Details

sample144.0ms

Algorithm

intervals

Results

55.0ms	74×	body	1280	valid
27.0ms	54×	body	640	valid
23.0ms	194×	body	80	valid
15.0ms	28×	body	320	valid
3.0ms	13×	body	160	valid

simplify29.0ms

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

prune5.0ms

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: 33.7b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
2.5b	(* (/ (pow t 3.0) (* l l)) (sin k))
14.2b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
21.2b	(/ (pow t 3.0) (* l l))

rewrite57.0ms

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))
26.0ms	(* (* (* (/ (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))

series327.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
56.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
161.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
38.0ms	(/ (pow t 3.0) (* l l))

simplify121.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (103.0ms)

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

prune326.0ms

Filtered

156 candidates to 96 candidates (38.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	142	14	156
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	143	14	157

Merged error: 21.3b

Counts

157 → 14

localize27.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.3b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.5b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
14.2b	(* (* (* (/ (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))

rewrite77.0ms

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))
11.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
29.0ms	(* (* (* (/ (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))

series355.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
54.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
42.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
179.0ms	(* (* (* (/ (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 (29.0ms)

Iter	Nodes	Cost
0	1430	3890
1	5002	3397

prune603.0ms

Filtered

241 candidates to 151 candidates (37.3%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	231	10	241
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	234	21	255

Merged error: 15.3b

Counts

255 → 21

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt t) 3.0)
2.2b	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.3b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
14.2b	(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

773×	`add-exp-log`
557×	`prod-exp`
171×	`div-exp`
115×	`add-cbrt-cube`
98×	`pow-to-exp` `pow-exp`
75×	`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` `associate-*r/`
26×	`unpow-prod-down`
17×	`pow-prod-down`
16×	`tan-quot`
13×	`cbrt-undiv` `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)
26.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (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))
38.0ms	(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series358.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(pow (cbrt t) 3.0)
78.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
54.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
179.0ms	(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify76.0ms

Algorithm

egg-herbie

Counts

310 → 310

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1565	5389
1	5002	4520

prune600.0ms

Filtered

310 candidates to 136 candidates (56.1%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	302	8	310
Fresh	5	15	20
Picked	1	0	1
Done	0	0	0
Total	308	23	331

Merged error: 15.0b

Counts

331 → 23

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt t) 3.0)
0.8b	(* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
3.3b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
15.7b	(* (* (* (pow (cbrt t) 3.0) (/ (pow (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

773×	`add-exp-log`
557×	`prod-exp`
171×	`div-exp`
115×	`add-cbrt-cube`
98×	`pow-to-exp` `pow-exp`
75×	`cbrt-unprod`
45×	`add-sqr-sqrt`
38×	`associate-l`
35×	`*-un-lft-identity`
34×	`times-frac`
33×	`associate-*r/`
31×	`frac-times`
30×	`pow1` `add-cube-cbrt`
27×	`associate-*l/`
26×	`unpow-prod-down`
17×	`pow-prod-down`
15×	`tan-quot`
13×	`cbrt-undiv` `cbrt-prod`
10×	`flip3-+` `flip-+`
9×	`associate-r`
6×	`unswap-sqr`
5×	`distribute-rgt-in` `distribute-lft-in` `sqr-pow`
4×	`add-log-exp`
3×	`pow-unpow` `*-commutative` `distribute-lft-out`
2×	`pow-pow`
1×	`pow1/3` `div-inv`

Counts

4 → 301

Calls

4 calls:

3.0ms	(pow (cbrt t) 3.0)
14.0ms	(* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
12.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
35.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(pow (cbrt t) 3.0)
18.0ms	(* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
55.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
180.0ms	(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

simplify74.0ms

Algorithm

egg-herbie

Counts

313 → 313

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1606	5726
1	5002	4973

prune480.0ms

Filtered

313 candidates to 140 candidates (55.3%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	306	7	313
Fresh	4	18	22
Picked	1	0	1
Done	0	0	0
Total	311	25	336

Merged error: 14.9b

Counts

336 → 25

regimes797.0ms

Accuracy

23.1% (2.6b remaining)

Error of 16.7b against oracle of 14.1b and baseline of 17.5b

bsearch110.0ms

Steps

Iters	Range		Point
8	1.4815107687111837e-142	8.335484339554941e-140	1.496211926208139e-142
9	-1.4595262460708148e-147	-1.3068141225436395e-152	-1.8549218288513938e-152

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	39
1	47	39

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.5s	2036×	body	1280	valid
1.1s	1720×	body	640	valid
722.0ms	5998×	body	80	valid
322.0ms	839×	body	320	valid
105.0ms	424×	body	160	valid

Details

sample144.0ms

simplify29.0ms

prune5.0ms

localize21.0ms

rewrite57.0ms

series327.0ms

simplify121.0ms

prune326.0ms

localize27.0ms

rewrite77.0ms

series355.0ms

simplify60.0ms

prune603.0ms

localize26.0ms

rewrite102.0ms

series358.0ms

simplify76.0ms

prune600.0ms

localize24.0ms

rewrite88.0ms

series300.0ms

simplify74.0ms

prune480.0ms

regimes797.0ms

bsearch110.0ms

simplify2.0ms

end0.0ms

sample4.2s

Profiling