+
    i              	          ^ RI Ht ^ RIHtHtHt ^ RIHt ^ RIH	t	 ^ RI
Ht ^ RIHt ^ RIHt ^ RIHt ^ R	IHtHtHt ^ R
IHt R tR tR tR tR tR tR tR t R t!R t"R t#R t$]%R8X  d[   ]]]]]]] ]"]#.	t&. t']& FE  t(]! 4       t)](! 4        ]! 4       ]),
          t)]*! R](PJ                  ](PV                  ])3,          4       KG  	  R# R# )    )random)IIntegerpi)Symbol)sympify)sqrt)sin)factor)simplifyxyz)default_timerc                     R p V ! V ! V ! V ! V ! V ! V ! V ! V ! V ! \         ^,          4      4      4      4      4      4      4      4      4      4      P                  4       ^ ,           R# )z'real(f(f(f(f(f(f(f(f(f(f(i/2)))))))))))c                 x    \        \        ^4      ^,          4      V ^,          ,          \        ^,          ,           #    )r	   r   r   )r   s   &/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/sympy/benchmarks/bench_symbench.pyfbench_R1.<locals>.f   s'    GAJqL!!Q$&1,,    N)r   as_real_imag)r   s    r   bench_R1r      sM    -a!Aa!Aa!fI, !
"#$%224Q77r   c                 .   a  V 3R lo S ! ^\         4       R# )z!Hermite polynomial hermite(15, y)c                    < V ^8X  d
   ^V,          # V ^ 8X  d   ^# ^V,          S! V ^,
          V4      ,          ^V ^,
          ,          S! V ^,
          V4      ,          ,
          P                  4       # r   )expand)nr   hermites   &&r   r    bench_R2.<locals>.hermite   s]    6Q3J6!GAE1%%1q5	'!a%2C(CCKKMMr   N)r   )r    s   @r   bench_R2r"      s    N BNr   c                     \         \        ,           \        ,           p \        ^
4       Uu. uF  p\	        W 8H  4      NK  	   pR# u upi )z#a = [bool(f==f) for _ in range(10)]N)r   r   r   rangeboolr   _s     r   bench_R3r(   !   s.    	A	A 9%9aT!&\9%%s   Ac                      R # N r+   r   r   bench_R4r,   '   s    r   c                 V    R p R p\         \        \        .pV ! V^4       V! V4      pR# )zblowup(L, 8); L=uniq(L)c                     \        V4       FB  pV P                  W,          W^,           ,          ,           W^,           ,          ,          4       KD  	  R# )r   N)r$   append)Lr   is   && r   blowupbench_R5.<locals>.blowup.   s3    qAHHqtaAh!E(24 r   c                     \        V 4      pV# r*   )set)r   vs   & r   uniqbench_R5.<locals>.uniq2   s    Fr   Nr   )r2   r7   r0   s      r   bench_R5r9   ,   s+    5 
Aq	A
1aLQAr   c                 <    \        R \        ^d4       4       4       R# )z<sum(simplify((x+sin(i))/x+(x-sin(i))/x) for i in range(100))c              3      "   T FU  p\        \        \        V4      ,           \        ,          \        \        V4      ,
          \        ,          ,           4      x  KW  	  R # 5ir*   )r   r   r
   ).0r1   s   & r   	<genexpr>bench_R6.<locals>.<genexpr><   s5     F:a!c!f*a1s1v:q.011:s   AAN)sumr$   r+   r   r   bench_R6r@   :   s    F5:FFr   c                    \         ^,          ^"\         ^,          ,          ,           ^-\         ^,          ,          ,           ^	\         ^,          ,          ,           ^"\         ^
,          ,          ,           ^ \         ^,          ,          ,           p \        R4       Uu. uF   qP                  \         \        4       4      NK"  	   pR# u upi )z+[f.subs(x, random()) for _ in range(10**4)]N'  )r   r$   subsr   r&   s     r   bench_R7rD   ?   sp    	21b52ad7"Qq"uW,r!R%x7"QU(BA"',/,QVVAvx,//s   &Cc                 8    R p V ! \         ^,          ^ ^R4       R# )zright(x^2,0,5,10^4)c                 "   \        V4      p\        V4      p\        V4      pV P                  \        4      P                  4       pW!,
          V,          pTp^ p\	        V4       F"  pWe,          pWpP                  WF4      ,          pK$  	  Wu,          # )r   )r   atomsr   popr$   rC   )	r   abr   r   Deltaxcestr1   s	   &&&&     r   rightbench_R8.<locals>.rightG   sw    AJAJAJGGFO!%qAKA66!<C  zr   NrB   )r   )rN   s    r   bench_R8rP   E   s     
!Q$1er   c                 z    \        \        ^,          \        ^,          \        ^,          ,          ,
          4       R# )zfactor(x^20 - pi^5*y^20)N)r   r   r   r   r+   r   r   	_bench_R9rR   W   s    
1b52q5B;r   c                 R    R p V ! \         ) \         \        ^4      ^
,          4       R# )zv = [-pi,-pi+1/10..,pi]c                     V .pWR,          ,
          P                  4       ^ 8  d"   VP                  VR,          V,           4       KC  VRR # )r   N)evalfr/   )minmaxstepr6   s   &&& r   srangebench_R10.<locals>.srange^   s?    ErU{!!#a'HHQrUT\""vr   N)r   r   )rZ   s    r   	bench_R10r\   \   s    
 B3GAJrM"r   c                     \        R4       U u. uF'  p \        4       \        4       \        ,          ,           NK)  	   p R# u up i )z.a = [random() + random()*I for w in [0..1000]]i  N)r$   r   r   )ws    r   	bench_R11r_   f   s+    $)$K0KqVX
K00s   -?c                     \         \        ,           \        ,           ^,           ^,          p W ^,           ,          pVP                  4        R# )z#e=(x+y+z+1)**7;f=e*(e+1);f.expand()N)r   r   r   r   )er   s     r   bench_S1rb   k   s,    	
QQA	q5	AHHJr   __main__z
%s%65s: %fN),sympy.core.randomr   sympy.core.numbersr   r   r   sympy.core.symbolr   sympy.core.sympifyr   (sympy.functions.elementary.miscellaneousr	   (sympy.functions.elementary.trigonometricr
   sympy.polys.polytoolsr   sympy.simplify.simplifyr   	sympy.abcr   r   r   timeitr   clockr   r"   r(   r,   r9   r@   rD   rP   rR   r\   r_   rb   __name__
benchmarksreportrJ   tprint__doc__r+   r   r   <module>ru      s    $ / / $ & 9 8 ( ,   )8	&	
G
0$ 
#1
 zJ FG	GaKlajj!))Q778	 ! r   