Details

Time bar (total: 20.4s)

sample134.0ms

Algorithm
intervals
Results
46.0ms57×body1280valid
24.0ms47×body640valid
23.0ms198×body80valid
13.0ms36×body320valid
3.0ms13×body160valid

simplify28.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04813
115813
290313
3500113

prune6.0ms

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: 30.6b

Counts
2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (/ (pow t 3.0) (* l l)) (sin k))
2.7b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
13.7b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
15.4b
(/ (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
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:
9.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
11.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan 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))

series330.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
74.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
158.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
42.0ms
(/ (pow t 3.0) (* l l))

simplify118.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (102.0ms)

IterNodesCost
08571728
147841448
250011444

prune1.2s

Filtered
156 candidates to 96 candidates (38.5%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New14313156
Fresh000
Picked101
Done000
Total14413157

Merged error: 18.7b

Counts
157 → 13

localize27.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
5.6b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
5.9b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
13.7b
(* (* (* (/ (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))

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
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))
5.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
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))

series357.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
44.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
52.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
180.0ms
(* (* (* (/ (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

prune3.6s

Filtered
241 candidates to 151 candidates (37.3%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New23011241
Fresh3912
Picked101
Done000
Total23420254

Merged error: 14.8b

Counts
254 → 20

localize27.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 2.0 (* (* (* (/ (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)))
2.7b
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
5.9b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
13.7b
(* (* (* (/ (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))

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
1254×add-exp-log
687×prod-exp
503×div-exp
187×add-cbrt-cube
145×pow-to-exp pow-exp
99×cbrt-unprod
78×associate-*l/
63×frac-times
49×cbrt-undiv
42×add-sqr-sqrt
37×times-frac
36×associate-*l*
34×*-un-lft-identity
29×pow1 add-cube-cbrt
28×tan-quot
25×associate-*r/
23×associate-/r/
20×unpow-prod-down
17×pow-prod-down
16×flip3-+ flip-+
11×associate-*r*
10×cbrt-prod
5×unswap-sqr
4×add-log-exp 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 → 397
Calls
4 calls:
62.0ms
(/ 2.0 (* (* (* (/ (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)))
40.0ms
(* (* (/ (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))
61.0ms
(* (* (* (/ (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))

series480.0ms

Counts
4 → 12
Calls
4 calls:
169.0ms
(/ 2.0 (* (* (* (/ (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)))
80.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
52.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
178.0ms
(* (* (* (/ (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))

simplify103.0ms

Algorithm
egg-herbie
Counts
409 → 409
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
019458399
150017476

prune3.6s

Filtered
409 candidates to 163 candidates (60.1%)
Pruning

23 alts after pruning (23 fresh and 0 done)

PrunedKeptTotal
New39811409
Fresh71219
Picked101
Done000
Total40623429

Merged error: 12.6b

Counts
429 → 23

localize24.0ms

Local error

Found 4 expressions with local error:

4.9b
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
5.9b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
6.2b
(* (/ 2.0 (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))) (/ l (pow (cbrt t) 3.0)))
11.9b
(* (* (* (pow (cbrt t) 3.0) (* (/ (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
658×add-exp-log
423×prod-exp
186×div-exp
120×add-cbrt-cube
75×add-sqr-sqrt
71×times-frac
68×pow-to-exp pow-exp
67×cbrt-unprod
54×*-un-lft-identity associate-*l*
49×add-cube-cbrt
45×associate-*r*
40×unpow-prod-down
29×associate-*l/
26×associate-*r/
24×cbrt-undiv
20×cbrt-prod frac-times
15×pow1
14×tan-quot
11×associate-/r/
10×unswap-sqr
8×flip3-+ flip-+ sqr-pow
6×pow-prod-down
4×*-commutative add-log-exp
3×div-inv distribute-lft-out
1×distribute-rgt-in distribute-lft-in
Counts
4 → 304
Calls
4 calls:
14.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
12.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
45.0ms
(* (/ 2.0 (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))) (/ l (pow (cbrt t) 3.0)))
29.0ms
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series495.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
52.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
169.0ms
(* (/ 2.0 (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))) (/ l (pow (cbrt t) 3.0)))
196.0ms
(* (* (* (pow (cbrt t) 3.0) (* (/ (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
316 → 316
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
018096087
150025450

prune4.0s

Filtered
316 candidates to 171 candidates (45.9%)
Pruning

31 alts after pruning (31 fresh and 0 done)

PrunedKeptTotal
New29917316
Fresh81422
Picked101
Done000
Total30831339

Merged error: 12.2b

Counts
339 → 31

regimes1.2s

Accuracy

0% (3.7b remaining)

Error of 14.7b against oracle of 11.0b and baseline of 14.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03331
13331

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.5s2029×body1280valid
864.0ms1678×body640valid
713.0ms6021×body80valid
308.0ms815×body320valid
111.0ms435×body160valid

Profiling

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