Details

sample144.0ms

Algorithm

intervals

Results

62.0ms	78×	body	1280	valid
28.0ms	54×	body	640	valid
24.0ms	191×	body	80	valid
9.0ms	23×	body	320	valid
3.0ms	12×	body	160	valid

simplify31.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (30.0ms)

Iter	Nodes	Cost
0	48	13
1	161	13
2	944	13
3	5002	12

prune12.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 35.6b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.9b	(* (/ (pow t 3.0) (* l l)) (sin k))
17.4b	(/ (pow t 3.0) (* l l))
18.3b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite55.0ms

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×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `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 → 152

Calls

4 calls:

11.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
9.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
6.0ms	(/ (pow t 3.0) (* l l))
23.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

332.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
256.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
187.0ms	(/ (pow t 3.0) (* l l))
653.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify119.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	817	1679
1	4726	1405
2	5001	1405

prune532.0ms

Filtered

164 candidates to 101 candidates (61.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	152	12	164
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	153	13	166

Merged error: 19.3b

Counts

166 → 13

localize26.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.1b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.4b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
18.3b	(* (* (* (/ (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))

rewrite82.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 237

Calls

4 calls:

20.0ms	(* (* (/ (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)
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))

series1.6s

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))
244.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
203.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
753.0ms	(* (* (* (/ (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

249 → 249

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1364	3882
1	5001	3394

prune1.0s

Filtered

249 candidates to 159 candidates (63.9%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	239	10	249
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	242	20	262

Merged error: 13.9b

Counts

262 → 20

localize29.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
2.4b	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.1b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
18.3b	(* (* (* (/ (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))

rewrite246.0ms

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×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-out`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-/r/`

Counts

4 → 718

Calls

4 calls:

61.0ms	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
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))

series1.9s

Counts

4 → 12

Calls

4 calls:

288.0ms	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
369.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
233.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
993.0ms	(* (* (* (/ (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))

simplify150.0ms

Algorithm

egg-herbie

Counts

730 → 730

Iterations

Useful iterations: 1 (51.0ms)

Iter	Nodes	Cost
0	2745	11522
1	5002	10788

prune3.1s

Filtered

730 candidates to 487 candidates (66.7%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	717	13	730
Fresh	6	13	19
Picked	1	0	1
Done	0	0	0
Total	724	26	750

Merged error: 11.4b

Counts

750 → 26

localize26.0ms

Local error

Found 4 expressions with local error:

2.5b	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
3.1b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.5b	(/ (* (* (* (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)))
13.5b	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite121.0ms

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×	`expm1-log1p-u` `frac-times` `flip3-+` `flip-+` `log1p-expm1-u` `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 → 272

Calls

4 calls:

15.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
11.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
39.0ms	(/ (* (* (* (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)))
27.0ms	(* (* (* (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:

252.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
247.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
724.0ms	(/ (* (* (* (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)))
571.0ms	(* (* (* (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

284 → 284

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1375	5522
1	5001	4850

prune797.0ms

Filtered

284 candidates to 136 candidates (47.9%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	273	11	284
Fresh	8	17	25
Picked	1	0	1
Done	0	0	0
Total	282	28	310

Merged error: 8.8b

Counts

310 → 28

regimes853.0ms

Accuracy

50.4% (4.1b remaining)

Error of 10.9b against oracle of 6.9b and baseline of 15.1b

bsearch330.0ms

Steps

Iters	Range		Point
7	1.8222587195312444e-155	1.1515555104326831e-153	1.0819204815086833e-153
9	-8.734865069047032e-104	-1.8709050215558939e-112	-3.0721932269682408e-105

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	119
1	72	119

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.5s	2015×	body	1280	valid
905.0ms	1710×	body	640	valid
726.0ms	5950×	body	80	valid
356.0ms	898×	body	320	valid
118.0ms	463×	body	160	valid