Details

Time bar (total: 43.0s)

sample88.0ms

Algorithm
intervals
Results
28.0ms193×body80valid
14.0ms24×body2560valid
11.0ms23×body1280valid
10.0ms256×pre80true
2.0ms5×body640valid
2.0ms6×body320valid
1.0ms4×body160valid
1.0ms1×body5120valid

simplify32.7s

Counts
1 → 1
Iterations
IterNodes
done5000
1664914
1654880
1644809
1634781
1624721
1614696
1604649
1594626
1584581
1574558
1564511
1554490
1544447
1534429
1524395
1514377
1504344
1494326
1484293
1474275
1464242
1454224
1444191
1434173
1424140
1414122
1404089
1394071
1384038
1374020
1363987
1353969
1343936
1333918
1323885
1313867
1303834
1293816
1283783
1273765
1263732
1253714
1243681
1233663
1223630
1213612
1203579
1193561
1183528
1173510
1163477
1153459
1143426
1133408
1123375
1113357
1103324
1093306
1083273
1073255
1063222
1053204
1043171
1033153
1023120
1013102
1003069
993051
983018
973000
962967
952949
942916
932898
922865
912847
902814
892796
882763
872745
862712
852694
842661
832643
822610
812592
802559
792541
782508
772490
762457
752439
742406
732388
722355
712337
702304
692286
682253
672235
662202
652184
642151
632133
622100
612082
602049
592031
581998
571980
561947
551929
541896
531878
521845
511827
501794
491776
481743
471725
461692
451674
441641
431623
421590
411572
401539
391521
381488
371470
361437
351419
341386
331368
321335
311317
301284
291266
281233
271215
261182
251164
241131
231113
221080
211062
201029
191011
18978
17960
16927
15909
14876
13858
12825
11786
10745
9598
8441
7301
6200
5145
4104
376
251
129
014

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* p (* 4 p)))
0.0b
(/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5))
0.9b
(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
12.8b
(sqrt (+ (* x x) (* p (* 4 p))))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
83×*-un-lft-identity
81×add-sqr-sqrt
80×add-cube-cbrt
39×sqrt-prod
22×associate-/r*
9×add-cbrt-cube add-exp-log
8×add-log-exp
5×pow1 div-inv
4×insert-posit16
3×cbrt-undiv flip3-+ div-exp associate-/r/ flip-+ associate-/l*
2×+-commutative sum-log sqrt-div
1×rem-sqrt-square clear-num frac-2neg distribute-lft1-in sqrt-pow1 distribute-rgt-out pow1/2 distribute-lft-out
Counts
4 → 150
Calls
4 calls:
9.0ms
(+ (* x x) (* p (* 4 p)))
15.0ms
(/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5))
62.0ms
(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
8.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series210.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ (* x x) (* p (* 4 p)))
56.0ms
(/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5))
72.0ms
(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
45.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify1.2s

Counts
162 → 162
Iterations
IterNodes
done5005
22235
1672
0257

prune514.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.7b

localize49.0ms

Local error

Found 4 expressions with local error:

3.5b
(/ (* x x) (+ (* x x) (* (* p 4) p)))
12.8b
(sqrt (+ (* x x) (* (* p 4) p)))
12.8b
(sqrt (+ (* x x) (* (* p 4) p)))
12.8b
(sqrt (+ (* x x) (* (* p 4) p)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×*-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt sqrt-prod
7×pow1
6×sqrt-div
4×flip3-+ flip-+ insert-posit16 add-log-exp
3×rem-sqrt-square associate-/r* sqrt-pow1 times-frac pow1/2
2×cbrt-undiv div-exp associate-/r/
1×clear-num frac-2neg prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 72
Calls
4 calls:
18.0ms
(/ (* x x) (+ (* x x) (* (* p 4) p)))
7.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
7.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
7.0ms
(sqrt (+ (* x x) (* (* p 4) p)))

series187.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ (* x x) (+ (* x x) (* (* p 4) p)))
43.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
46.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
44.0ms
(sqrt (+ (* x x) (* (* p 4) p)))

simplify985.0ms

Counts
84 → 84
Iterations
IterNodes
done5001
21029
1230
080

prune452.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.7b

localize49.0ms

Local error

Found 4 expressions with local error:

4.3b
(+ (* 0.5 (* 0.5 0.5)) (* (* (* 0.5 (* 0.5 0.5)) (* (* x x) (/ 1 (+ (* x x) (* (* p 4) p))))) (/ x (sqrt (+ (* x x) (* (* p 4) p))))))
12.8b
(sqrt (+ (* x x) (* (* p 4) p)))
12.8b
(sqrt (+ (* x x) (* (* p 4) p)))
12.8b
(sqrt (+ (* x x) (* (* p 4) p)))

rewrite366.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div add-log-exp
4×flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16
3×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative sum-log
Counts
4 → 60
Calls
4 calls:
339.0ms
(+ (* 0.5 (* 0.5 0.5)) (* (* (* 0.5 (* 0.5 0.5)) (* (* x x) (/ 1 (+ (* x x) (* (* p 4) p))))) (/ x (sqrt (+ (* x x) (* (* p 4) p))))))
7.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
8.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
12.0ms
(sqrt (+ (* x x) (* (* p 4) p)))

series222.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(+ (* 0.5 (* 0.5 0.5)) (* (* (* 0.5 (* 0.5 0.5)) (* (* x x) (/ 1 (+ (* x x) (* (* p 4) p))))) (/ x (sqrt (+ (* x x) (* (* p 4) p))))))
43.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
46.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
43.0ms
(sqrt (+ (* x x) (* (* p 4) p)))

simplify1.4s

Counts
72 → 72
Iterations
IterNodes
done5001
2799
1209
075

prune457.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.6b

localize48.0ms

Local error

Found 4 expressions with local error:

2.5b
(/ x (/ (+ (* x x) (* (* p 4) p)) x))
12.8b
(sqrt (+ (* x x) (* (* p 4) p)))
12.8b
(sqrt (+ (* x x) (* (* p 4) p)))
12.8b
(sqrt (+ (* x x) (* (* p 4) p)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
52×add-sqr-sqrt
49×*-un-lft-identity add-cube-cbrt
13×associate-/r*
9×add-cbrt-cube add-exp-log sqrt-prod
7×pow1
6×sqrt-div
5×div-inv
4×insert-posit16 add-log-exp
3×cbrt-undiv rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 div-exp flip-+ associate-/l*
1×clear-num frac-2neg associate-/r/
Counts
4 → 119
Calls
4 calls:
13.0ms
(/ x (/ (+ (* x x) (* (* p 4) p)) x))
7.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
7.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
13.0ms
(sqrt (+ (* x x) (* (* p 4) p)))

series185.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ x (/ (+ (* x x) (* (* p 4) p)) x))
45.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
43.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
46.0ms
(sqrt (+ (* x x) (* (* p 4) p)))

simplify1.2s

Counts
131 → 131
Iterations
IterNodes
done5010
21923
1474
0178

prune661.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 12.6b

regimes212.0ms

Accuracy

0% (0.6b remaining)

Error of 13.8b against oracle of 13.2b and baseline of 13.8b

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
done37
137
025

end0.0ms

sample1.7s

Algorithm
intervals
Results
490.0ms8000×pre80true
354.0ms5998×body80valid
299.0ms767×body2560valid
235.0ms612×body1280valid
65.0ms325×body640valid
55.0ms174×body320valid
33.0ms49×body5120valid
7.0ms75×body160valid