Details

Time bar (total: 15.3s)

sample193.0ms

Algorithm
intervals
Results
58.0ms149×body160valid
41.0ms284×body80nan
34.0ms540×pre80true
22.0ms49×body320valid
9.0ms58×body80valid

simplify142.0ms

Counts
1 → 1
Iterations
IterNodes
done105
7105
6104
5102
494
377
244
125
014

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.8b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4 a) c)))
0.2b
(- (* b b) (* (* 4 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
36.1b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×fma-def add-cube-cbrt add-log-exp
9×add-cbrt-cube add-exp-log
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×neg-sub0 cbrt-undiv sum-log flip3-+ flip3-- sqrt-div div-exp associate-+l- flip-+ flip-- associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-/r* neg-mul-1 sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 94
Calls
4 calls:
18.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
16.0ms
(- (* b b) (* (* 4 a) c))
70.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
17.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))

series427.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
76.0ms
(- (* b b) (* (* 4 a) c))
119.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
128.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))

simplify1.1s

Counts
106 → 106
Iterations
IterNodes
done2000
32000
21454
1435
0166

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.2b

localize5.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
done0
00

prune82.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.2b

localize27.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (* a c) b)
0.2b
(/ (* -2 (/ (* a c) b)) (* 2 a))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
39×add-cbrt-cube add-exp-log
14×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
4×add-sqr-sqrt associate-/r* *-un-lft-identity times-frac add-cube-cbrt
2×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u div-inv associate-/l* add-log-exp
1×associate-*r/ associate-/l/
Counts
2 → 57
Calls
2 calls:
24.0ms
(/ (* a c) b)
37.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))

series49.0ms

Counts
2 → 6
Calls
2 calls:
27.0ms
(/ (* a c) b)
21.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))

simplify771.0ms

Counts
63 → 63
Iterations
IterNodes
done2004
22004
1346
0113

prune557.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 5.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b
(log1p (/ (* a c) b))
0.2b
(/ (* a c) b)
0.2b
(/ (* -2 (expm1 (log1p (/ (* a c) b)))) (* 2 a))
0.3b
(expm1 (log1p (/ (* a c) b)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
21×add-cbrt-cube add-exp-log
6×add-sqr-sqrt cbrt-undiv *-un-lft-identity div-exp add-cube-cbrt
5×expm1-log1p-u prod-exp cbrt-unprod
4×pow1 associate-/r* times-frac insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg div-inv associate-/l*
1×log1p-udef expm1-log1p log1p-expm1 expm1-udef
Counts
4 → 72
Calls
4 calls:
0.0ms
(log1p (/ (* a c) b))
10.0ms
(/ (* a c) b)
23.0ms
(/ (* -2 (expm1 (log1p (/ (* a c) b)))) (* 2 a))
1.0ms
(expm1 (log1p (/ (* a c) b)))

series349.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(log1p (/ (* a c) b))
36.0ms
(/ (* a c) b)
106.0ms
(/ (* -2 (expm1 (log1p (/ (* a c) b)))) (* 2 a))
120.0ms
(expm1 (log1p (/ (* a c) b)))

simplify1.2s

Counts
84 → 84
Iterations
IterNodes
done2009
32009
21781
1364
0146

prune739.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 5.1b

regimes1.2s

Accuracy

19.4% (5.2b remaining)

Error of 10.3b against oracle of 5.1b and baseline of 11.6b

bsearch6.0ms

simplify1.0s

Iterations
IterNodes
done2001
2162001
2151993
2141983
2131975
2121965
2111957
2101947
2091939
2081929
2071921
2061911
2051903
2041893
2031885
2021875
2011867
2001857
1991849
1981839
1971831
1961821
1951813
1941803
1931795
1921785
1911777
1901767
1891759
1881749
1871741
1861731
1851723
1841713
1831705
1821695
1811687
1801677
1791669
1781659
1771651
1761641
1751633
1741623
1731615
1721605
1711597
1701587
1691579
1681569
1671561
1661551
1651543
1641533
1631525
1621515
1611507
1601497
1591489
1581479
1571471
1561461
1551453
1541443
1531435
1521425
1511417
1501407
1491399
1481389
1471381
1461371
1451363
1441353
1431345
1421335
1411327
1401317
1391309
1381299
1371291
1361281
1351273
1341263
1331255
1321245
1311237
1301227
1291219
1281209
1271201
1261191
1251183
1241173
1231165
1221155
1211147
1201137
1191129
1181119
1171111
1161101
1151093
1141083
1131075
1121065
1111057
1101047
1091039
1081029
1071021
1061011
1051003
104993
103985
102975
101967
100957
99949
98939
97931
96921
95913
94903
93895
92885
91877
90867
89859
88849
87841
86831
85823
84813
83805
82795
81787
80777
79769
78759
77751
76741
75733
74723
73715
72705
71697
70687
69679
68669
67661
66651
65643
64633
63625
62615
61607
60597
59589
58579
57571
56561
55553
54543
53535
52525
51517
50507
49499
48489
47481
46471
45463
44453
43445
42435
41427
40417
39409
38399
37391
36381
35373
34363
33355
32345
31337
30327
29319
28309
27301
26291
25283
24273
23265
22255
21247
20237
19229
18219
17211
16201
15193
14183
13175
12165
11157
10147
9139
8129
7121
6113
5107
491
383
268
164
051

end0.0ms

sample5.9s

Algorithm
intervals
Results
1.9s4897×body160valid
1.3s8107×body80nan
1.1s16107×pre80true
695.0ms1380×body320valid
309.0ms1723×body80valid