Details

Time bar (total: 19.2s)

sample137.0ms

Algorithm
intervals
Results
54.0ms74×body1280valid
32.0ms58×body640valid
23.0ms195×body80valid
8.0ms21×body320valid
3.0ms11×body160valid

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04813
115813
290313
3500113

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 37.2b

Counts
2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

3.4b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.7b
(* (/ (pow t 3.0) (* l l)) (sin k))
15.7b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
19.9b
(/ (pow t 3.0) (* l l))

rewrite61.0ms

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))
10.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
28.0ms
(* (* (* (/ (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))

series1.4s

Counts
4 → 12
Calls
4 calls:
325.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
256.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
652.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
184.0ms
(/ (pow t 3.0) (* l l))

simplify126.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08011619
146461348
250021348

prune477.0ms

Filtered
156 candidates to 93 candidates (59.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New14610156
Fresh000
Picked101
Done000
Total14710157

Merged error: 21.6b

Counts
157 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

3.4b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.5b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.1b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
15.7b
(* (* (* (/ (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))

rewrite87.0ms

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:
22.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
12.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
33.0ms
(* (* (* (/ (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))

series1.6s

Counts
4 → 12
Calls
4 calls:
365.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
247.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
199.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
752.0ms
(* (* (* (/ (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))

simplify63.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
013473795
150013312

prune1.2s

Filtered
241 candidates to 149 candidates (61.8%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New22912241
Fresh189
Picked101
Done000
Total23120251

Merged error: 15.3b

Counts
251 → 20

localize44.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt t) 3.0)
3.4b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.5b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
15.7b
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
3594×add-exp-log
2366×prod-exp
1039×div-exp
474×pow-exp
284×pow-to-exp
253×add-cbrt-cube
187×cbrt-unprod
116×associate-*l/
98×frac-times
57×cbrt-undiv
50×pow1
43×add-sqr-sqrt
36×associate-*l*
35×*-un-lft-identity
34×times-frac
33×pow-prod-down
32×tan-quot
30×add-cube-cbrt associate-*r/
26×unpow-prod-down
16×flip3-+ flip-+
13×cbrt-prod
11×associate-*r*
5×unswap-sqr sqr-pow
4×add-log-exp
3×pow-unpow *-commutative distribute-lft-out
2×pow-pow
1×distribute-rgt-in distribute-lft-in pow1/3 div-inv
Counts
4 → 688
Calls
4 calls:
3.0ms
(pow (cbrt t) 3.0)
39.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
14.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
61.0ms
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
315.0ms
(pow (cbrt t) 3.0)
385.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
236.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
734.0ms
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify211.0ms

Algorithm
egg-herbie
Counts
700 → 700
Iterations

Useful iterations: 1 (51.0ms)

IterNodesCost
0321820075
1500317696

prune1.5s

Filtered
700 candidates to 189 candidates (27.0%)
Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New68911700
Fresh61319
Picked101
Done000
Total69624720

Merged error: 14.9b

Counts
720 → 24

localize44.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 2.0 (* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow t (* 1/3 3.0)) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
3.4b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow t (* 1/3 3.0)) l) (sin k))) (tan k))
3.5b
(* (/ (pow t (* 1/3 3.0)) l) (sin k))
15.7b
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow t (* 1/3 3.0)) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite365.0ms

Algorithm
rewrite-expression-head
Rules
5733×add-exp-log
3663×prod-exp
1790×div-exp
709×pow-exp
424×pow-to-exp
412×add-cbrt-cube
291×cbrt-unprod
206×associate-*l/
179×frac-times
109×cbrt-undiv
56×tan-quot
53×associate-*r/
49×pow1
47×associate-/r/
33×add-sqr-sqrt pow-prod-down
32×flip3-+ flip-+
28×*-un-lft-identity
27×times-frac associate-*l*
23×add-cube-cbrt
11×associate-*r*
10×unpow-prod-down
4×add-log-exp unswap-sqr sqr-pow
3×*-commutative distribute-lft-out associate-/l*
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r*
Counts
4 → 978
Calls
4 calls:
75.0ms
(/ 2.0 (* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow t (* 1/3 3.0)) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
41.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow t (* 1/3 3.0)) l) (sin k))) (tan k))
10.0ms
(* (/ (pow t (* 1/3 3.0)) l) (sin k))
59.0ms
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow t (* 1/3 3.0)) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.5s

Counts
4 → 12
Calls
4 calls:
864.0ms
(/ 2.0 (* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow t (* 1/3 3.0)) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
497.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow t (* 1/3 3.0)) l) (sin k))) (tan k))
216.0ms
(* (/ (pow t (* 1/3 3.0)) l) (sin k))
906.0ms
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow t (* 1/3 3.0)) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify316.0ms

Algorithm
egg-herbie
Counts
990 → 990
Iterations

Useful iterations: 1 (56.0ms)

IterNodesCost
0411131510
1500128576

prune1.7s

Filtered
990 candidates to 234 candidates (23.6%)
Pruning

25 alts after pruning (25 fresh and 0 done)

PrunedKeptTotal
New9819990
Fresh71623
Picked101
Done000
Total989251014

Merged error: 14.2b

Counts
1014 → 25

regimes763.0ms

Accuracy

17.7% (6.5b remaining)

Error of 17.0b against oracle of 10.5b and baseline of 18.4b

bsearch604.0ms

Steps
ItersRangePoint
8
7.799800287930273e-177
5.47745878163041e-174
4.691113552954904e-176
9
-4.3568189538739675e-215
-3.774756488102585e-223
-6.0361605514595116e-223
10
-3.769875924126648e-148
-2.713829648593553e-159
-1.5092185083587785e-150

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
095168
195168

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.7s2030×body1280valid
916.0ms1760×body640valid
724.0ms5977×body80valid
299.0ms810×body320valid
109.0ms436×body160valid

Profiling

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