Details

sample100.0ms

Algorithm

intervals

Results

32.0ms	72×	body	1280	valid
22.0ms	72×	body	640	valid
16.0ms	287×	body	80	valid
7.0ms	44×	body	320	valid
3.0ms	20×	body	160	valid

simplify372.0ms

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	271	9
5	533	9
6	1023	9
7	1395	9
8	4367	9
9	5002	9

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 16.5b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U)
0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
6.1b	(- (exp l) (exp (- l)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

20.0ms	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U)
11.0ms	(* J (- (exp l) (exp (- l))))
13.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
5.0ms	(- (exp l) (exp (- l)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U)
59.0ms	(* J (- (exp l) (exp (- l))))
96.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
38.0ms	(- (exp l) (exp (- l)))

simplify49.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	377	928
1	1432	833
2	5001	826

prune235.0ms

Filtered

101 candidates to 71 candidates (70.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	2	102

Merged error: 0.0b

Counts

102 → 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))

rewrite118.0ms

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:

57.0ms	(+ (* (* 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))
42.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
7.0ms	(* 1/3 (pow l 3))

series632.0ms

Counts

4 → 12

Calls

4 calls:

364.0ms	(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
48.0ms	(* 1/60 (pow l 5))
176.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
44.0ms	(* 1/3 (pow l 3))

simplify76.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (16.0ms)

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

prune316.0ms

Filtered

122 candidates to 75 candidates (61.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	116	8	124

Merged error: 0.0b

Counts

124 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
38×	`associate-l`
35×	`add-sqr-sqrt`
33×	`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×	`add-log-exp` `sqr-pow`
2×	`pow-to-exp` `associate-*l/` `pow-exp`
1×	`flip3-+` `unpow3` `flip-+`

Counts

4 → 114

Calls

4 calls:

6.0ms	(* 1/60 (pow l 5))
41.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (* J (cos (/ K 2.0))))
5.0ms	(* J (cos (/ K 2.0)))
6.0ms	(* 1/3 (pow l 3))

series269.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* 1/60 (pow l 5))
127.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (* J (cos (/ K 2.0))))
49.0ms	(* J (cos (/ K 2.0)))
37.0ms	(* 1/3 (pow l 3))

simplify70.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	430	914
1	2158	825
2	5001	825

prune329.0ms

Filtered

126 candidates to 76 candidates (60.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	126	8	134

Merged error: 0b

Counts

134 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

80×	`associate-l`
72×	`*-un-lft-identity`
36×	`distribute-lft-out`
35×	`add-sqr-sqrt`
24×	`associate-r`
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` `associate-*l/` `cbrt-unprod`
5×	`*-commutative`
4×	`add-log-exp` `sqr-pow`
2×	`pow-to-exp` `flip3-+` `pow-exp` `flip-+`
1×	`unpow3`

Counts

4 → 126

Calls

4 calls:

6.0ms	(* 1/60 (pow l 5))
44.0ms	(* (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))) J)
44.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
8.0ms	(* 1/3 (pow l 3))

series315.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* 1/60 (pow l 5))
116.0ms	(* (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))) J)
98.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
45.0ms	(* 1/3 (pow l 3))

simplify72.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	450	1203
1	2095	1085
2	5001	1085

prune506.0ms

Filtered

138 candidates to 80 candidates (58.0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	138	8	146

Merged error: 0b

Counts

146 → 8

regimes263.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b 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

sample3.1s

Algorithm

intervals

Results

1.1s	2642×	body	1280	valid
703.0ms	2615×	body	640	valid
488.0ms	8571×	body	80	valid
269.0ms	1432×	body	320	valid
90.0ms	765×	body	160	valid