Details

Time bar (total: 40.0s)

sample404.0ms

Algorithm
intervals
Results
121.0ms68×body2560valid
101.0ms116×body1280valid
82.0ms26×body5120valid
46.0ms79×body640valid
18.0ms44×body320valid
8.0ms58×body80valid
2.0ms9×body160valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 4 (742.0ms)

IterNodesCost
01925
14425
214325
371023
4378621
done500021

prune15.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 40.5b

Counts
2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin k) (tan k))
0.5b
(/ 2.0 (* (pow (/ k t) 2.0) (* (sin k) (tan k))))
19.3b
(* (/ (/ 2.0 (* (pow (/ k t) 2.0) (* (sin k) (tan k)))) (pow t 3.0)) (* l l))
29.3b
(/ (/ 2.0 (* (pow (/ k t) 2.0) (* (sin k) (tan k)))) (pow t 3.0))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
470×add-exp-log
214×prod-exp
200×div-exp
163×times-frac
81×add-sqr-sqrt
74×add-cbrt-cube
73×add-cube-cbrt *-un-lft-identity
70×pow-exp
63×associate-*l*
52×unpow-prod-down
50×pow-to-exp
33×associate-*r/
28×cbrt-unprod
24×cbrt-undiv
18×div-inv sqr-pow
17×tan-quot
16×associate-/r/
11×pow1 associate-/l*
8×associate-/r*
5×unswap-sqr
4×associate-*r* pow-prod-down add-log-exp
2×frac-2neg clear-num *-commutative
1×associate-*l/ associate-/l/
Counts
4 → 313
Calls
4 calls:
5.0ms
(* (sin k) (tan k))
11.0ms
(/ 2.0 (* (pow (/ k t) 2.0) (* (sin k) (tan k))))
30.0ms
(* (/ (/ 2.0 (* (pow (/ k t) 2.0) (* (sin k) (tan k)))) (pow t 3.0)) (* l l))
16.0ms
(/ (/ 2.0 (* (pow (/ k t) 2.0) (* (sin k) (tan k)))) (pow t 3.0))

series407.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(* (sin k) (tan k))
82.0ms
(/ 2.0 (* (pow (/ k t) 2.0) (* (sin k) (tan k))))
214.0ms
(* (/ (/ 2.0 (* (pow (/ k t) 2.0) (* (sin k) (tan k)))) (pow t 3.0)) (* l l))
100.0ms
(/ (/ 2.0 (* (pow (/ k t) 2.0) (* (sin k) (tan k)))) (pow t 3.0))

simplify1.4s

Counts
325 → 325
Iterations

Useful iterations: 2 (767.0ms)

IterNodesCost
04808088
114287495
246626741
done50006741

prune689.0ms

Filtered
183 candidates to 325 candidates (-77.6%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New30916325
Fresh101
Picked101
Done000
Total31116327

Merged error: 27.8b

Counts
327 → 16

localize28.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 2.0 (pow (* (cbrt t) (cbrt t)) 3.0))
6.3b
(* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))
16.1b
(/ (* l l) (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k)))))
25.7b
(* (/ 2.0 (pow (* (cbrt t) (cbrt t)) 3.0)) (/ (* l l) (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
2099×add-exp-log
1330×prod-exp
646×div-exp
389×pow-exp
253×pow-to-exp
140×add-cbrt-cube
72×cbrt-unprod
36×add-sqr-sqrt
35×times-frac
34×cbrt-undiv
29×associate-*l*
27×add-cube-cbrt *-un-lft-identity
14×unpow-prod-down
10×associate-*r/
9×sqr-pow
7×associate-*r*
6×pow1 associate-/r*
4×div-inv associate-/l* add-log-exp unswap-sqr
3×tan-quot cbrt-prod
2×frac-2neg clear-num associate-/r/ *-commutative
1×frac-times pow-prod-down associate-*l/
Counts
4 → 510
Calls
4 calls:
5.0ms
(/ 2.0 (pow (* (cbrt t) (cbrt t)) 3.0))
15.0ms
(* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))
20.0ms
(/ (* l l) (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k)))))
31.0ms
(* (/ 2.0 (pow (* (cbrt t) (cbrt t)) 3.0)) (/ (* l l) (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))))

series497.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(/ 2.0 (pow (* (cbrt t) (cbrt t)) 3.0))
85.0ms
(* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))
139.0ms
(/ (* l l) (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k)))))
194.0ms
(* (/ 2.0 (pow (* (cbrt t) (cbrt t)) 3.0)) (/ (* l l) (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))))

simplify721.0ms

Counts
522 → 522
Iterations

Useful iterations: done (699.0ms)

IterNodesCost
051117889
1173915584
done500015375

prune491.0ms

Filtered
113 candidates to 522 candidates (-361.9%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New5148522
Fresh31215
Picked101
Done000
Total51820538

Merged error: 25.1b

Counts
538 → 20

localize35.0ms

Local error

Found 4 expressions with local error:

6.3b
(* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))
7.1b
(* (/ 1 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* (/ 2.0 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (/ (* l l) (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k)))))))
9.5b
(* (/ 2.0 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (/ (* l l) (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))))
16.1b
(/ (* l l) (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k)))))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
29820×add-exp-log
20361×prod-exp
10314×div-exp
6315×pow-exp
3801×pow-to-exp
1144×rec-exp 1-exp
383×add-cbrt-cube
210×cbrt-unprod
102×cbrt-undiv
48×associate-*l*
35×add-sqr-sqrt times-frac
26×add-cube-cbrt *-un-lft-identity
15×associate-*r/
13×unpow-prod-down
11×pow1
8×associate-*r* sqr-pow
6×frac-times
4×pow-prod-down associate-*l/ div-inv add-log-exp unswap-sqr
3×tan-quot cbrt-prod *-commutative
2×associate-/r/
1×frac-2neg clear-num associate-/r* associate-/l*
Counts
4 → 4265
Calls
4 calls:
15.0ms
(* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))
94.0ms
(* (/ 1 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* (/ 2.0 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (/ (* l l) (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k)))))))
32.0ms
(* (/ 2.0 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (/ (* l l) (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))))
18.0ms
(/ (* l l) (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k)))))

series555.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))
192.0ms
(* (/ 1 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* (/ 2.0 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (/ (* l l) (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k)))))))
132.0ms
(* (/ 2.0 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (/ (* l l) (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))))
146.0ms
(/ (* l l) (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k)))))

simplify1.1s

Counts
4277 → 4277
Iterations

Useful iterations: 0 (440.0ms)

IterNodesCost
01842218583
done5000218583

prune10.4s

Filtered
1574 candidates to 4277 candidates (-171.7%)
Pruning

28 alts after pruning (28 fresh and 0 done)

PrunedKeptTotal
New4264134277
Fresh41519
Picked101
Done000
Total4269284297

Merged error: 17.9b

Counts
4297 → 28

localize34.0ms

Local error

Found 4 expressions with local error:

5.8b
(/ (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k)))) l)
6.3b
(* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))
7.1b
(* (/ 1 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* (/ 2.0 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (/ l (/ (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k)))) l))))
9.5b
(* (/ 2.0 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (/ l (/ (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k)))) l)))

rewrite625.0ms

Algorithm
rewrite-expression-head
Rules
16425×add-exp-log
9472×prod-exp
7338×div-exp
3258×pow-exp
1953×pow-to-exp
604×rec-exp 1-exp
248×add-cbrt-cube
110×cbrt-unprod
89×cbrt-undiv
73×times-frac
63×add-sqr-sqrt
48×associate-*l*
41×add-cube-cbrt *-un-lft-identity
28×associate-*r*
14×unpow-prod-down
12×associate-*r/
11×pow1
9×sqr-pow
8×unswap-sqr
7×div-inv
6×frac-times
4×pow-prod-down associate-*l/ add-log-exp
3×cbrt-prod associate-/r* *-commutative
2×tan-quot
1×frac-2neg clear-num associate-/r/ associate-/l/ associate-/l*
Counts
4 → 2353
Calls
4 calls:
17.0ms
(/ (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k)))) l)
15.0ms
(* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))
61.0ms
(* (/ 1 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* (/ 2.0 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (/ l (/ (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k)))) l))))
33.0ms
(* (/ 2.0 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (/ l (/ (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k)))) l)))

series538.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(/ (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k)))) l)
87.0ms
(* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))
190.0ms
(* (/ 1 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* (/ 2.0 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (/ l (/ (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k)))) l))))
135.0ms
(* (/ 2.0 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (/ l (/ (* (pow (cbrt t) 3.0) (* (pow (/ k t) 2.0) (* (sin k) (tan k)))) l)))

simplify1.3s

Counts
2365 → 2365
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01269120163
1464899893
done500099871

prune1.0s

Filtered
189 candidates to 2365 candidates (-1151.3%)
Pruning

36 alts after pruning (36 fresh and 0 done)

PrunedKeptTotal
New2352132365
Fresh42327
Picked101
Done000
Total2357362393

Merged error: 16.6b

Counts
2393 → 36

regimes1.3s

Accuracy

-8.1% (12.1b remaining)

Error of 27.8b against oracle of 15.7b and baseline of 26.9b

bsearch617.0ms

Steps
ItersRangePoint
7
18.076566431700634
848.6737351236724
21.185942955599955
8
-1.8944825309129615e-153
-1.1429704915917432e-156
-7.465391659498034e-155

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
069152
189152
done89152

end0.0ms

sample14.4s

Algorithm
intervals
Results
4.4s2217×body2560valid
3.5s4112×body1280valid
3.5s897×body5120valid
1.5s2478×body640valid
415.0ms954×body320valid
290.0ms2016×body80valid
120.0ms426×body160valid

Profiling

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