Details

Time bar (total: 22.9s)

analyze5.0s (21.8%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
15.6%84.3%0.1%8
15.6%84.3%0.1%9
15.6%84.3%0.1%10
30.4%69.4%0.1%11
30.4%69.4%0.1%12
30.4%69.4%0.1%13
39.6%60.3%0.1%14
Compiler

Compiled 28 to 23 computations (17.9% saved)

sample4.9s (21.3%)

Results
2.6s2069×body1024valid
1.0s4680×body128valid
680.0ms992×body512valid
451.0ms510×body256valid
90.0msbody2048valid
1.0msbody512invalid
1.0msbody128invalid
Compiler

Compiled 56 to 46 computations (17.9% saved)

preprocess1.9s (8.2%)

Algorithm
egg-herbie
Rules
1796×sqr-pow_binary64
hypot-1-def_binary64
rem-sqrt-square_binary64
unpow1_binary64
unpow1/2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
047148
162128
281128
397128
4112128
5123128
6134128
7145128
8156128
9167128
10178128
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033
Stop Event
saturated
node limit
Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify2.3s (10.1%)

Algorithm
egg-herbie
Rules
996×sqr-pow_binary64
hypot-1-def_binary64
rem-sqrt-square_binary64
1-exp_binary64
unpow1_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01837
12432
23132
33832
44432
54932
65432
75932
86432
96932
107432
117932
128432
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853428932
854429432
855429932
856430432
857430932
858431432
859431932
860432432
861432932
862433432
863433932
864434432
865434932
866435432
867435932
868436432
869436932
870437432
871437932
872438432
873438932
874439432
875439932
876440432
877440932
878441432
879441932
880442432
881442932
882443432
883443932
884444432
885444932
886445432
887445932
888446432
889446932
890447432
891447932
892448432
893448932
894449432
895449932
896450432
897450932
898451432
899451932
900452432
901452932
902453432
903453932
904454432
905454932
906455432
907455932
908456432
909456932
910457432
911457932
912458432
913458932
914459432
915459932
916460432
917460932
918461432
919461932
920462432
921462932
922463432
923463932
924464432
925464932
926465432
927465932
928466432
929466932
930467432
931467932
932468432
933468932
934469432
935469932
936470432
937470932
938471432
939471932
940472432
941472932
942473432
943473932
944474432
945474932
946475432
947475932
948476432
949476932
950477432
951477932
952478432
953478932
954479432
955479932
956480432
957480932
958481432
959481932
960482432
961482932
962483432
963483932
964484432
965484932
966485432
967485932
968486432
969486932
970487432
971487932
972488432
973488932
974489432
975489932
976490432
977490932
978491432
979491932
980492432
981492932
982493432
983493932
984494432
985494932
986495432
987495932
988496432
989496932
990497432
991497932
992498432
993498932
994499432
995499932
Stop Event
node limit
Counts
1 → 2

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
6.8b
Counts
3 → 1
Alt Table
StatusErrorProgram
6.8b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))
Compiler

Compiled 96 to 76 computations (20.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))
0.1b
(*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))
0.1b
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))
6.4b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))

series159.0ms (0.7%)

Counts
4 → 120
Calls

30 calls:

24.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))
K
0
18.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))
K
-inf
18.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))
K
inf
8.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))
J
inf
6.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))
J
0

rewrite50.0ms (0.2%)

Algorithm
batch-egg-rewrite
Rules
352×log-prod_binary64
271×log-pow_binary64
265×expm1-udef_binary64
265×log1p-udef_binary64
248×pow3_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01671
128971
2288371
Stop Event
node limit
Counts
4 → 68

simplify487.0ms (2.1%)

Algorithm
egg-herbie
Rules
1679×sqr-pow_binary64
776×pow-sqr_binary64
105×cube-mult_binary64
105×unpow3_binary64
104×cube-prod_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02083233
13163233
23673233
34143233
44813233
55583233
66423233
77383233
88423233
99593233
1010823233
1112183233
1213623233
1315193233
1416833233
1518603233
1620433233
1722403233
1824443233
1924603233
2024683233
2124683233
2226813233
2328973233
2431343233
2533783233
2636353233
2738993233
2841763233
2942433233
3042513233
3142513233
3245303233
3348143233
Stop Event
node limit
Counts
188 → 135

prune129.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1305135
Fresh000
Picked011
Done000
Total1306136
Error
0.0b
Counts
136 → 6
Alt Table
StatusErrorProgram
34.7b
(pow.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) 2)
7.9b
(pow.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) 3)
6.8b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))
47.4b
U
51.1b
(*.f64 -1 U)
40.5b
(*.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 -2 J) 3) (pow.f64 (cos.f64 (/.f64 K 2)) 3))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))
Compiler

Compiled 4810 to 3601 computations (25.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))
0.5b
(cbrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
0.7b
(pow.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) 3)
6.4b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series1.6s (6.9%)

Counts
3 → 76
Calls

27 calls:

192.0ms
(pow.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) 3)
K
-inf
174.0ms
(pow.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) 3)
K
inf
168.0ms
(pow.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) 3)
K
0
160.0ms
(cbrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
K
inf
158.0ms
(cbrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
K
-inf

rewrite55.0ms (0.2%)

Algorithm
batch-egg-rewrite
Rules
396×log-prod_binary64
298×log-pow_binary64
292×expm1-udef_binary64
292×log1p-udef_binary64
167×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01998
134898
2331098
Stop Event
node limit
Counts
3 → 61

simplify617.0ms (2.7%)

Algorithm
egg-herbie
Rules
1701×sqr-pow_binary64
452×pow-sqr_binary64
85×cube-mult_binary64
85×unpow3_binary64
80×cube-prod_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03755483
15785483
26955483
38105483
49445483
510875483
612375483
713995483
815705483
917545483
1019445483
1121475483
1223585483
1325825483
1426285483
1526665483
1626905483
1726905483
1828845483
1930845483
2033415483
2136005483
2238725483
2341515483
2444435483
2547425483
2647585483
2747665483
2847665483
Stop Event
node limit
Counts
137 → 120

prune178.0ms (0.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1430143
Fresh044
Picked011
Done011
Total1436149
Error
0.0b
Counts
149 → 6
Alt Table
StatusErrorProgram
34.7b
(pow.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) 2)
7.9b
(pow.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) 3)
6.8b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))
47.4b
U
51.1b
(*.f64 -1 U)
40.5b
(*.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 -2 J) 3) (pow.f64 (cos.f64 (/.f64 K 2)) 3))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))
Compiler

Compiled 7373 to 5632 computations (23.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))
0.1b
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))
0.3b
(pow.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) 2)
6.4b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series191.0ms (0.8%)

Counts
2 → 44
Calls

15 calls:

78.0ms
(pow.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) 2)
K
0
26.0ms
(pow.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) 2)
K
inf
24.0ms
(pow.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) 2)
K
-inf
12.0ms
(pow.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) 2)
U
0
11.0ms
(pow.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) 2)
J
0

rewrite41.0ms (0.2%)

Algorithm
batch-egg-rewrite
Rules
376×log-prod_binary64
291×log-pow_binary64
278×expm1-udef_binary64
278×log1p-udef_binary64
160×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01844
133244
2312644
Stop Event
node limit
Counts
2 → 35

simplify359.0ms (1.6%)

Algorithm
egg-herbie
Rules
1675×sqr-pow_binary64
732×pow-sqr_binary64
105×cube-mult_binary64
105×unpow3_binary64
104×cube-prod_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01862065
12771965
23441955
34141955
44931955
55781955
66701955
77741955
88861955
910111955
1011421955
1112861955
1214371955
1316021955
1417741955
1519591955
1621501955
1723551955
1823711955
1923791955
2023791955
2125871955
2228041955
2330361955
2432811955
2535331955
2637981955
2740701955
2843551955
2943711955
3043791955
3143791955
3246671955
3349641955
Stop Event
node limit
Counts
79 → 69

prune160.0ms (0.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1471148
Fresh123
Picked011
Done022
Total1486154
Error
0.0b
Counts
154 → 6
Alt Table
StatusErrorProgram
34.7b
(pow.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) 2)
7.9b
(pow.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) 3)
6.8b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))
47.4b
U
51.1b
(neg.f64 U)
40.5b
(*.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 -2 J) 3) (pow.f64 (cos.f64 (/.f64 K 2)) 3))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))
Compiler

Compiled 6649 to 4865 computations (26.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))
0.4b
(pow.f64 (cos.f64 (/.f64 K 2)) 3)
6.4b
(*.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 -2 J) 3) (pow.f64 (cos.f64 (/.f64 K 2)) 3))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))
38.0b
(cbrt.f64 (*.f64 (pow.f64 (*.f64 -2 J) 3) (pow.f64 (cos.f64 (/.f64 K 2)) 3)))

series279.0ms (1.2%)

Counts
3 → 72
Calls

18 calls:

37.0ms
(*.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 -2 J) 3) (pow.f64 (cos.f64 (/.f64 K 2)) 3))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))
K
0
36.0ms
(*.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 -2 J) 3) (pow.f64 (cos.f64 (/.f64 K 2)) 3))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))
K
inf
35.0ms
(*.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 -2 J) 3) (pow.f64 (cos.f64 (/.f64 K 2)) 3))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))
K
-inf
26.0ms
(cbrt.f64 (*.f64 (pow.f64 (*.f64 -2 J) 3) (pow.f64 (cos.f64 (/.f64 K 2)) 3)))
J
0
23.0ms
(cbrt.f64 (*.f64 (pow.f64 (*.f64 -2 J) 3) (pow.f64 (cos.f64 (/.f64 K 2)) 3)))
J
inf

rewrite45.0ms (0.2%)

Algorithm
batch-egg-rewrite
Rules
329×log-pow_binary64
316×expm1-udef_binary64
316×log1p-udef_binary64
184×add-sqr-sqrt_binary64
173×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02053
137453
2366453
Stop Event
node limit
Counts
3 → 50

simplify434.0ms (1.9%)

Algorithm
egg-herbie
Rules
1679×sqr-pow_binary64
776×pow-sqr_binary64
105×cube-mult_binary64
105×unpow3_binary64
104×cube-prod_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02072838
13002838
23422838
33882838
44542838
55322838
66152838
77112838
88142838
99312838
1010542838
1111902838
1213332838
1314902838
1416542838
1518312838
1620152838
1722112838
1824152838
1924312838
2024392838
2124392838
2226522838
2328682838
2431052838
2533492838
2636062838
2738702838
2841472838
2942142838
3042222838
3142222838
3245012838
3347852838
Stop Event
node limit
Counts
122 → 118

prune901.0ms (3.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1411142
Fresh022
Picked101
Done033
Total1426148
Error
0.0b
Counts
148 → 6
Alt Table
StatusErrorProgram
6.8b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))
40.6b
(*.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 -2 J) 3) (*.f64 (cos.f64 (/.f64 K 2)) (+.f64 1/2 (*.f64 1/2 (cos.f64 K)))))) (hypot.f64 1 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))
34.7b
(pow.f64 (sqrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) 2)
7.9b
(pow.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))) 3)
47.4b
U
51.1b
(neg.f64 U)
Compiler

Compiled 5438 to 4246 computations (21.9% saved)

regimes2.8s (12.3%)

Accuracy

Total 9.2b remaining (99.5%)

Threshold costs 0b (0%)

Counts
65 → 3
Compiler

Compiled 9566 to 7878 computations (17.6% saved)

bsearch167.0ms (0.7%)

Algorithm
binary-search
Calls

2 calls:

89.0ms
J
75.0ms
J
Steps
ItersPointRange
1.7426832413312863e-211
∈ [
1.641168146779419e-211
,
6.373044783174535e-205
]
-4.408789605579126e-200
∈ [
-2.0378593241815798e-191
,
-1.1350617092662925e-200
]
Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02377
12577
Stop Event
saturated

end137.0ms (0.6%)

Stop Event
fuel
Compiler

Compiled 229 to 180 computations (21.4% saved)

Profiling

Loading profile data...