Details

sample150.0ms

Algorithm

intervals

Results

57.0ms	76×	body	1280	valid
26.0ms	176×	body	80	valid
24.0ms	46×	body	640	valid
8.0ms	22×	body	320	valid
4.0ms	17×	body	160	valid

simplify32.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune8.0ms

Filtered

1 candidates to 0 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: 29.8b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
4.0b	(* (/ (pow t 3.0) (* l l)) (sin k))
11.4b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
15.5b	(/ (pow t 3.0) (* l l))

rewrite53.0ms

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:

11.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
9.0ms	(* (/ (pow t 3.0) (* l l)) (sin 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:

76.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
56.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
157.0ms	(* (* (* (/ (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))

simplify123.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	857	1728
1	4784	1448
2	5001	1444

prune331.0ms

Filtered

156 candidates to 96 candidates (38.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	144	12	156
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	12	157

Merged error: 17.6b

Counts

157 → 12

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))
4.9b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
6.9b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
11.4b	(* (* (* (/ (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:

16.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
10.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
31.0ms	(* (* (* (/ (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))

series362.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
55.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
43.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
182.0ms	(* (* (* (/ (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

241 → 241

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1430	3890
1	5002	3397

prune609.0ms

Filtered

241 candidates to 151 candidates (37.3%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	229	12	241
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	233	20	253

Merged error: 13.7b

Counts

253 → 20

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt t) 3.0)
2.4b	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.9b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
11.4b	(* (* (* (/ (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))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

773×	`add-exp-log`
437×	`prod-exp`
291×	`div-exp`
115×	`add-cbrt-cube`
98×	`pow-to-exp` `pow-exp`
63×	`cbrt-unprod`
44×	`associate-*l/`
43×	`add-sqr-sqrt`
36×	`associate-l`
35×	`*-un-lft-identity`
34×	`frac-times` `times-frac`
30×	`pow1` `add-cube-cbrt`
26×	`unpow-prod-down`
25×	`cbrt-undiv`
17×	`pow-prod-down`
16×	`tan-quot`
14×	`associate-*r/`
13×	`cbrt-prod`
11×	`associate-r`
8×	`flip3-+` `flip-+`
5×	`unswap-sqr` `sqr-pow`
4×	`add-log-exp`
3×	`pow-unpow` `*-commutative` `distribute-lft-out`
2×	`pow-pow`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/3` `div-inv`

Counts

4 → 298

Calls

4 calls:

3.0ms	(pow (cbrt t) 3.0)
43.0ms	(* (* (/ (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))
57.0ms	(* (* (* (/ (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))

series357.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(pow (cbrt t) 3.0)
80.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
53.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
177.0ms	(* (* (* (/ (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))

simplify79.0ms

Algorithm

egg-herbie

Counts

310 → 310

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1605	5429
1	5001	4779

prune620.0ms

Filtered

310 candidates to 136 candidates (56.1%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	300	10	310
Fresh	8	11	19
Picked	1	0	1
Done	0	0	0
Total	309	21	330

Merged error: 10.9b

Counts

330 → 21

localize26.0ms

Local error

Found 4 expressions with local error:

3.9b	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
4.9b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
6.3b	(/ (* (* (* (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)))
8.6b	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite113.0ms

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:

18.0ms	(* (* (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))
34.0ms	(/ (* (* (* (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)))
28.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series426.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
55.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
176.0ms	(/ (* (* (* (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)))
136.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify76.0ms

Algorithm

egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1470	5541
1	5001	4874

prune519.0ms

Filtered

276 candidates to 129 candidates (53.3%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	261	15	276
Fresh	9	11	20
Picked	1	0	1
Done	0	0	0
Total	271	26	297

Merged error: 9.8b

Counts

297 → 26

regimes890.0ms

Accuracy

0% (3.2b remaining)

Error of 12.8b against oracle of 9.6b and baseline of 12.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	35
1	39	35

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.6s	2011×	body	1280	valid
846.0ms	1605×	body	640	valid
703.0ms	5640×	body	80	valid
320.0ms	829×	body	320	valid
121.0ms	449×	body	160	valid

Details

sample150.0ms

simplify32.0ms

prune8.0ms

localize20.0ms

rewrite53.0ms

series330.0ms

simplify123.0ms

prune331.0ms

localize26.0ms

rewrite78.0ms

series362.0ms

simplify62.0ms

prune609.0ms

localize26.0ms

rewrite144.0ms

series357.0ms

simplify79.0ms

prune620.0ms

localize26.0ms

rewrite113.0ms

series426.0ms

simplify76.0ms

prune519.0ms

regimes890.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample4.0s

Profiling