Details

Time bar (total: 45.7s)

sample108.0ms

Algorithm
intervals
Results
33.0ms199×body80valid
21.0ms21×body2560valid
13.0ms19×body1280valid
12.0ms256×pre80true
4.0ms3×body5120valid
3.0ms6×body640valid
3.0ms6×body320valid
1.0ms2×body160valid

simplify34.2s

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: 11.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))
0.0b
(+ (* x x) (* p (* 4 p)))
1.0b
(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
14.4b
(sqrt (+ (* x x) (* p (* 4 p))))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
9×sqrt-prod
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt
4×flip3-+ add-cbrt-cube sqrt-div add-exp-log associate-/r/ flip-+ insert-posit16
2×+-commutative rem-sqrt-square sum-log distribute-lft1-in sqrt-pow1 distribute-rgt-out pow1/2 distribute-lft-out
Counts
4 → 62
Calls
4 calls:
31.0ms
(sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))
10.0ms
(+ (* x x) (* p (* 4 p)))
27.0ms
(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
7.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series345.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))
38.0ms
(+ (* x x) (* p (* 4 p)))
72.0ms
(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
45.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify1.7s

Counts
74 → 74
Iterations
IterNodes
done5001
33060
2721
1236
0100

prune280.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.2b

localize31.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ 0.5 (/ x (/ (sqrt (+ (* x x) (* (* p 4) p))) 0.5)))
1.0b
(+ 0.5 (/ x (/ (sqrt (+ (* x x) (* (* p 4) p))) 0.5)))
14.4b
(sqrt (+ (* x x) (* (* p 4) p)))
14.4b
(sqrt (+ (* x x) (* (* p 4) p)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt sqrt-prod
4×flip3-+ add-cbrt-cube sqrt-div add-exp-log associate-/r/ flip-+ insert-posit16
2×+-commutative rem-sqrt-square sum-log sqrt-pow1 distribute-rgt-out pow1/2 distribute-rgt1-in distribute-lft-out
Counts
4 → 62
Calls
4 calls:
14.0ms
(+ 0.5 (/ x (/ (sqrt (+ (* x x) (* (* p 4) p))) 0.5)))
14.0ms
(+ 0.5 (/ x (/ (sqrt (+ (* x x) (* (* p 4) p))) 0.5)))
6.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
10.0ms
(sqrt (+ (* x x) (* (* p 4) p)))

series235.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(+ 0.5 (/ x (/ (sqrt (+ (* x x) (* (* p 4) p))) 0.5)))
73.0ms
(+ 0.5 (/ x (/ (sqrt (+ (* x x) (* (* p 4) p))) 0.5)))
43.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
45.0ms
(sqrt (+ (* x x) (* (* p 4) p)))

simplify1.4s

Counts
74 → 74
Iterations
IterNodes
done5000
31563
2487
1172
072

prune359.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (+ (* x x) (* p (* 4 p))))) (sqrt (sqrt (+ (* x x) (* p (* 4 p))))))
6.8b
(+ (/ x (/ (* (sqrt (sqrt (+ (* x x) (* p (* 4 p))))) (sqrt (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)) 0.5)
14.4b
(sqrt (+ (* x x) (* p (* 4 p))))
14.4b
(sqrt (+ (* x x) (* p (* 4 p))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
50×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
21×*-un-lft-identity
18×pow1/2 add-cube-cbrt
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-cbrt-cube add-exp-log add-log-exp
5×pow-prod-down pow-sqr
4×frac-times insert-posit16
2×rem-sqrt-square associate-*l/ associate-*r/ associate-/r/
1×pow2 +-commutative sum-log rem-square-sqrt distribute-lft1-in pow-plus distribute-rgt-out sqrt-unprod prod-exp *-commutative cbrt-unprod distribute-lft-out
Counts
4 → 131
Calls
4 calls:
36.0ms
(* (sqrt (sqrt (+ (* x x) (* p (* 4 p))))) (sqrt (sqrt (+ (* x x) (* p (* 4 p))))))
18.0ms
(+ (/ x (/ (* (sqrt (sqrt (+ (* x x) (* p (* 4 p))))) (sqrt (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)) 0.5)
10.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series208.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (sqrt (sqrt (+ (* x x) (* p (* 4 p))))) (sqrt (sqrt (+ (* x x) (* p (* 4 p))))))
73.0ms
(+ (/ x (/ (* (sqrt (sqrt (+ (* x x) (* p (* 4 p))))) (sqrt (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)) 0.5)
46.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
44.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify1.6s

Counts
143 → 143
Iterations
IterNodes
done5045
33041
2772
1323
0146

prune487.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.2b

localize50.0ms

Local error

Found 4 expressions with local error:

14.4b
(sqrt (+ (* x x) (* p (* 4 p))))
14.4b
(sqrt (+ (* x x) (* p (* 4 p))))
14.4b
(sqrt (+ (* x x) (* p (* 4 p))))
14.4b
(sqrt (+ (* x x) (* p (* 4 p))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity sqrt-div add-cube-cbrt
4×rem-sqrt-square sqrt-pow1 flip3-+ add-cbrt-cube pow1/2 add-exp-log flip-+ insert-posit16 add-log-exp
Counts
4 → 64
Calls
4 calls:
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series181.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
44.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
46.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
44.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify1.4s

Counts
76 → 76
Iterations
IterNodes
done5000
42275
3663
2258
197
042

prune461.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 11.2b

regimes177.0ms

Accuracy

0% (0.3b remaining)

Error of 13.2b against oracle of 12.9b and baseline of 13.2b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done20
120
015

end0.0ms

sample2.4s

Algorithm
intervals
Results
673.0ms6046×body80valid
568.0ms8000×pre80true
450.0ms716×body2560valid
265.0ms601×body1280valid
150.0ms308×body640valid
58.0ms58×body5120valid
47.0ms181×body320valid
15.0ms90×body160valid