Details

Time bar (total: 16.8s)

sample35.0ms

Algorithm
intervals
Results
13.0ms271×body80valid

simplify10.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
117
011

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize14.0ms

Local error

Found 1 expressions with local error:

22.6b
(/ (fma a c (* b d)) (fma d d (* c c)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
3×associate-/r* add-cbrt-cube add-exp-log associate-/l*
1×expm1-log1p-u pow1 cbrt-undiv clear-num frac-2neg div-exp log1p-expm1-u div-inv add-log-exp
Counts
1 → 29
Calls
1 calls:
6.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))

series132.0ms

Counts
1 → 3
Calls
1 calls:
132.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))

simplify2.2s

Counts
32 → 32
Iterations
IterNodes
done5000
44396
3906
2240
195
058

prune243.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 22.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
14.2b
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
27.1b
(sqrt (fma d d (* c c)))
27.1b
(sqrt (fma d d (* c c)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
160×add-sqr-sqrt
158×*-un-lft-identity add-cube-cbrt
150×sqrt-prod
25×associate-/l*
12×associate-/r*
11×add-cbrt-cube add-exp-log
9×div-inv
6×pow1
4×expm1-log1p-u cbrt-undiv div-exp log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 fma-udef hypot-def
1×associate-/l/
Counts
4 → 250
Calls
4 calls:
36.0ms
(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
9.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
3.0ms
(sqrt (fma d d (* c c)))
2.0ms
(sqrt (fma d d (* c c)))

series467.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
175.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
67.0ms
(sqrt (fma d d (* c c)))
83.0ms
(sqrt (fma d d (* c c)))

simplify1.7s

Counts
262 → 262
Iterations
IterNodes
done5000
22237
1565
0259

prune1.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot d c)
0.0b
(hypot d c)
0.1b
(/ (/ (fma c a (* b d)) (hypot d c)) (hypot d c))
14.2b
(/ (fma c a (* b d)) (hypot d c))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/l*
11×add-cbrt-cube add-exp-log
6×associate-/r* div-inv
4×expm1-log1p-u pow1 cbrt-undiv div-exp log1p-expm1-u add-log-exp
2×hypot-udef clear-num frac-2neg
1×associate-/l/
Counts
4 → 121
Calls
4 calls:
0.0ms
(hypot d c)
0.0ms
(hypot d c)
9.0ms
(/ (/ (fma c a (* b d)) (hypot d c)) (hypot d c))
4.0ms
(/ (fma c a (* b d)) (hypot d c))

series450.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(hypot d c)
87.0ms
(hypot d c)
149.0ms
(/ (/ (fma c a (* b d)) (hypot d c)) (hypot d c))
149.0ms
(/ (fma c a (* b d)) (hypot d c))

simplify1.4s

Counts
133 → 133
Iterations
IterNodes
done5000
21628
1355
0161

prune1.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (hypot d c))
0.3b
(fma b d (* c a))
0.3b
(* (/ 1 (hypot d c)) (/ (fma b d (* c a)) (hypot d c)))
14.2b
(/ (fma b d (* c a)) (hypot d c))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
43×times-frac
36×*-un-lft-identity
34×add-cube-cbrt
32×add-exp-log
20×add-cbrt-cube
13×associate-*r* associate-*l*
11×div-exp
8×prod-exp
7×pow1
6×cbrt-undiv associate-/r* associate-/l* unswap-sqr
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv add-log-exp
3×rec-exp 1-exp
2×clear-num frac-2neg
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative fma-udef pow-flip inv-pow
Counts
4 → 130
Calls
4 calls:
8.0ms
(/ 1 (hypot d c))
0.0ms
(fma b d (* c a))
31.0ms
(* (/ 1 (hypot d c)) (/ (fma b d (* c a)) (hypot d c)))
4.0ms
(/ (fma b d (* c a)) (hypot d c))

series650.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ 1 (hypot d c))
81.0ms
(fma b d (* c a))
299.0ms
(* (/ 1 (hypot d c)) (/ (fma b d (* c a)) (hypot d c)))
173.0ms
(/ (fma b d (* c a)) (hypot d c))

simplify2.2s

Counts
142 → 142
Iterations
IterNodes
done5001
23206
1405
0153

prune1.0s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 1.6b

regimes463.0ms

Accuracy

26.8% (10.8b remaining)

Error of 13.4b against oracle of 2.5b and baseline of 17.3b

bsearch89.0ms

Steps
ItersRangePoint
10
1.24073274788346e+181
2.9731570004810616e+193
1.5574364947325323e+181
4
-4.107403045473856e+168
-2.8943372089698357e+168
-3.1232252928212438e+168

simplify1.7s

Iterations
IterNodes
done5001
6204995
6194987
6184979
6174971
6164963
6154955
6144947
6134939
6124931
6114923
6104915
6094907
6084899
6074891
6064883
6054875
6044867
6034859
6024851
6014843
6004835
5994827
5984819
5974811
5964803
5954795
5944787
5934779
5924771
5914763
5904755
5894747
5884739
5874731
5864723
5854715
5844707
5834699
5824691
5814683
5804675
5794667
5784659
5774651
5764643
5754635
5744627
5734619
5724611
5714603
5704595
5694587
5684579
5674571
5664563
5654555
5644547
5634539
5624531
5614523
5604515
5594507
5584499
5574491
5564483
5554475
5544467
5534459
5524451
5514443
5504435
5494427
5484419
5474411
5464403
5454395
5444387
5434379
5424371
5414363
5404355
5394347
5384339
5374331
5364323
5354315
5344307
5334299
5324291
5314283
5304275
5294267
5284259
5274251
5264243
5254235
5244227
5234219
5224211
5214203
5204195
5194187
5184179
5174171
5164163
5154155
5144147
5134139
5124131
5114123
5104115
5094107
5084099
5074091
5064083
5054075
5044067
5034059
5024051
5014043
5004035
4994027
4984019
4974011
4964003
4953995
4943987
4933979
4923971
4913963
4903955
4893947
4883939
4873931
4863923
4853915
4843907
4833899
4823891
4813883
4803875
4793867
4783859
4773851
4763843
4753835
4743827
4733819
4723811
4713803
4703795
4693787
4683779
4673771
4663763
4653755
4643747
4633739
4623731
4613723
4603715
4593707
4583699
4573691
4563683
4553675
4543667
4533659
4523651
4513643
4503635
4493627
4483619
4473611
4463603
4453595
4443587
4433579
4423571
4413563
4403555
4393547
4383539
4373531
4363523
4353515
4343507
4333499
4323491
4313483
4303475
4293467
4283459
4273451
4263443
4253435
4243427
4233419
4223411
4213403
4203395
4193387
4183379
4173371
4163363
4153355
4143347
4133339
4123331
4113323
4103315
4093307
4083299
4073291
4063283
4053275
4043267
4033259
4023251
4013243
4003235
3993227
3983219
3973211
3963203
3953195
3943187
3933179
3923171
3913163
3903155
3893147
3883139
3873131
3863123
3853115
3843107
3833099
3823091
3813083
3803075
3793067
3783059
3773051
3763043
3753035
3743027
3733019
3723011
3713003
3702995
3692987
3682979
3672971
3662963
3652955
3642947
3632939
3622931
3612923
3602915
3592907
3582899
3572891
3562883
3552875
3542867
3532859
3522851
3512843
3502835
3492827
3482819
3472811
3462803
3452795
3442787
3432779
3422771
3412763
3402755
3392747
3382739
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3362723
3352715
3342707
3332699
3322691
3312683
3302675
3292667
3282659
3272651
3262643
3252635
3242627
3232619
3222611
3212603
3202595
3192587
3182579
3172571
3162563
3152555
3142547
3132539
3122531
3112523
3102515
3092507
3082499
3072491
3062483
3052475
3042467
3032459
3022451
3012443
3002435
2992427
2982419
2972411
2962403
2952395
2942387
2932379
2922371
2912363
2902355
2892347
2882339
2872331
2862323
2852315
2842307
2832299
2822291
2812283
2802275
2792267
2782259
2772251
2762243
2752235
2742227
2732219
2722211
2712203
2702195
2692187
2682179
2672171
2662163
2652155
2642147
2632139
2622131
2612123
2602115
2592107
2582099
2572091
2562083
2552075
2542067
2532059
2522051
2512043
2502035
2492027
2482019
2472011
2462003
2451995
2441987
2431979
2421971
2411963
2401955
2391947
2381939
2371931
2361923
2351915
2341907
2331899
2321891
2311883
2301875
2291867
2281859
2271851
2261843
2251835
2241827
2231819
2221811
2211803
2201795
2191787
2181779
2171771
2161763
2151755
2141747
2131739
2121731
2111723
2101715
2091707
2081699
2071691
2061683
2051675
2041667
2031659
2021651
2011643
2001635
1991627
1981619
1971611
1961603
1951595
1941587
1931579
1921571
1911563
1901555
1891547
1881539
1871531
1861523
1851515
1841507
1831499
1821491
1811483
1801475
1791467
1781459
1771451
1761443
1751435
1741427
1731419
1721411
1711403
1701395
1691387
1681379
1671371
1661363
1651355
1641347
1631339
1621331
1611323
1601315
1591307
1581299
1571291
1561283
1551275
1541267
1531259
1521251
1511243
1501235
1491227
1481219
1471211
1461203
1451195
1441187
1431179
1421171
1411163
1401155
1391147
1381139
1371131
1361123
1351115
1341107
1331099
1321091
1311083
1301075
1291067
1281059
1271051
1261043
1251035
1241027
1231019
1221011
1211003
120995
119987
118979
117971
116963
115955
114947
113939
112931
111923
110915
109907
108899
107891
106883
105875
104867
103859
102851
101843
100835
99827
98819
97811
96803
95795
94787
93779
92771
91763
90755
89747
88739
87731
86723
85715
84707
83699
82691
81683
80675
79667
78659
77651
76643
75635
74627
73619
72611
71603
70595
69587
68579
67571
66563
65555
64547
63539
62531
61523
60515
59507
58499
57491
56483
55475
54467
53459
52451
51443
50435
49427
48419
47411
46403
45395
44387
43379
42371
41363
40355
39347
38339
37331
36323
35315
34307
33299
32291
31283
30275
29267
28259
27251
26243
25235
24227
23219
22211
21203
20195
19187
18179
17171
16163
15155
14147
13139
12131
11123
10115
9107
899
791
683
575
467
357
243
132
023

end0.0ms

sample1.1s

Algorithm
intervals
Results
629.0ms8463×body80valid