Details

Time bar (total: 26.8s)

sample132.0ms

Algorithm
intervals
Results
41.0ms57×body1280valid
24.0ms47×body640valid
23.0ms198×body80valid
13.0ms36×body320valid
3.0ms13×body160valid

simplify29.0ms

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

localize26.0ms

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))

series1.6s

Counts
4 → 12
Calls
4 calls:
284.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
360.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
712.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
207.0ms
(/ (pow t 3.0) (* l l))

simplify118.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08011619
146461348
250021348

prune1.1s

Filtered
156 candidates to 93 candidates (40.4%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New14214156
Fresh000
Picked101
Done000
Total14314157

Merged error: 14.0b

Counts
157 → 14

localize29.0ms

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))

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:
20.0ms
(* (* (/ (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)
10.0ms
(* (/ (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))

series1.8s

Counts
4 → 12
Calls
4 calls:
422.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
234.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
281.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
842.0ms
(* (* (* (/ (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))

simplify60.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013473795
150013312

prune3.5s

Filtered
241 candidates to 149 candidates (38.2%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New2347241
Fresh31013
Picked101
Done000
Total23817255

Merged error: 10.4b

Counts
255 → 17

localize25.0ms

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))

rewrite215.0ms

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:
61.0ms
(/ 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))
58.0ms
(* (* (* (/ (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))

series2.3s

Counts
4 → 12
Calls
4 calls:
757.0ms
(/ 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)))
404.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
263.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
828.0ms
(* (* (* (/ (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))

simplify105.0ms

Algorithm
egg-herbie
Counts
409 → 409
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
018718293
150017380

prune3.4s

Filtered
409 candidates to 162 candidates (60.4%)
Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New39811409
Fresh31316
Picked101
Done000
Total40224426

Merged error: 8.4b

Counts
426 → 24

localize26.0ms

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))

rewrite131.0ms

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:
18.0ms
(* (* (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))
46.0ms
(* (/ 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)))
31.0ms
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.5s

Counts
4 → 12
Calls
4 calls:
416.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
283.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
762.0ms
(* (/ 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)))
989.0ms
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify79.0ms

Algorithm
egg-herbie
Counts
316 → 316
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
017095978
150015341

prune4.2s

Filtered
316 candidates to 171 candidates (45.9%)
Pruning

30 alts after pruning (30 fresh and 0 done)

PrunedKeptTotal
New30016316
Fresh91423
Picked101
Done000
Total31030340

Merged error: 6.7b

Counts
340 → 30

regimes1.2s

Accuracy

52.3% (3.7b remaining)

Error of 10.6b against oracle of 6.9b and baseline of 14.7b

bsearch316.0ms

Steps
ItersRangePoint
7
2.5811307772558914e+54
3.3048994100069047e+56
2.623038162696802e+54
9
-8.454561893044275e-38
-1.1451828241200583e-42
-2.5068389416539186e-40

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06146
16146

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.5s2029×body1280valid
860.0ms1678×body640valid
697.0ms6021×body80valid
288.0ms815×body320valid
105.0ms435×body160valid

Profiling

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