_polynomial = 9^x + 3^x + 2
+    exp_eq = 5*2^(x+1) + 7^(x+3)
     PrecompileTools.@compile_workload begin
+        symbolic_solve(equation1, x)
+        symbolic_solve(equation_polynomial, x)
+        symbolic_solve(exp_eq)
         symbolic_solve(expr_with_params, x, dropmultiplicity=false)
         symbolic_solve(x^10 - a^10, x, dropmultiplicity=false)
     end

src/solver/postprocess.jl

@@ -104,38 +104,27 @@ function _postprocess_root(x::SymbolicUtils.BasicSymbolic)
         end
     end
 
-    isnegone(x) = isequal(-1, expand(x))
-    ishalf(x) = isequal(1/2, expand(x))
-    isneghalf(x) = isequal(-1/2, expand(x))
-    symiszero(x) = isequal(0, expand(x))
-    symisone(x) = isequal(1, expand(x))
-    acos_rules = [(@rule acos(~x::symiszero) => Symbolics.term(/, pi, 2)),
-        (@rule acos(~x::symisone) => 0),
-        (@rule acos(~x::isnegone) => Symbolics.term(*, pi)),
-        (@rule acos(~x::ishalf) => Symbolics.term(/, pi, 3)),
-        (@rule acos(~x::isneghalf) => Symbolics.term(/, Symbolics.term(*,2,pi), 3))
+    opers = [acos, asin, atan]
+    exacts = [0, Symbolics.term(*, pi), Symbolics.term(/,pi,3),
+        Symbolics.term(/, pi, 2),
+        Symbolics.term(/, Symbolics.term(*, 2, pi), 3),
+        Symbolics.term(/, pi, 6),
+        Symbolics.term(/, Symbolics.term(*, 5, pi), 6),
+        Symbolics.term(/, pi, 4)
     ]
 
-    asin_rules = [(@rule asin(~x::symiszero) => 0), 
-        (@rule asin(~x::symisone) => Symbolics.term(/, pi, 2)),
-        (@rule asin(~x::isnegone) => -Symbolics.term(/, pi, 2)),
-        (@rule asin(~x::ishalf) => Symbolics.term(/, pi, 6)),
-        (@rule asin(~x::isneghalf) => Symbolics.term(/, Symbolics.term(*,-1,pi), 6))
-    ]
-
-    if oper === acos
-        for r in acos_rules
-            after_r = r(x)
-            !isnothing(after_r) && return after_r
-        end
-    elseif oper === asin
-        for r in asin_rules
-            after_r = r(x)
-            !isnothing(after_r) && return after_r
+    if any(isequal(oper, o) for o in opers) && isempty(Symbolics.get_variables(x))
+        val = eval(Symbolics.toexpr(x))
+        for i in eachindex(exacts)
+            exact_val = eval(Symbolics.toexpr(exacts[i]))
+            if isapprox(exact_val, val, atol=1e-6)
+                return exacts[i]
+            elseif isapprox(-exact_val, val, atol=1e-6)
+                return -exacts[i]
+            end
         end
     end
 
-
     if oper === (+)
         args = arguments(x)
         for arg in args