§
    OŠtjµ  ã            	       ó‚  — d dl mZ d dlmZmZmZ d dlmZ d dlm	Z	 d dl
mZ d dlmZ d dlmZ d dlmZ d d	lmZmZmZ d d
lmZ d„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z d„ Z!d„ Z"d„ Z#d„ Z$e%dk    rNeeeeeee e"e#g	Z&g Z'e&D ]@Z( e¦   «         Z) e(¦   «           e¦   «         e)z
  Z) e*de(j%        e(j+        e)fz  ¦  «         Œ?dS dS )é    )Úrandom)ÚIÚIntegerÚpi)ÚSymbol)Úsympify)Úsqrt)Úsin)Úfactor)Úsimplify©ÚxÚyÚz)Údefault_timerc                  ó  — d„ }  |  |  |  |  |  |  |  |  |  | t           dz  ¦  «        ¦  «        ¦  «        ¦  «        ¦  «        ¦  «        ¦  «        ¦  «        ¦  «        ¦  «                             ¦   «         d          dS )z'real(f(f(f(f(f(f(f(f(f(f(i/2)))))))))))c                 ób   — t          t          d¦  «        dz  ¦  «        | dz  z  t          dz  z   S )Né   é   é   )r	   r   r   )r   s    ú]/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/sympy/benchmarks/bench_symbench.pyÚfzbench_R1.<locals>.f   s,   € Ý•G˜A‘J”J˜q‘LÑ!Ô! ! Q¡$Ñ&­¨1©Ñ,Ð,ó    r   r   N)r   Úas_real_imag©r   s    r   Úbench_R1r      sŽ   € ð-ð -ð -à€A€a€aˆˆˆ!ˆ!ˆAˆAˆaˆa���!�!�A�A�a�a�˜!™‘f”f‘I”I‘,”,‘”Ñ Ô Ñ!Ô!Ñ
"Ô
"Ñ#Ô#Ñ$Ô$Ñ%Ô%×2Ò2Ñ4Ô4°QÔ7Ð7Ð7Ð7r   c                  ó4   ‡ — ˆ fd„Š  ‰ dt           ¦  «         dS )z!Hermite polynomial hermite(15, y)c                 óª   •— | dk    rd|z  S | dk    rdS d|z   ‰| dz
  |¦  «        z  d| dz
  z   ‰| dz
  |¦  «        z  z
                        ¦   «         S )Nr   r   r   )Úexpand)Únr   Úhermites     €r   r!   zbench_R2.<locals>.hermite   sp   ø€ Ø�Š6ˆ6Ø�Q‘3ˆJØ�Š6ˆ6Ø�1Ø�!‘�G�G˜A ™E 1Ñ%Ô%Ñ%¨¨1¨q©5©	°'°'¸!¸a¹%ÀÑ2CÔ2CÑ(CÑC×KÒKÑMÔMÐMr   é   N)r   )r!   s   @r   Úbench_R2r#      s6   ø€ ðNð Nð Nð Nð Nð €GˆB•�N„N€N€N€Nr   c                  ól   ‡ — t           t          z   t          z   Š ˆ fd„t          d¦  «        D ¦   «          dS )z#a = [bool(f==f) for _ in range(10)]c                 ó6   •— g | ]}t          ‰‰k    ¦  «        ‘ŒS © )Úbool©Ú.0Ú_r   s     €r   ú
<listcomp>zbench_R3.<locals>.<listcomp>$   s#   ø€ Ð%Ð%Ð%�a…Tˆ!ˆqŠ&�\„\Ð%Ð%Ð%r   é
   N)r   r   r   Úranger   s   @r   Úbench_R3r.   !   s6   ø€ å	�A‰•‰	€AØ%Ð%Ð%Ð%�5 ™9œ9Ð%Ñ%Ô%Ð%Ð%Ð%r   c                  ó   — d S ©Nr&   r&   r   r   Úbench_R4r1   '   s   € à€Dr   c                  óh   — d„ } d„ }t           t          t          g} | |d¦  «          ||¦  «        }dS )zblowup(L, 8); L=uniq(L)c                 ó�   — t          |¦  «        D ]5}|                      | |         | |dz            z   | |dz            z  ¦  «         Œ6d S )Nr   r   )r-   Úappend)ÚLr    Úis      r   Úblowupzbench_R5.<locals>.blowup.   sS   € Ý�q‘”ð 	5ð 	5ˆAØ�HŠH�q˜”t˜a  A¡œh‘¨!¨A°©E¬(Ñ2Ñ4Ô4Ð4Ð4ð	5ð 	5r   c                 ó$   — t          | ¦  «        }|S r0   )Úset)r   Úvs     r   Úuniqzbench_R5.<locals>.uniq2   s   € Ý�‰FŒFˆØˆr   é   Nr   )r7   r;   r5   s      r   Úbench_R5r=   ,   sM   € ð5ð 5ð 5ðð ð õ 
�A�qˆ	€AØ
€Fˆ1ˆa�L„L€LØˆˆQ‰Œ€A€A€Ar   c                  óR   — t          d„ t          d¦  «        D ¦   «         ¦  «         dS )z<sum(simplify((x+sin(i))/x+(x-sin(i))/x) for i in range(100))c              3   ó®   K  — | ]P}t          t          t          |¦  «        z   t          z  t          t          |¦  «        z
  t          z  z   ¦  «        V — ŒQd S r0   )r   r   r
   )r)   r6   s     r   ú	<genexpr>zbench_R6.<locals>.<genexpr><   sK   è è € ÐFÐF°a�•!•c˜!‘f”f‘*�a‘¥1¥s¨1¡v¤v¡:­q¡.Ñ0Ñ1Ô1ÐFÐFÐFÐFÐFÐFr   éd   N)Úsumr-   r&   r   r   Úbench_R6rC   :   s+   € åÐFÐF½5À¹:¼:ÐFÑFÔFÑFÔFÐFÐFÐFr   c                  óÞ   ‡ — t           dz  dt           dz  z  z   dt           dz  z  z   dt           dz  z  z   dt           dz  z  z   d	t           d
z  z  z   Š ˆ fd„t          d¦  «        D ¦   «          dS )z+[f.subs(x, random()) for _ in range(10**4)]é   é"   é   é-   r   é	   é   r,   é    é   c                 ó^   •— g | ])}‰                      t          t          ¦   «         ¦  «        ‘Œ*S r&   )Úsubsr   r   r(   s     €r   r+   zbench_R7.<locals>.<listcomp>B   s+   ø€ Ð/Ð/Ð/˜Q€Q‡V‚V�A�v‰xŒxÑÔÐ/Ð/Ð/r   é'  N)r   r-   r   s   @r   Úbench_R7rP   ?   ss   ø€ å	ˆ2‰�•1�b‘5‘Ñ˜2�a ™d™7Ñ" Q¥q¨"¡u¡WÑ,¨rµ!°R±%©xÑ7¸"½QÀ¹U¹(ÑB€AØ/Ð/Ð/Ð/¥%¨¡,¤,Ð/Ñ/Ô/Ð/Ð/Ð/r   c                  ó8   — d„ }  | t           dz  ddd¦  «         dS )zright(x^2,0,5,10^4)c                 ó6  — t          |¦  «        }t          |¦  «        }t          |¦  «        }|                      t          ¦  «                             ¦   «         }||z
  |z  }|}d}t	          |¦  «        D ] }||z  }||                      ||¦  «        z  }Œ!||z  S )Nr   )r   Úatomsr   Úpopr-   rN   )	r   ÚaÚbr    r   ÚDeltaxÚcÚestr6   s	            r   Úrightzbench_R8.<locals>.rightG   s•   € Ý�A‰JŒJˆÝ�A‰JŒJˆÝ�A‰JŒJˆØ�GŠG•F‰OŒO×ÒÑ!Ô!ˆØ�a‘%˜‘ˆØˆØˆÝ�q‘”ð 	 ð 	 ˆAØ�‰KˆAØ�1—6’6˜!˜Q‘<”<ÑˆCˆCØ�6‰zÐr   r   r   é   rO   N)r   )rZ   s    r   Úbench_R8r\   E   s3   € ðð ð ð 
€E�!ˆQ‰$��1�eÑÔÐÐÐr   c                  ó`   — t          t          dz  t          dz  t          dz  z  z
  ¦  «         dS )zfactor(x^20 - pi^5*y^20)é   r[   N)r   r   r   r   r&   r   r   Ú	_bench_R9r_   W   s+   € å
�1ˆb‰5•2�q‘5�˜B™‘;ÑÑÔÐÐÐr   c                  ó\   — d„ }  | t            t           t          d¦  «        dz  ¦  «         dS )zv = [-pi,-pi+1/10..,pi]c                 óÜ   — | g}||d         z
                        ¦   «         dk    r?|                     |d         |z   ¦  «         ||d         z
                        ¦   «         dk    °?|d d…         S )Néÿÿÿÿr   )Úevalfr4   )ÚminÚmaxÚstepr:   s       r   Úsrangezbench_R10.<locals>.srange^   sp   € ØˆEˆØ�Q�r”U‰{×!Ò!Ñ#Ô# aÒ'Ð'Ø�HŠH�Q�r”U˜T‘\Ñ"Ô"Ð"ð �Q�r”U‰{×!Ò!Ñ#Ô# aÒ'Ð'à��"�Œvˆr   r   r,   N)r   r   )rg   s    r   Ú	bench_R10rh   \   s9   € ðð ð ð
 €F�Bˆ3••G˜A‘J”J˜r‘MÑ"Ô"Ð"Ð"Ð"r   c                  ó8   — d„ t          d¦  «        D ¦   «          dS )z.a = [random() + random()*I for w in [0..1000]]c                 óX   — g | ]'}t          ¦   «         t          ¦   «         t          z  z   ‘Œ(S r&   )r   r   )r)   Úws     r   r+   zbench_R11.<locals>.<listcomp>h   s)   € Ð0Ð0Ð0˜q…V�X„X•‘”�‘
ÑÐ0Ð0Ð0r   iè  N)r-   r&   r   r   Ú	bench_R11rl   f   s"   € à0Ð0¥E¨$¡K¤KÐ0Ñ0Ô0Ð0Ð0Ð0r   c                  óx   — t           t          z   t          z   dz   dz  } | | dz   z  }|                     ¦   «          dS )z#e=(x+y+z+1)**7;f=e*(e+1);f.expand()r   é   N)r   r   r   r   )Úer   s     r   Úbench_S1rp   k   s6   € å	
�Q‰•‰�Q‰˜Ñ€AØ	ˆ1ˆq‰5‰	€AØ‡H‚H�J„J€J€J€Jr   Ú__main__z
%s%65s: %fN),Úsympy.core.randomr   Úsympy.core.numbersr   r   r   Úsympy.core.symbolr   Úsympy.core.sympifyr   Ú(sympy.functions.elementary.miscellaneousr	   Ú(sympy.functions.elementary.trigonometricr
   Úsympy.polys.polytoolsr   Úsympy.simplify.simplifyr   Ú	sympy.abcr   r   r   Útimeitr   Úclockr   r#   r.   r1   r=   rC   rP   r\   r_   rh   rl   rp   Ú__name__Ú
benchmarksÚreportrV   ÚtÚprintÚ__doc__r&   r   r   ú<module>rƒ      s'  ðà $Ð $Ð $Ð $Ð $Ð $Ø /Ð /Ð /Ð /Ð /Ð /Ð /Ð /Ð /Ð /Ø $Ð $Ð $Ð $Ð $Ð $Ø &Ð &Ð &Ð &Ð &Ð &Ø 9Ð 9Ð 9Ð 9Ð 9Ð 9Ø 8Ð 8Ð 8Ð 8Ð 8Ð 8Ø (Ð (Ð (Ð (Ð (Ð (Ø ,Ð ,Ð ,Ð ,Ð ,Ð ,Ø Ð Ð Ð Ð Ð Ð Ð Ð Ð Ø )Ð )Ð )Ð )Ð )Ð )ð8ð 8ð 8ð	ð 	ð 	ð&ð &ð &ð	ð 	ð 	ð
ð ð ðGð Gð Gð
0ð 0ð 0ðð ð ð$ ð  ð  ð
#ð #ð #ð1ð 1ð 1ð
ð ð ð ˆzÒÐàØØØØØØàØð€Jð €FØð 9ð 9ˆØˆE‰GŒGˆØ	ˆ‰ŒˆØˆE‰GŒG�a‰KˆØˆˆl˜aœj¨!¬)°QÐ7Ñ7Ñ8Ô8Ð8Ð8ð) Ðð 9ð 9r   