+ iA- Rt^RIHt^RIHt^RIHt^RIHt^RI H t H t ^RI H t Ht^RIHtHtHt^RIHtHt^R IHtHtHtHt^R IHt^R IHt^R IH t ^R I!H"t"H#t#^RI$H%t%H&t&^RI'H(t(^RI)H*t*^RI+H,t,!RR4t-!RR]-4t.Rt/].!RR4t0]!RR.R7t1]!RR.R7t2]!R4t3]!R4t4]!R R!.R7t5].!]!]44]4, ]!]444t6].!]!]5]4,4]4, ]5]!]5]4,4,4t7]6]73t8].!]3] !]44,] !^4, ]3]!]44,R"R#7t9].!] !^4]!]44,] !]444t:].!R$R%4t;!R&R'].4t<]]]?3tIR/#)0a Classes and functions useful for rewriting expressions for optimized code generation. Some languages (or standards thereof), e.g. C99, offer specialized math functions for better performance and/or precision. Using the ``optimize`` function in this module, together with a collection of rules (represented as instances of ``Optimization``), one can rewrite the expressions for this purpose:: >>> from sympy import Symbol, exp, log >>> from sympy.codegen.rewriting import optimize, optims_c99 >>> x = Symbol('x') >>> optimize(3*exp(2*x) - 3, optims_c99) 3*expm1(2*x) >>> optimize(exp(2*x) - 1 - exp(-33), optims_c99) expm1(2*x) - exp(-33) >>> optimize(log(3*x + 3), optims_c99) log1p(x) + log(3) >>> optimize(log(2*x + 3), optims_c99) log(2*x + 3) The ``optims_c99`` imported above is tuple containing the following instances (which may be imported from ``sympy.codegen.rewriting``): - ``expm1_opt`` - ``log1p_opt`` - ``exp2_opt`` - ``log2_opt`` - ``log2const_opt`` ) expand_log)S)Wild)sign)explog)MaxMin)cossinsinc)Qask)log1plog2exp2expm1) MatrixSolve)UnevaluatedExpr)Pow) logaddexp logaddexp2)cosm1powm1)Mul) MatrixSymbol)siftc4a]tRt^4toRtRRltRtRtVtR#) OptimizationzAbstract base class for rewriting optimization. Subclasses should implement ``__call__`` taking an expression as argument. Parameters ========== cost_function : callable returning number priority : number NcWnW nR#N cost_functionpriority)selfr"r#s&&&w/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/sympy/codegen/rewriting.py__init__Optimization.__init__@s * c.\WPR7#))key)minr")r$argss&*r%cheapestOptimization.cheapestDs4//00r(r!)N) __name__ __module__ __qualname____firstlineno____doc__r&r-__static_attributes____classdictcell__) __classdict__s@r%rr4s 11r(rc<aa]tRt^HtoRtV3RltRtRtVtV;t #) ReplaceOptima|Rewriting optimization calling replace on expressions. Explanation =========== The instance can be used as a function on expressions for which it will apply the ``replace`` method (see :meth:`sympy.core.basic.Basic.replace`). Parameters ========== query : First argument passed to replace. value : Second argument passed to replace. Examples ======== >>> from sympy import Symbol >>> from sympy.codegen.rewriting import ReplaceOptim >>> from sympy.codegen.cfunctions import exp2 >>> x = Symbol('x') >>> exp2_opt = ReplaceOptim(lambda p: p.is_Pow and p.base == 2, ... lambda p: exp2(p.exp)) >>> exp2_opt(2**x) exp2(x) c @<\SV`!R/VBWnW nR#)N)superr&queryvalue)r$r=r>kwargs __class__s&&&,r%r&ReplaceOptim.__init__hs "6"  r(cNVPVPVP4#r )replacer=r>)r$exprs&&r%__call__ReplaceOptim.__call__ms||DJJ 33r()r=r>) r0r1r2r3r4r&rEr5r6 __classcell__r@r7s@@r%r9r9Hs> 44r(r9c\VRRR7F.pV!V4pVPfTpKVPW4pK0 V#)aApply optimizations to an expression. Parameters ========== expr : expression optimizations : iterable of ``Optimization`` instances The optimizations will be sorted with respect to ``priority`` (highest first). Examples ======== >>> from sympy import log, Symbol >>> from sympy.codegen.rewriting import optims_c99, optimize >>> x = Symbol('x') >>> optimize(log(x+3)/log(2) + log(x**2 + 1), optims_c99) log1p(x**2) + log2(x + 3) cVP#r )r#)opts&r%optimize..ss||r(T)r*reverse)sortedr"r-)rD optimizationsoptimnew_exprs&& r%optimizerSqsH* +CTR;    &D>>$1D S Kr(cHVP;'dVP^8H#))is_Powbaseps&r%rLrLsahh&&166Q;&r(c,\VP4#r )rrrXs&r%rLrLs d155kr(dcVP#r )is_Dummyxs&r%rLrLsQZZr() propertiesucVVP'*;'dVP'*#r ) is_numberis_Addr^s&r%rLrLs_%E%EQXX%Er(vwncVP#r rcr^s&r%rLrLsQ[[r(c&VPR4#)cVP;'dVPP;'gA\V\\ 34;'d#VP ^,P'*#)rVr is_negative isinstancerrr,rces&r%rL..sT &&QUU&& D D q3+ & B Bqvvay/B/B+B Dr()count)rDs&r%rLrLsSWS]S]ETr(r"c\V\4;'dVP^,P;'d\ VP^,P4^8H;'dk\ ;QJd7RVP^,P4F 'dK R# R#!RVP^,P44#)rmc3B"TFp\V\4xK R#5ir )ror).0ts& r% ..sB>az!S))>sFT)rorr,rdlenallls&r%rLrLsz!S!CC66!9##CCqvvay~~&!+CC3B166!9>>B33CCB166!9>>BBCr(c T\VP^,PUu.uFqP^,NK up!\\\ VP^,PUu.uFqP^,NK up!44,#uupiuupirl)rr,rrr )r~rqs& r%rLrLsm  0AffQii 01 c#166!9>>:>aq >:;<= > 0:s B 2B%cRaa]tRt^toRtRV3RlltRtRtV3RltRt Vt V;t #)FuncMinusOneOptima}Specialization of ReplaceOptim for functions evaluating "f(x) - 1". Explanation =========== Numerical functions which go toward one as x go toward zero is often best implemented by a dedicated function in order to avoid catastrophic cancellation. One such example is ``expm1(x)`` in the C standard library which evaluates ``exp(x) - 1``. Such functions preserves many more significant digits when its argument is much smaller than one, compared to subtracting one afterwards. Parameters ========== func : The function which is subtracted by one. func_m_1 : The specialized function evaluating ``func(x) - 1``. opportunistic : bool When ``True``, apply the transformation as long as the magnitude of the remaining number terms decreases. When ``False``, only apply the transformation if it completely eliminates the number term. Examples ======== >>> from sympy import symbols, exp >>> from sympy.codegen.rewriting import FuncMinusOneOptim >>> from sympy.codegen.cfunctions import expm1 >>> x, y = symbols('x y') >>> expm1_opt = FuncMinusOneOptim(exp, expm1) >>> expm1_opt(exp(x) + 2*exp(5*y) - 3) expm1(x) + 2*expm1(5*y) cz<aa^ o\SV`RVPVV3RlR7WnSVnW0nR#) cVP#r )rdrps&r%rL,FuncMinusOneOptim.__init__..s188r(c^<VP4SVPS4,, #r ) count_opsrs)rDfunc_m_1weights&r%rLrs DNN4DvdjjYaNbGb4br(rtN)r<r&replace_in_Addfuncr opportunistic)r$rrrrr@s&&f&@r%r&FuncMinusOneOptim.__init__s; +T-@-@'b  d   *r(ca\VPRRR7wr#\V4p\VV3RlRR7wrVWEV3#)cVP#r riargs&r%rL4FuncMinusOneOptim._group_Add_terms..scmmr(Tbinaryc:<VPSP4#r )hasrrr$s&r%rLrs377499;Mr()rr,sum)r$addnumbersnon_numnumsumterms_with_funcothersf& r%_group_Add_terms"FuncMinusOneOptim._group_Add_termss@*CDQW!%g/MVZ![--r(c 0aSPV4wr#pV^8XdV#..reVEFWpVP'dT\VPV3RlRR7wr\ V4^8Xd#\ V 4^8XdV^,V ^,rM2Rp M/VP SP 8XdT\ PrMRp V eV P'd\V 4\V4)8XdSP'd\W,4\V48p M W,^8Hp V 'd<W), pVPV SP!XP!,4EKFVPV4EKZ VP !V.VOVOVO5!#)z0passed as second argument to Basic.replace(...) c6<VPSP8H#r )rrs&r%rL2FuncMinusOneOptim.replace_in_Add..ssxx499?Tr(TrN)ris_Mulrr,r{rrOnercrrabsappendr) r$rqrrother_non_num_terms substituted untouched with_funcrcoeff do_substitutes f& r%r FuncMinusOneOptim.replace_in_AddsI7;7L7LQ7O4!4 Q;H!#RY(I"9>>3T]ab t9>c%jAo"&q'58% E499,'e U___ef 9U%%%$' $5F $CM$)LA$5M OF&&uT]]DII-F'FG   Y '-)0vvfM{MYM9LMMr(c~<\SV`V4p\SV`VP44pVPW#4#r )r<rEfactorr-)r$rDalt1alt2r@s&& r%rEFuncMinusOneOptim.__call__ s6w%w .}}T((r()rrr)T) r0r1r2r3r4r&rrrEr5r6rGrHs@@r%rrs&$L+. N@))r(rc"\V\4#r )rorrps&r%rLrLs jC r(c\VP\R44P\\^,4\ \44#)c4\VP44#r )rrrs&r%rLrrsSZZ\*r()rrCr_urr}s&r%rLrLs7j *ws2a4y%)$%r(base_reqcVP#r ) is_symbol)bs&r%rLrLs r(c*aa\VV3RlR4#)aCreates an instance of :class:`ReplaceOptim` for expanding ``Pow``. Explanation =========== The requirements for expansions are that the base needs to be a symbol and the exponent needs to be an Integer (and be less than or equal to ``limit``). Parameters ========== limit : int The highest power which is expanded into multiplication. base_req : function returning bool Requirement on base for expansion to happen, default is to return the ``is_symbol`` attribute of the base. Examples ======== >>> from sympy import Symbol, sin >>> from sympy.codegen.rewriting import create_expand_pow_optimization >>> x = Symbol('x') >>> expand_opt = create_expand_pow_optimization(3) >>> expand_opt(x**5 + x**3) x**5 + x*x*x >>> expand_opt(x**5 + x**3 + sin(x)**3) x**5 + sin(x)**3 + x*x*x >>> opt2 = create_expand_pow_optimization(3, base_req=lambda b: not b.is_Function) >>> opt2((x+1)**2 + sin(x)**2) sin(x)**2 + (x + 1)*(x + 1) c<VP;'dQS!VP4;'d7VPP;'d\ VP4S8*#r )rVrWr is_Integerr)rqrlimits&r%rL0create_expand_pow_optimization..BsE!((\\x/\\AEE4D4D\\QUUW\I\\r(cVP^8d2\\VP.VP5,RR/4#^\\VP.VP),RR/4, #)rmevaluateF)rrrrWrXs&r%rLrCsbHIPQ OC166(AEE6/CUC D G ocQVVHaeeVOEuEF F Gr()r9)rrsfdr%create_expand_pow_optimizationrsF \   r(cvVP'd\VP4^8XdVPwrVP'dmVP^,^8XdUVP p\ V\4'd3\\\P!VP 444#R#)rUF) is_MatMulr{r, is_Inverseshaperrorboolrr fullrankrDleftrightinv_args& r%_matinv_predicaterIss ~~~#dii.A-ii  ???u{{1~2hhG'<00C 488 4566 r(cLVPwrVPp\W24#r )r,rrrs& r%_matinv_transformrTs!))KDhhG w &&r(N)Jr4sympy.core.functionrsympy.core.singletonrsympy.core.symbolr$sympy.functions.elementary.complexesr&sympy.functions.elementary.exponentialrr(sympy.functions.elementary.miscellaneousrr (sympy.functions.elementary.trigonometricr r r sympy.assumptionsr rsympy.codegen.cfunctionsrrrrsympy.codegen.matrix_nodesrsympy.core.exprrsympy.core.powerrsympy.codegen.numpy_nodesrrsympy.codegen.scipy_nodesrrsympy.core.mulr"sympy.matrices.expressions.matexprrsympy.utilities.iterablesrrr9rSexp2_opt_dr_v_w_n sinc_opt1 sinc_opt2 sinc_optslog2_opt log2const_optlogsumexp_2terms_optr expm1_opt cosm1_opt powm1_opt log1p_optrrr matinv_opt logaddexp_optlogaddexp2_opt optims_c99 optims_numpy optims_scipyr;r(r%rsa@+""5=?EE$==2+ ;2;*11(&4<&4R< &   #/01 #EFG #Y #Y #012 GBJR   2JrM2d2b5k>   " 3r7 3q6)2d2h;G SVDH_c"g6 #D X) X)v c5 ) c5 ) c5 )  %  ( 6K( V ' +-> ? 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