Details

sample127.0ms

Algorithm

intervals

Results

51.0ms	74×	body	1280	valid
25.0ms	51×	body	640	valid
21.0ms	186×	body	80	valid
8.0ms	23×	body	320	valid
3.0ms	12×	body	160	valid

simplify31.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	13
1	158	13
2	903	13
3	5001	13

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 30.8b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

2.0b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.4b	(* (/ (pow t 3.0) (* l l)) (sin k))
12.9b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
16.3b	(/ (pow t 3.0) (* l l))

rewrite60.0ms

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:

12.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
10.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
25.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
7.0ms	(/ (pow t 3.0) (* l l))

series1.5s

Counts

4 → 12

Calls

4 calls:

342.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
264.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
672.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
188.0ms	(/ (pow t 3.0) (* l l))

simplify130.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	801	1619
1	4646	1348
2	5002	1348

prune475.0ms

Filtered

156 candidates to 93 candidates (59.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	146	10	156
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	147	10	157

Merged error: 18.4b

Counts

157 → 10

localize26.0ms

Local error

Found 4 expressions with local error:

2.0b	(* (* (/ (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))
7.5b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
12.9b	(* (* (* (/ (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))

rewrite88.0ms

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:

18.0ms	(* (* (/ (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))
9.0ms	(/ (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:

386.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
257.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
210.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
783.0ms	(* (* (* (/ (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 (31.0ms)

Iter	Nodes	Cost
0	1347	3795
1	5001	3312

prune945.0ms

Filtered

241 candidates to 150 candidates (62.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	232	9	241
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	234	17	251

Merged error: 10.9b

Counts

251 → 17

localize25.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
2.0b	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.5b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
12.9b	(* (* (* (/ (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))

rewrite279.0ms

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:

68.0ms	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
50.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (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))
67.0ms	(* (* (* (/ (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))

series1.9s

Counts

4 → 12

Calls

4 calls:

522.0ms	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
384.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
249.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
783.0ms	(* (* (* (/ (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))

simplify154.0ms

Algorithm

egg-herbie

Counts

722 → 722

Iterations

Useful iterations: 1 (55.0ms)

Iter	Nodes	Cost
0	2727	11417
1	5001	10598

prune3.1s

Filtered

722 candidates to 479 candidates (66.3%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	708	14	722
Fresh	7	9	16
Picked	1	0	1
Done	0	0	0
Total	716	23	739

Merged error: 9.8b

Counts

739 → 23

localize26.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
4.5b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.4b	(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
10.1b	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite125.0ms

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:

16.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
12.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
43.0ms	(/ (* (* (* (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)))
29.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.8s

Counts

4 → 12

Calls

4 calls:

261.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
258.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
758.0ms	(/ (* (* (* (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)))
563.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify81.0ms

Algorithm

egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1356	5415
1	5002	4747

prune764.0ms

Filtered

276 candidates to 128 candidates (46.4%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	268	8	276
Fresh	6	16	22
Picked	1	0	1
Done	0	0	0
Total	275	24	299

Merged error: 8.7b

Counts

299 → 24

Details

sample127.0ms

simplify31.0ms

prune4.0ms

localize25.0ms

rewrite60.0ms

series1.5s

simplify130.0ms

prune475.0ms

localize26.0ms

rewrite88.0ms

series1.6s

simplify63.0ms

prune945.0ms

localize25.0ms

rewrite279.0ms

series1.9s

simplify154.0ms

prune3.1s

localize26.0ms

rewrite125.0ms

series1.8s

simplify81.0ms

prune764.0ms

regimes670.0ms

bsearch6.0ms

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