Details

sample92.0ms

Algorithm

intervals

Results

31.0ms	75×	body	1280	valid
19.0ms	78×	body	640	valid
14.0ms	251×	body	80	valid
8.0ms	45×	body	320	valid
2.0ms	19×	body	160	valid

simplify365.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	9
1	41	9
2	83	9
3	173	9
4	271	9
5	533	9
6	1023	9
7	1395	9
8	4367	9
9	5002	9

prune6.0ms

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: 17.3b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
5.6b	(- (exp l) (exp (- l)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`associate-l`
15×	`*-un-lft-identity`
13×	`associate-r`
10×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt`
5×	`add-log-exp` `unswap-sqr`
4×	`associate-*r/` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`sub-neg` `flip3--` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/`
1×	`diff-log`

Counts

3 → 75

Calls

3 calls:

8.0ms	(* J (- (exp l) (exp (- l))))
12.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
5.0ms	(- (exp l) (exp (- l)))

series185.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(* J (- (exp l) (exp (- l))))
96.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
36.0ms	(- (exp l) (exp (- l)))

simplify39.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	288	712
1	1165	627
2	5001	620

prune192.0ms

Filtered

84 candidates to 59 candidates (29.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	2	85

Merged error: 0.1b

Counts

85 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
47×	`associate-l`
31×	`add-sqr-sqrt` `associate-r`
21×	`distribute-lft-out`
19×	`add-exp-log`
14×	`add-cube-cbrt`
13×	`pow1` `add-cbrt-cube`
10×	`unswap-sqr`
9×	`prod-exp`
8×	`unpow-prod-down`
6×	`add-log-exp`
5×	`pow-prod-down` `cbrt-unprod`
4×	`*-commutative` `sqr-pow`
2×	`pow-to-exp` `flip3-+` `associate-r/` `associate-l/` `pow-exp` `flip-+`
1×	`+-commutative` `unpow3` `sum-log`

Counts

4 → 110

Calls

4 calls:

52.0ms	(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
6.0ms	(* 1/60 (pow l 5))
40.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
6.0ms	(* 1/3 (pow l 3))

series605.0ms

Counts

4 → 12

Calls

4 calls:

348.0ms	(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
47.0ms	(* 1/60 (pow l 5))
167.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
42.0ms	(* 1/3 (pow l 3))

simplify71.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	499	1079
1	2253	1002
2	5003	1002

prune290.0ms

Filtered

122 candidates to 75 candidates (38.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	119	5	124

Merged error: 0.0b

Counts

124 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 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))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
61×	`associate-l`
43×	`associate-r`
36×	`distribute-lft-out`
35×	`add-sqr-sqrt`
21×	`add-exp-log`
16×	`add-cube-cbrt`
15×	`pow1` `add-cbrt-cube`
11×	`unswap-sqr`
10×	`prod-exp`
8×	`unpow-prod-down`
6×	`pow-prod-down` `cbrt-unprod`
5×	`*-commutative`
4×	`associate-*l/` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `flip3-+` `associate-*r/` `pow-exp` `flip-+`
1×	`unpow3`

Counts

4 → 126

Calls

4 calls:

6.0ms	(* 1/60 (pow l 5))
44.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
34.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
6.0ms	(* 1/3 (pow l 3))

series352.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* 1/60 (pow l 5))
172.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
90.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
41.0ms	(* 1/3 (pow l 3))

simplify82.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	468	1112
1	2269	993
2	5001	993

prune321.0ms

Filtered

138 candidates to 78 candidates (43.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	138	5	143

Merged error: 0.0b

Counts

143 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/60 (pow l 5))
0.1b	(* (* J (cos (/ K 2.0))) (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
0.1b	(* 1/3 (pow l 3))
0.2b	(* J (cos (/ K 2.0)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
37×	`associate-l`
35×	`add-sqr-sqrt`
34×	`associate-r`
21×	`add-exp-log`
18×	`distribute-lft-out`
16×	`add-cube-cbrt`
15×	`pow1` `add-cbrt-cube`
11×	`unswap-sqr`
10×	`prod-exp`
8×	`unpow-prod-down`
6×	`pow-prod-down` `cbrt-unprod`
5×	`*-commutative`
4×	`+-commutative` `distribute-rgt-in` `associate-+r+` `distribute-lft-in` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `associate-*r/` `pow-exp`
1×	`flip3-+` `unpow3` `flip-+`

Counts

4 → 122

Calls

4 calls:

9.0ms	(* 1/60 (pow l 5))
40.0ms	(* (* J (cos (/ K 2.0))) (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
6.0ms	(* 1/3 (pow l 3))
5.0ms	(* J (cos (/ K 2.0)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* 1/60 (pow l 5))
265.0ms	(* (* J (cos (/ K 2.0))) (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
43.0ms	(* 1/3 (pow l 3))
42.0ms	(* J (cos (/ K 2.0)))

simplify83.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	548	960
1	2815	871
2	5001	871

prune327.0ms

Filtered

134 candidates to 82 candidates (38.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	134	5	139

Merged error: 0.0b

Counts

139 → 5

regimes220.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	12
1	30	12

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.1s	2623×	body	1280	valid
691.0ms	2614×	body	640	valid
484.0ms	8516×	body	80	valid
252.0ms	1429×	body	320	valid
94.0ms	775×	body	160	valid