Details

Time bar (total: 1.9m)

sample48.0ms

Algorithm
intervals
Results
10.0ms189×body80valid
8.0ms25×body2560valid
6.0ms23×body1280valid
6.0ms256×pre80true
2.0ms10×body640valid
1.0ms2×body5120valid
0.0ms3×body320valid
0.0ms4×body160valid

simplify1.7m

Counts
1 → 1
Iterations
IterNodes
done5001
4854999
4844966
4834959
4824927
4814921
4804891
4794885
4784855
4774849
4764825
4754819
4744794
4734788
4724761
4714755
4704730
4694724
4684703
4674697
4664678
4654672
4644651
4634645
4624624
4614618
4604598
4594592
4584572
4574566
4564548
4554542
4544525
4534519
4524502
4514496
4504479
4494473
4484457
4474451
4464435
4454429
4444413
4434406
4424390
4414384
4404368
4394362
4384346
4374340
4364324
4354318
4344302
4334296
4324280
4314274
4304259
4294253
4284238
4274232
4264217
4254211
4244196
4234190
4224177
4214171
4204158
4194152
4184139
4174133
4164120
4154114
4144101
4134095
4124082
4114076
4104063
4094057
4084044
4074038
4064025
4054019
4044006
4034000
4023987
4013981
4003968
3993962
3983949
3973943
3963930
3953924
3943911
3933905
3923892
3913886
3903873
3893867
3883854
3873848
3863835
3853829
3843816
3833810
3823797
3813791
3803778
3793772
3783759
3773753
3763740
3753734
3743721
3733715
3723702
3713696
3703683
3693677
3683664
3673658
3663645
3653639
3643626
3633620
3623607
3613601
3603588
3593582
3583569
3573563
3563550
3553544
3543531
3533525
3523512
3513506
3503493
3493487
3483474
3473468
3463455
3453449
3443436
3433430
3423417
3413411
3403398
3393392
3383379
3373373
3363360
3353354
3343341
3333335
3323322
3313316
3303303
3293297
3283284
3273278
3263265
3253259
3243246
3233240
3223227
3213221
3203208
3193202
3183189
3173183
3163170
3153164
3143151
3133145
3123132
3113126
3103113
3093107
3083094
3073088
3063075
3053069
3043056
3033050
3023037
3013031
3003018
2993012
2982999
2972993
2962980
2952974
2942961
2932955
2922942
2912936
2902923
2892917
2882904
2872898
2862885
2852879
2842866
2832860
2822847
2812841
2802828
2792822
2782809
2772803
2762790
2752784
2742771
2732765
2722752
2712746
2702733
2692727
2682714
2672708
2662695
2652689
2642676
2632670
2622657
2612651
2602638
2592632
2582619
2572613
2562600
2552594
2542581
2532575
2522562
2512556
2502543
2492537
2482524
2472518
2462505
2452499
2442486
2432480
2422467
2412461
2402448
2392442
2382429
2372423
2362410
2352404
2342391
2332385
2322372
2312366
2302353
2292347
2282334
2272328
2262315
2252309
2242296
2232290
2222277
2212271
2202258
2192252
2182239
2172233
2162220
2152214
2142201
2132195
2122182
2112176
2102163
2092157
2082144
2072138
2062125
2052119
2042106
2032100
2022087
2012081
2002068
1992062
1982049
1972043
1962030
1952024
1942011
1932005
1921992
1911986
1901973
1891967
1881954
1871948
1861935
1851929
1841916
1831910
1821897
1811891
1801878
1791872
1781859
1771853
1761840
1751834
1741821
1731815
1721802
1711796
1701783
1691777
1681764
1671758
1661745
1651739
1641726
1631720
1621707
1611701
1601688
1591682
1581669
1571663
1561650
1551644
1541631
1531625
1521612
1511606
1501593
1491587
1481574
1471568
1461555
1451549
1441536
1431530
1421517
1411511
1401498
1391492
1381479
1371473
1361460
1351454
1341441
1331435
1321422
1311416
1301403
1291397
1281384
1271378
1261365
1251359
1241346
1231340
1221327
1211321
1201308
1191302
1181289
1171283
1161270
1151264
1141251
1131245
1121232
1111226
1101213
1091207
1081194
1071188
1061175
1051169
1041156
1031150
1021137
1011131
1001118
991112
981099
971093
961080
951074
941061
931055
921042
911036
901023
891017
881004
87998
86985
85979
84966
83960
82947
81941
80928
79922
78909
77903
76890
75884
74871
73865
72852
71846
70833
69827
68814
67808
66795
65789
64776
63770
62757
61751
60738
59732
58719
57713
56700
55694
54681
53675
52662
51656
50643
49637
48624
47618
46605
45599
44586
43580
42567
41561
40548
39542
38529
37523
36510
35504
34491
33485
32472
31466
30453
29447
28434
27428
26415
25409
24396
23390
22377
21371
20358
19352
18339
17333
16320
15314
14301
13295
12282
11276
10263
9257
8244
7229
6217
5190
4147
395
258
130
014

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (fma p (* 4 p) (* x x))))
0.0b
(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
1.0b
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
15.2b
(sqrt (fma p (* 4 p) (* x x)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
4 → 85
Calls
4 calls:
4.0ms
(/ x (sqrt (fma p (* 4 p) (* x x))))
1.0ms
(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
0.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
1.0ms
(sqrt (fma p (* 4 p) (* x x)))

series356.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ x (sqrt (fma p (* 4 p) (* x x))))
183.0ms
(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
70.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
50.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify1.5s

Counts
97 → 97
Iterations
IterNodes
done5007
42916
3868
2329
1166
0110

prune357.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))))
1.0b
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
1.1b
(log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
15.2b
(sqrt (fma p (* 4 p) (* x x)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×sqrt-prod
9×*-un-lft-identity add-cube-cbrt
8×pow1 log-pow
6×exp-prod
4×expm1-log1p-u log-prod add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
1×rem-log-exp exp-sum
Counts
4 → 66
Calls
4 calls:
3.0ms
(sqrt (log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))))
0.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
2.0ms
(log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
1.0ms
(sqrt (fma p (* 4 p) (* x x)))

series374.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(sqrt (log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))))
71.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
72.0ms
(log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
50.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify1.5s

Counts
78 → 78
Iterations
IterNodes
done5011
52046
4571
3261
2171
1121
091

prune358.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.5b

localize43.0ms

Local error

Found 4 expressions with local error:

1.1b
(log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
15.2b
(sqrt (fma p (* 4 p) (* x x)))
15.2b
(sqrt (fma p (* 4 p) (* x x)))
15.2b
(sqrt (fma p (* 4 p) (* x x)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt sqrt-prod
8×pow1
4×expm1-log1p-u log-prod add-cbrt-cube add-exp-log log-pow insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square exp-prod sqrt-pow1 pow1/2
1×rem-log-exp exp-sum fma-udef
Counts
4 → 67
Calls
4 calls:
2.0ms
(log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
1.0ms
(sqrt (fma p (* 4 p) (* x x)))
1.0ms
(sqrt (fma p (* 4 p) (* x x)))
1.0ms
(sqrt (fma p (* 4 p) (* x x)))

series211.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(log (exp (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
46.0ms
(sqrt (fma p (* 4 p) (* x x)))
48.0ms
(sqrt (fma p (* 4 p) (* x x)))
46.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify2.0s

Counts
79 → 79
Iterations
IterNodes
done5000
53232
41007
3338
2156
191
066

prune503.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 14.5b

localize36.0ms

Local error

Found 4 expressions with local error:

7.5b
(sqrt (* (cbrt (fma p (* 4 p) (* x x))) (cbrt (fma p (* 4 p) (* x x)))))
15.9b
(cbrt (fma p (* 4 p) (* x x)))
15.9b
(cbrt (fma p (* 4 p) (* x x)))
15.9b
(cbrt (fma p (* 4 p) (* x x)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1
9×cbrt-prod sqrt-pow1 pow1/3
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Counts
4 → 64
Calls
4 calls:
5.0ms
(sqrt (* (cbrt (fma p (* 4 p) (* x x))) (cbrt (fma p (* 4 p) (* x x)))))
1.0ms
(cbrt (fma p (* 4 p) (* x x)))
1.0ms
(cbrt (fma p (* 4 p) (* x x)))
1.0ms
(cbrt (fma p (* 4 p) (* x x)))

series500.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(sqrt (* (cbrt (fma p (* 4 p) (* x x))) (cbrt (fma p (* 4 p) (* x x)))))
125.0ms
(cbrt (fma p (* 4 p) (* x x)))
125.0ms
(cbrt (fma p (* 4 p) (* x x)))
125.0ms
(cbrt (fma p (* 4 p) (* x x)))

simplify1.7s

Counts
76 → 76
Iterations
IterNodes
done5000
54144
41301
3516
2244
1123
070

prune361.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 14.5b

regimes135.0ms

Accuracy

0% (0.8b remaining)

Error of 13.6b against oracle of 12.8b and baseline of 13.6b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done18
118
016

end0.0ms

sample1.6s

Algorithm
intervals
Results
499.0ms621×body1280valid
421.0ms6036×body80valid
230.0ms725×body2560valid
199.0ms8000×pre80true
87.0ms319×body640valid
27.0ms69×body5120valid
23.0ms159×body320valid
7.0ms71×body160valid