
    \h              	          S SK Jr  S SKJrJrJr  S SKJr  S SKJ	r	  S SK
Jr  S SKJr  S SKJr  S SKJr  S S	KJrJrJr  S S
KJr  S rS rS rS rS rS rS rS r S r!S r"S r#S r$\%S:X  aQ  \\\\\\\ \"\#/	r&/ r'\& H=  r(\" 5       r)\(" 5         \" 5       \)-
  r)\*" S\(RJ                  \(RV                  \)4-  5        M?     gg)    )random)IIntegerpi)Symbol)sympify)sqrt)sin)factor)simplifyxyz)default_timerc                      S n U " U " U " U " U " U " U " U " U " U " [         S-  5      5      5      5      5      5      5      5      5      5      R                  5       S     g)z'real(f(f(f(f(f(f(f(f(f(f(i/2)))))))))))c                 P    [        [        S5      S-  5      U S-  -  [        S-  -   $ )N         )r	   r   r   )r   s    W/var/www/auris/envauris/lib/python3.13/site-packages/sympy/benchmarks/bench_symbench.pyfbench_R1.<locals>.f   s'    GAJqL!!Q$&1,,    r   r   N)r   as_real_imag)r   s    r   bench_R1r      sJ    -a!Aa!Aa!fI, !
"#$%224Q7r   c                  ,   ^  U 4S jm T " S[         5        g)z!Hermite polynomial hermite(15, y)c                    > U S:X  a  SU-  $ U S:X  a  gSU-  T" U S-
  U5      -  SU S-
  -  T" U S-
  U5      -  -
  R                  5       $ )Nr   r   r   )expand)nr   hermites     r   r!   bench_R2.<locals>.hermite   s]    6Q3J6!GAE1%%1q5	'!a%2C(CCKKMMr      N)r   )r!   s   @r   bench_R2r$      s    N BNr   c                      [         [        -   [        -   n [        S5       Vs/ s H  n[	        X :H  5      PM       ngs  snf )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   <c                      g N r.   r   r   bench_R4r/   '   s    r   c                  T    S n S n[         [        [        /nU " US5        U" U5      ng)zblowup(L, 8); L=uniq(L)c                 n    [        U5       H&  nU R                  X   XS-      -   XS-      -  5        M(     g )Nr   r   )r'   append)Lr    is      r   blowupbench_R5.<locals>.blowup.   s3    qAHHqtaAh!E(24 r   c                     [        U 5      nU$ r-   )set)r   vs     r   uniqbench_R5.<locals>.uniq2   s    Fr      Nr   )r5   r:   r3   s      r   bench_R5r=   ,   s+    5 
Aq	A
1aLQAr   c                  :    [        S [        S5       5       5        g)z<sum(simplify((x+sin(i))/x+(x-sin(i))/x) for i in range(100))c              3      #    U  HA  n[        [        [        U5      -   [        -  [        [        U5      -
  [        -  -   5      v   MC     g 7fr-   )r   r   r
   ).0r4   s     r   	<genexpr>bench_R6.<locals>.<genexpr><   s5     F:a!c!f*a1s1v:q.011:s   A	Ad   N)sumr'   r.   r   r   bench_R6rE   :   s    F5:FFr   c                     [         S-  S[         S-  -  -   S[         S-  -  -   S[         S-  -  -   S[         S-  -  -   S	[         S
-  -  -   n [        S5       Vs/ s H   oR                  [         [        5       5      PM"       ngs  snf )z+[f.subs(x, random()) for _ in range(10**4)]   "      -   r   	      r&          '  N)r   r'   subsr   r)   s     r   bench_R7rQ   ?   sp    	21b52ad7"Qq"uW,r!R%x7"QU(BA"',/,QVVAvx,//s   'Bc                  .    S n U " [         S-  SSS5        g)zright(x^2,0,5,10^4)c                     [        U5      n[        U5      n[        U5      nU R                  [        5      R                  5       nX!-
  U-  nUnSn[	        U5       H  nXe-  nXpR                  XF5      -  nM     Xu-  $ )Nr   )r   atomsr   popr'   rP   )	r   abr    r   Deltaxcestr4   s	            r   rightbench_R8.<locals>.rightG   sw    AJAJAJGGFO!%qAKA66!<C  zr   r   r      rO   N)r   )r[   s    r   bench_R8r^   E   s     
!Q$1er   c                  P    [        [        S-  [        S-  [        S-  -  -
  5        g)zfactor(x^20 - pi^5*y^20)   r]   N)r   r   r   r   r.   r   r   	_bench_R9ra   W   s    
1b52q5B;r   c                  H    S n U " [         * [         [        S5      S-  5        g)zv = [-pi,-pi+1/10..,pi]c                     U /nXS   -
  R                  5       S:  a2  UR                  US   U-   5        XS   -
  R                  5       S:  a  M2  US S $ )Nr   )evalfr2   )minmaxstepr9   s       r   srangebench_R10.<locals>.srange^   sX    ErU{!!#a'HHQrUT\" rU{!!#a'"vr   r   r&   N)r   r   )ri   s    r   	bench_R10rk   \   s    
 B3GAJrM"r   c                  x    [        S5       V s/ s H  n [        5       [        5       [        -  -   PM!       n gs  sn f )z.a = [random() + random()*I for w in [0..1000]]i  N)r'   r   r   )ws    r   	bench_R11rn   f   s(    $)$K0KqVX
K00s   &7c                  f    [         [        -   [        -   S-   S-  n X S-   -  nUR                  5         g)z#e=(x+y+z+1)**7;f=e*(e+1);f.expand()r      N)r   r   r   r   )er   s     r   bench_S1rr   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$   r+   r/   r=   rE   rQ   r^   ra   rk   rn   rr   __name__
benchmarksreportrW   tprint__doc__r.   r   r   <module>r      s    $ / / $ & 9 8 ( ,   )8	&	
G
0$ 
#1
 zJ FG	GaKlajj!))Q778	 ! r   