Details

sample6.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 43.136597%

Results

50.0ms	61×	body	1280	valid
41.0ms	65×	body	640	valid
25.0ms	184×	body	80	valid
16.0ms	37×	body	320	valid
3.0ms	11×	body	160	valid

simplify30.0ms

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

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:

3.2b	(* (/ (pow t 3.0) (* l l)) (sin k))
3.4b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
15.1b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
15.8b	(/ (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:

9.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
11.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
25.0ms	(* (* (* (/ (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))

series331.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
74.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
163.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
39.0ms	(/ (pow t 3.0) (* l l))

simplify116.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (99.0ms)

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

prune313.0ms

Filtered

96 candidates to 156 candidates (-62.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	147	9	156
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	148	9	157

Merged error: 22.2b

Counts

157 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

3.1b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.4b	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
7.5b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
15.1b	(* (* (* (/ (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:

10.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
16.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
5.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
32.0ms	(* (* (* (/ (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))

series360.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
82.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
44.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
180.0ms	(* (* (* (/ (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))

simplify65.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1430	3890
1	5002	3397

prune615.0ms

Filtered

151 candidates to 241 candidates (-59.6%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	229	12	241
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	232	18	250

Merged error: 16.5b

Counts

250 → 18

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt t) 3.0)
3.1b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.4b	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
15.1b	(* (* (* (/ (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))

rewrite147.0ms

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)
10.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
48.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
59.0ms	(* (* (* (/ (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))

series366.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(pow (cbrt t) 3.0)
54.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
82.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
183.0ms	(* (* (* (/ (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))

simplify74.0ms

Algorithm

egg-herbie

Counts

310 → 310

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1605	5429
1	5001	4779

prune656.0ms

Filtered

136 candidates to 310 candidates (-127.9%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	299	11	310
Fresh	6	11	17
Picked	1	0	1
Done	0	0	0
Total	306	22	328

Merged error: 13.7b

Counts

328 → 22

localize26.0ms

Local error

Found 4 expressions with local error:

2.8b	(* (* (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))
4.5b	(/ (* (* (* (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)))
12.5b	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite113.0ms

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×	`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 → 320

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))
38.0ms	(/ (* (* (* (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)))
27.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series510.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
56.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
177.0ms	(/ (* (* (* (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)))
197.0ms	(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify91.0ms

Algorithm

egg-herbie

Counts

332 → 332

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1842	6305
1	5001	5784

prune785.0ms

Filtered

191 candidates to 332 candidates (-73.8%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	314	18	332
Fresh	12	9	21
Picked	1	0	1
Done	0	0	0
Total	327	27	354

Merged error: 12.6b

Counts

354 → 27

regimes689.0ms

Accuracy

0% (2.8b remaining)

Error of 14.5b against oracle of 11.7b and baseline of 14.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	35
1	32	35

end0.0ms

sample10.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 43.136597%

Results

1.8s	2084×	body	1280	valid
1.1s	6018×	body	80	valid
1.0s	1729×	body	640	valid
349.0ms	840×	body	320	valid
127.0ms	429×	body	160	valid

Details

sample6.4s

simplify30.0ms

prune5.0ms

localize21.0ms

rewrite57.0ms

series331.0ms

simplify116.0ms

prune313.0ms

localize28.0ms

rewrite77.0ms

series360.0ms

simplify65.0ms

prune615.0ms

localize26.0ms

rewrite147.0ms

series366.0ms

simplify74.0ms

prune656.0ms

localize26.0ms

rewrite113.0ms

series510.0ms

simplify91.0ms

prune785.0ms

regimes689.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample10.8s

Profiling