Details

sample140.0ms

Algorithm

intervals

Results

50.0ms	67×	body	1280	valid
33.0ms	64×	body	640	valid
21.0ms	172×	body	80	valid
10.0ms	25×	body	320	valid
8.0ms	18×	body	160	valid

simplify31.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (29.0ms)

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: 30.6b

Counts

2 → 2

localize27.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.6b	(* (/ (pow t 3.0) (* l l)) (sin k))
12.3b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
16.5b	(/ (pow t 3.0) (* l l))

rewrite56.0ms

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))
23.0ms	(* (* (* (/ (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:

311.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
244.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
630.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
181.0ms	(/ (pow t 3.0) (* l l))

simplify128.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 1 (23.0ms)

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

prune525.0ms

Filtered

164 candidates to 101 candidates (61.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	153	11	164
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	154	12	166

Merged error: 15.7b

Counts

166 → 12

localize31.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.8b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.1b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
12.3b	(* (* (* (/ (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))

rewrite83.0ms

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:

17.0ms	(* (* (/ (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))

series1.5s

Counts

4 → 12

Calls

4 calls:

358.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
239.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
193.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
723.0ms	(* (* (* (/ (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))

simplify69.0ms

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 158 candidates (63.5%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	238	11	249
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	242	19	261

Merged error: 9.5b

Counts

261 → 19

localize26.0ms

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)))
1.6b	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.8b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
12.3b	(* (* (* (/ (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))

rewrite264.0ms

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:

63.0ms	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
46.0ms	(* (* (/ (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))

series1.8s

Counts

4 → 12

Calls

4 calls:

277.0ms	(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
351.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
231.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
907.0ms	(* (* (* (/ (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))

simplify152.0ms

Algorithm

egg-herbie

Counts

730 → 730

Iterations

Useful iterations: 1 (53.0ms)

Iter	Nodes	Cost
0	2745	11522
1	5002	10788

prune3.2s

Filtered

730 candidates to 487 candidates (66.7%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	716	14	730
Fresh	7	11	18
Picked	1	0	1
Done	0	0	0
Total	724	25	749

Merged error: 6.9b

Counts

749 → 25

localize27.0ms

Local error

Found 4 expressions with local error:

3.0b	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.8b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.9b	(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (cbrt t) 3.0)))
9.0b	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

576×	`add-exp-log`
347×	`prod-exp`
183×	`div-exp`
128×	`times-frac`
103×	`add-cbrt-cube`
80×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
67×	`pow-to-exp` `add-cube-cbrt` `pow-exp`
56×	`unpow-prod-down`
53×	`cbrt-unprod`
36×	`associate-l`
34×	`associate-/r*`
28×	`cbrt-prod` `associate-*l/`
25×	`associate-*r/`
23×	`cbrt-undiv`
19×	`frac-times`
14×	`tan-quot`
13×	`pow1`
11×	`associate-r` `associate-/l/`
10×	`sqr-pow`
8×	`flip3-+` `flip-+`
5×	`pow-prod-down` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`*-commutative` `distribute-lft-out`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r/` `associate-/l*`

Counts

4 → 328

Calls

4 calls:

15.0ms	(* (* (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))
40.0ms	(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (cbrt t) 3.0)))
28.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.1s

Counts

4 → 12

Calls

4 calls:

352.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
232.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
729.0ms	(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (cbrt t) 3.0)))
823.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify95.0ms

Algorithm

egg-herbie

Counts

340 → 340

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1759	6282
1	5002	5767

prune1.2s

Filtered

340 candidates to 199 candidates (58.5%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	330	10	340
Fresh	9	15	24
Picked	1	0	1
Done	0	0	0
Total	340	25	365

Merged error: 5.8b

Counts

365 → 25

regimes680.0ms

Accuracy

52.6% (3.6b remaining)

Error of 10.4b against oracle of 6.8b and baseline of 14.3b

bsearch319.0ms

Steps

Iters	Range		Point
9	4.551365472929582e-09	14.716166499582775	6.442870362593039e-06
7	-1.4827304130402651e-151	-1.3532601870290134e-153	-1.4624216300770186e-151

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	95
1	64	95

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.6s	2042×	body	1280	valid
978.0ms	1781×	body	640	valid
737.0ms	5965×	body	80	valid
318.0ms	821×	body	320	valid
111.0ms	417×	body	160	valid