Details

Time bar (total: 16.3s)

analyze2.2s

Algorithm
search

sample136.0ms

Algorithm
intervals
Results
51.0ms55×body1280valid
29.0ms52×body640valid
15.0ms112×body80valid
10.0ms26×body320valid
6.0ms49×body80invalid
3.0ms11×body160valid
3.0msbody320invalid
1.0msbody640invalid
1.0msbody160invalid
1.0msbody1280invalid

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04813
115813
290313
3500113

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.7b

Counts
2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.2b
(* (/ (pow t 3.0) (* l l)) (sin k))
12.6b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
17.3b
(/ (pow t 3.0) (* l l))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
108×add-exp-log
58×prod-exp
52×add-cbrt-cube
26×cbrt-unprod
24×div-exp
21×add-sqr-sqrt
20×pow1
19×*-un-lft-identity
17×times-frac
16×associate-*l/
14×add-cube-cbrt
13×associate-*l*
11×associate-*r*
10×frac-times unpow-prod-down pow-prod-down
tan-quot cbrt-undiv pow-to-exp pow-exp
associate-/l*
associate-*r/
flip3-+ flip-+ add-log-exp unswap-sqr sqr-pow
*-commutative distribute-lft-out
div-inv
distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r*
Counts
4 → 144
Calls
4 calls:
11.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
9.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
22.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
6.0ms
(/ (pow t 3.0) (* l l))

series341.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
57.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
163.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
43.0ms
(/ (pow t 3.0) (* l l))

simplify115.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (99.0ms)

IterNodesCost
08571728
147841448
250011444

prune370.0ms

Filtered
96 candidates to 156 candidates (-62.5%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New14313156
Fresh000
Picked101
Done000
Total14413157

Merged error: 18.8b

Counts
157 → 13

localize27.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.5b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.6b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
12.6b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
304×add-exp-log
184×prod-exp
78×add-cbrt-cube
77×div-exp
50×add-sqr-sqrt
49×times-frac
44×associate-*l/ cbrt-unprod
42×*-un-lft-identity
37×add-cube-cbrt
36×associate-*l*
34×frac-times
33×pow-exp
29×pow1
24×unpow-prod-down
22×pow-to-exp
17×pow-prod-down
16×tan-quot
14×associate-*r/
12×cbrt-undiv
11×associate-*r*
10×cbrt-prod
flip3-+ flip-+ sqr-pow
associate-/l* unswap-sqr
add-log-exp
associate-/r* *-commutative distribute-lft-out
div-inv
distribute-rgt-in frac-2neg distribute-lft-in clear-num
Counts
4 → 229
Calls
4 calls:
17.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
13.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
30.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series367.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
56.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
43.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
184.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify61.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
014303890
150023397

prune702.0ms

Filtered
151 candidates to 241 candidates (-59.6%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New22714241
Fresh4812
Picked101
Done000
Total23222254

Merged error: 14.5b

Counts
254 → 22

localize27.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
2.2b
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.5b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
12.6b
(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
1050×add-exp-log
734×prod-exp
255×div-exp
151×add-cbrt-cube
145×pow-to-exp pow-exp
96×cbrt-unprod
47×associate-*l/
40×add-sqr-sqrt
37×associate-*l*
35×frac-times
34×pow1 times-frac
33×associate-*r/
32×*-un-lft-identity
27×add-cube-cbrt
20×unpow-prod-down pow-prod-down
19×cbrt-undiv
16×tan-quot
12×associate-*r*
10×cbrt-prod
flip3-+ flip-+
unswap-sqr
*-commutative add-log-exp sqr-pow
distribute-lft-out
distribute-rgt-in distribute-lft-in div-inv
Counts
4 → 366
Calls
4 calls:
18.0ms
(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
29.0ms
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
38.0ms
(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series398.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
85.0ms
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
57.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
193.0ms
(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify85.0ms

Algorithm
egg-herbie
Counts
378 → 378
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
015406680
150025480

prune760.0ms

Filtered
138 candidates to 378 candidates (-173.9%)
Pruning

28 alts after pruning (28 fresh and 0 done)

PrunedKeptTotal
New36612378
Fresh51621
Picked101
Done000
Total37228400

Merged error: 13.5b

Counts
400 → 28

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt t) 3.0)
1.1b
(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
4.5b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
14.0b
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
1049×add-exp-log
733×prod-exp
255×div-exp
149×add-cbrt-cube
146×pow-to-exp pow-exp
95×cbrt-unprod
41×add-sqr-sqrt
36×associate-*l*
34×times-frac associate-*r/
33×pow1
30×frac-times
29×associate-*l/
28×add-cube-cbrt *-un-lft-identity
26×unpow-prod-down
19×cbrt-undiv pow-prod-down
13×cbrt-prod
12×tan-quot
flip3-+ flip-+
associate-*r* unswap-sqr sqr-pow
distribute-rgt-in distribute-lft-in add-log-exp
pow-unpow *-commutative
pow-pow
pow1/3 div-inv
Counts
4 → 363
Calls
4 calls:
3.0ms
(pow (cbrt t) 3.0)
18.0ms
(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
39.0ms
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

series353.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(pow (cbrt t) 3.0)
68.0ms
(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
57.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
181.0ms
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

simplify87.0ms

Algorithm
egg-herbie
Counts
375 → 375
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
015776847
150025929

prune560.0ms

Filtered
132 candidates to 375 candidates (-184.1%)
Pruning

27 alts after pruning (27 fresh and 0 done)

PrunedKeptTotal
New3669375
Fresh91827
Picked101
Done000
Total37627403

Merged error: 12.9b

Counts
403 → 27

regimes975.0ms

Accuracy

37.2% (2.2b remaining)

Error of 16.6b against oracle of 14.4b and baseline of 17.9b

bsearch2.0s

Steps
ItersRangePoint
9
14264115.309849303
393785734436759.1
5838554505.504952
7
-2.3882684830878263e+91
-1.9473777764221412e+89
-7.124702578692672e+89

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04940
14940

end0.0ms

analyze2.2s

Algorithm
search

sample4.1s

Algorithm
intervals
Results
1.6s1965×body1280valid
937.0ms1627×body640valid
450.0ms3309×body80valid
316.0ms753×body320valid
196.0ms1452×body80invalid
95.0ms346×body160valid
71.0ms119×body640invalid
41.0ms103×body320invalid
26.0ms93×body160invalid
22.0ms27×body1280invalid

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