Details

Time bar (total: 10.0m)

sample209.0ms

Algorithm
intervals
Results
20.0ms40×body2560valid
15.0ms183×body80valid
14.0ms35×body1280valid
9.0ms79×body80nan
5.0ms16×body640valid
1.0ms2×body5120valid
1.0ms5×body160valid
0.0ms2×body320valid

simplify41.0ms

Counts
1 → 1
Iterations
IterNodes
done29
529
427
325
222
114
010

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b
(- (* b_2 b_2) (* a c))
1.1b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
16×add-sqr-sqrt
15×times-frac add-cube-cbrt
10×distribute-lft-out add-log-exp
6×add-cbrt-cube add-exp-log
5×pow1 distribute-rgt-neg-in associate-/l*
3×associate-/r* sqrt-prod
2×neg-sub0 sum-log flip3-+ flip3-- sqrt-div associate-+l- flip-+ flip-- associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp neg-log div-inv
Counts
4 → 80
Calls
4 calls:
95.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
25.0ms
(- (* b_2 b_2) (* a c))
39.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series370.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
58.0ms
(- (* b_2 b_2) (* a c))
101.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
102.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify660.0ms

Counts
92 → 92
Iterations
IterNodes
done5000
21560
1378
0151

prune456.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.7b

localize39.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.5b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
7.8b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
186×times-frac
158×add-sqr-sqrt
157×*-un-lft-identity
89×add-cube-cbrt
34×distribute-lft-out-- difference-of-squares
30×associate-/l*
20×sqrt-prod
17×distribute-rgt-neg-in
11×add-cbrt-cube add-exp-log
10×associate-/r* associate-/r/
8×add-log-exp
7×flip3-- flip--
6×div-inv
5×pow1
4×cbrt-undiv div-exp
3×associate-/l/
2×clear-num frac-2neg sqrt-div diff-log
1×associate--l- neg-sub0 rem-sqrt-square sub-neg sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 206
Calls
4 calls:
18.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
70.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
92.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series694.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
201.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
288.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
77.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts
218 → 218
Iterations
IterNodes
done5001
24229
1777
0307

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.6b

localize40.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.2b
(sqrt (- (* b_2 b_2) (* a c)))
24.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×*-un-lft-identity
8×sqrt-prod add-log-exp
6×pow1 add-cube-cbrt
4×flip3-- add-cbrt-cube sqrt-div add-exp-log flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
41.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
45.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series398.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
124.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
85.0ms
(sqrt (- (* b_2 b_2) (* a c)))
103.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts
72 → 72
Iterations
IterNodes
done5000
33680
2717
1191
078

prune470.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b_2 b_2) (* c a))
1.6b
(+ b_2 (sqrt (- (* b_2 b_2) (* c a))))
14.5b
(/ (+ 0 (* a c)) (* (- (+ b_2 (sqrt (- (* b_2 b_2) (* c a))))) a))
24.2b
(sqrt (- (* b_2 b_2) (* c a)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity add-cbrt-cube add-exp-log
8×add-sqr-sqrt add-log-exp
7×add-cube-cbrt
5×pow1
3×flip3-+ times-frac sqrt-prod flip-+ associate-/l*
2×cbrt-undiv flip3-- sqrt-div div-exp associate-*l/ associate-/r/ flip-- distribute-neg-frac associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-/r* sum-log sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log prod-exp cbrt-unprod div-inv distribute-lft-out
Counts
4 → 64
Calls
4 calls:
12.0ms
(- (* b_2 b_2) (* c a))
19.0ms
(+ b_2 (sqrt (- (* b_2 b_2) (* c a))))
63.0ms
(/ (+ 0 (* a c)) (* (- (+ b_2 (sqrt (- (* b_2 b_2) (* c a))))) a))
9.0ms
(sqrt (- (* b_2 b_2) (* c a)))

series510.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(- (* b_2 b_2) (* c a))
127.0ms
(+ b_2 (sqrt (- (* b_2 b_2) (* c a))))
208.0ms
(/ (+ 0 (* a c)) (* (- (+ b_2 (sqrt (- (* b_2 b_2) (* c a))))) a))
115.0ms
(sqrt (- (* b_2 b_2) (* c a)))

simplify1.7s

Counts
76 → 76
Iterations
IterNodes
done5000
22935
1434
0153

prune490.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.6b

regimes379.0ms

bsearch278.0ms

Steps
ItersRangePoint
5
3.2290769646163133e+91
1.2231553772410281e+92
3.2953985246168684e+91
5
20118063.614914328
50368582.18160708
40129468.05228401
8
7.330240579218375e-87
2.2788496293637407e-84
7.395307770437281e-87
5
-4.0529501114613944e+21
-1.3554105129294137e+21
-3.9950858563514354e+21

simplify9.8m

Iterations
IterNodes
2663250
2653238
2643226
2633214
2623202
2613190
2603178
2593166
2583154
2573142
2563130
2553118
2543106
2533094
2523082
2513070
2503058
2493046
2483034
2473022
2463010
2452998
2442986
2432974
2422962
2412950
2402938
2392926
2382914
2372902
2362890
2352878
2342866
2332854
2322842
2312830
2302818
2292806
2282794
2272782
2262770
2252758
2242746
2232734
2222722
2212710
2202698
2192686
2182674
2172662
2162650
2152638
2142626
2132614
2122602
2112590
2102578
2092566
2082554
2072542
2062530
2052518
2042506
2032494
2022482
2012470
2002458
1992446
1982434
1972422
1962410
1952398
1942386
1932374
1922362
1912350
1902338
1892326
1882314
1872302
1862290
1852278
1842266
1832254
1822242
1812230
1802218
1792206
1782194
1772182
1762170
1752158
1742146
1732134
1722122
1712110
1702098
1692086
1682074
1672062
1662050
1652038
1642026
1632014
1622002
1611990
1601978
1591966
1581954
1571942
1561930
1551918
1541906
1531894
1521882
1511870
1501858
1491846
1481834
1471822
1461810
1451798
1441786
1431774
1421762
1411750
1401738
1391726
1381714
1371702
1361690
1351678
1341666
1331654
1321642
1311630
1301618
1291606
1281594
1271582
1261570
1251558
1241546
1231534
1221522
1211510
1201498
1191486
1181474
1171462
1161450
1151438
1141426
1131414
1121402
1111390
1101378
1091366
1081354
1071342
1061330
1051318
1041306
1031294
1021282
1011270
1001258
991246
981234
971222
961210
951198
941186
931174
921162
911150
901138
891126
881114
871102
861090
851078
841066
831054
821042
811030
801018
791006
78994
77982
76970
75958
74946
73934
72922
71910
70898
69886
68874
67862
66850
65838
64826
63814
62802
61790
60778
59766
58754
57742
56730
55718
54706
53694
52682
51670
50658
49646
48634
47622
46610
45598
44586
43574
42562
41550
40538
39526
38514
37502
36490
35478
34466
33454
32442
31430
30418
29406
28394
27382
26370
25358
24346
23334
22322
21310
20298
19286
18274
17262
16250
15238
14226
13214
12202
11190
10178
9166
8154
7142
6130
5118
4106
394
277
163
047