Details

analyze1.3s

Algorithm

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 9.551872%

Guaranteed chance to sample good point: 76.885776%

sample122.0ms

Algorithm

intervals

Results

22.0ms	36×	body	1280	valid
19.0ms	54×	body	640	valid
15.0ms	37×	body	1280	invalid
12.0ms	44×	body	640	invalid
12.0ms	125×	body	80	valid
7.0ms	98×	body	80	invalid
6.0ms	25×	body	320	valid
5.0ms	24×	body	320	invalid
2.0ms	16×	body	160	valid
1.0ms	7×	body	160	invalid

simplify191.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	9
1	41	9
2	83	9
3	173	9
4	284	9
5	556	9
6	919	9
7	1220	9
8	3918	9
9	5002	9

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: 19.4b

Counts

2 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0)))
7.3b	(- (exp l) (exp (neg l)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`add-log-exp`
3×	`add-cube-cbrt` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3--` `associate-r/` `associate-l/` `flip--`
1×	`sub-neg` `diff-log` `associate-l` `*-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 34

Calls

2 calls:

9.0ms	(* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0)))
5.0ms	(- (exp l) (exp (neg l)))

series26.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0)))
5.0ms	(- (exp l) (exp (neg l)))

simplify130.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	227	370
1	860	305
2	4686	304
3	5002	304

prune79.0ms

Filtered

29 candidates to 40 candidates (-37.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	3	41

Merged error: 0.1b

Counts

41 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))
0.1b	(* 1/60 (pow l 5))
0.1b	(* 1/3 (pow l 3))
0.1b	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
22×	`associate-r`
19×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `prod-exp` `add-log-exp`
8×	`unpow-prod-down`
7×	`associate-l` `unswap-sqr`
5×	`cbrt-unprod`
4×	`cube-prod` `sqr-pow`
3×	`pow-prod-down` `sum-log` `*-commutative`
2×	`pow-to-exp` `flip3-+` `associate-r/` `associate-l/` `pow-exp` `flip-+`
1×	`+-commutative` `cube-mult` `associate-+r+` `unpow3`

Counts

4 → 89

Calls

4 calls:

7.0ms	(+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))
5.0ms	(* 1/60 (pow l 5))
6.0ms	(* 1/3 (pow l 3))
11.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))
4.0ms	(* 1/60 (pow l 5))
4.0ms	(* 1/3 (pow l 3))
39.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

simplify65.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	443	717
1	2193	619
2	5001	619

prune216.0ms

Filtered

64 candidates to 101 candidates (-57.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	97	7	104

Merged error: 0.0b

Counts

104 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/60 (pow l 5))
0.1b	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
0.1b	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
0.1b	(* 1/3 (pow l 3))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
23×	`associate-r`
21×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-l`
11×	`pow1`
10×	`prod-exp`
8×	`unpow-prod-down` `unswap-sqr`
6×	`cbrt-unprod`
4×	`cube-prod` `pow-prod-down` `associate-l/` `-commutative` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `flip3-+` `associate-*r/` `pow-exp` `flip-+`
1×	`cube-mult` `unpow3`

Counts

4 → 96

Calls

4 calls:

5.0ms	(* 1/60 (pow l 5))
11.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
10.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
6.0ms	(* 1/3 (pow l 3))

series60.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* 1/60 (pow l 5))
36.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
13.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
6.0ms	(* 1/3 (pow l 3))

simplify67.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	444	856
1	2079	731
2	5001	731

prune229.0ms

Filtered

69 candidates to 108 candidates (-56.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	107	8	115

Merged error: 0.0b

Counts

115 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

5.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))

series80.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
17.0ms	(cbrt (cos (/ K 2.0)))
17.0ms	(cbrt (cos (/ K 2.0)))
17.0ms	(cbrt (cos (/ K 2.0)))

simplify78.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	134	575
1	452	524
2	2183	487
3	5002	482

prune253.0ms

Filtered

60 candidates to 85 candidates (-41.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	86	7	93

Merged error: 0.0b

Counts

93 → 7

regimes572.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	12
1	30	12

end0.0ms

analyze1.4s

Algorithm

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 9.551872%

Guaranteed chance to sample good point: 76.885776%

sample3.6s

Algorithm

intervals

Results

742.0ms	1217×	body	1280	valid
605.0ms	1485×	body	1280	invalid
485.0ms	1368×	body	640	valid
360.0ms	1225×	body	640	invalid
295.0ms	4143×	body	80	valid
195.0ms	2764×	body	80	invalid
187.0ms	817×	body	320	valid
139.0ms	646×	body	320	invalid
69.0ms	455×	body	160	valid
42.0ms	298×	body	160	invalid

Details

analyze1.3s

sample122.0ms

simplify191.0ms

prune5.0ms

localize13.0ms

rewrite14.0ms

series26.0ms

simplify130.0ms

prune79.0ms

localize18.0ms

rewrite31.0ms

series52.0ms

simplify65.0ms

prune216.0ms

localize18.0ms

rewrite34.0ms

series60.0ms

simplify67.0ms

prune229.0ms

localize25.0ms

rewrite10.0ms

series80.0ms

simplify78.0ms

prune253.0ms

regimes572.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.4s

sample3.6s

Profiling