Details

Time bar (total: 12.5s)

sample139.0ms

Algorithm
intervals
Results
50.0ms67×body1280valid
25.0ms49×body640valid
23.0ms194×body80valid
12.0ms34×body320valid
4.0ms16×body160valid

simplify29.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04813
115813
290313
3500113

prune5.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.5b

Counts
2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.9b
(* (/ (pow t 3.0) (* l l)) (sin k))
13.1b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
16.5b
(/ (pow t 3.0) (* l l))

rewrite58.0ms

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
8×tan-quot cbrt-undiv pow-to-exp pow-exp
7×associate-/l*
6×associate-*r/
4×flip3-+ flip-+ add-log-exp unswap-sqr sqr-pow
3×*-commutative distribute-lft-out
2×div-inv
1×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))
12.0ms
(* (/ (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))

series339.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
56.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
165.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
40.0ms
(/ (pow t 3.0) (* l l))

simplify119.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (102.0ms)

IterNodesCost
08571728
147841448
250011444

prune363.0ms

Filtered
156 candidates to 96 candidates (38.5%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New14016156
Fresh000
Picked101
Done000
Total14116157

Merged error: 20.0b

Counts
157 → 16

localize28.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
2.1b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.4b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
13.1b
(* (* (* (/ (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))

rewrite80.0ms

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
8×flip3-+ flip-+ sqr-pow
5×associate-/l* unswap-sqr
4×add-log-exp
3×associate-/r* *-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num
Counts
4 → 229
Calls
4 calls:
19.0ms
(* (* (/ (pow (* (cbrt t) (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))
5.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
31.0ms
(* (* (* (/ (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))

series372.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(* (* (/ (pow (* (cbrt t) (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))
43.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
187.0ms
(* (* (* (/ (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))

simplify62.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
014303890
150023397

prune643.0ms

Filtered
241 candidates to 151 candidates (37.3%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New23011241
Fresh41115
Picked101
Done000
Total23522257

Merged error: 13.7b

Counts
257 → 22

localize28.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
1.1b
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
2.1b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
13.1b
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite247.0ms

Algorithm
rewrite-expression-head
Rules
1050×add-exp-log
674×times-frac
554×prod-exp
435×div-exp
404×unpow-prod-down
381×associate-*l*
343×add-sqr-sqrt
335×*-un-lft-identity
330×add-cube-cbrt
202×cbrt-prod
151×add-cbrt-cube
145×pow-to-exp pow-exp
78×cbrt-unprod
68×sqr-pow
47×associate-*l/
37×cbrt-undiv
35×frac-times
34×pow1
20×pow-prod-down
16×tan-quot
15×associate-*r/
12×associate-*r* div-inv
8×flip3-+ flip-+
5×unswap-sqr
4×*-commutative add-log-exp
3×distribute-lft-out
1×distribute-rgt-in distribute-lft-in associate-/r/
Counts
4 → 710
Calls
4 calls:
62.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
42.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
63.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series394.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
84.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
57.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
190.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify149.0ms

Algorithm
egg-herbie
Counts
722 → 722
Iterations

Useful iterations: 1 (47.0ms)

IterNodesCost
0278811518
1500210775

prune3.1s

Filtered
722 candidates to 479 candidates (33.7%)
Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New71111722
Fresh81321
Picked101
Done000
Total72024744

Merged error: 12.2b

Counts
744 → 24

localize29.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
2.1b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.0b
(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
11.4b
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
745×add-exp-log
479×prod-exp
210×div-exp
142×add-cbrt-cube
79×cbrt-unprod
75×pow-to-exp pow-exp
40×add-sqr-sqrt
36×associate-*l*
35×times-frac
32×*-un-lft-identity
30×cbrt-undiv
27×add-cube-cbrt
20×unpow-prod-down
18×associate-*l/
13×pow1
11×associate-*r/ associate-*r*
10×cbrt-prod
5×pow-prod-down associate-/l/ unswap-sqr
4×frac-times flip3-+ flip-+ add-log-exp sqr-pow
3×*-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r* associate-/r/ associate-/l*
Counts
4 → 264
Calls
4 calls:
14.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
16.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
36.0ms
(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
28.0ms
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series440.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
56.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
179.0ms
(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
142.0ms
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify72.0ms

Algorithm
egg-herbie
Counts
276 → 276
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
014705541
150014874

prune511.0ms

Filtered
276 candidates to 128 candidates (53.6%)
Pruning

28 alts after pruning (27 fresh and 1 done)

PrunedKeptTotal
New2679276
Fresh51823
Picked011
Done000
Total27228300

Merged error: 10.5b

Counts
300 → 28

regimes1.0s

Accuracy

11.8% (3.2b remaining)

Error of 14.5b against oracle of 11.3b and baseline of 14.9b

bsearch118.0ms

Steps
ItersRangePoint
8
1.1849000275972928e-294
1.6729956818436637e-291
2.127101027440168e-292
8
-6.499707771303285e-91
-9.242625349516869e-95
-9.392224339322686e-95

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
072103
172103

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.6s2100×body1280valid
877.0ms1710×body640valid
692.0ms5920×body80valid
324.0ms866×body320valid
100.0ms396×body160valid

Profiling

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