Details

sample109.0ms

Algorithm

intervals

Results

39.0ms	85×	body	1280	valid
22.0ms	84×	body	640	valid
14.0ms	258×	body	80	valid
10.0ms	56×	body	320	valid
3.0ms	27×	body	160	valid

simplify371.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	8
1	44	8
2	91	8
3	195	8
4	332	8
5	652	8
6	1279	8
7	1694	8
8	4980	8
9	5001	8

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 14.9b

Counts

2 → 1

localize13.0ms

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)))) (cos (/ K 2.0)))
0.3b	(* J (- (exp l) (exp (- l))))
4.8b	(- (exp l) (exp (- l)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
27×	`prod-diff`
26×	`add-cube-cbrt`
11×	`pow1` `add-exp-log` `distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
8×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `associate-r/` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `fma-neg` `flip--`
2×	`associate-l/` `-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `fma-def` `flip3-+` `diff-log` `sum-log` `flip-+` `unswap-sqr`

Counts

4 → 110

Calls

4 calls:

10.0ms	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U)
10.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
9.0ms	(* J (- (exp l) (exp (- l))))
9.0ms	(- (exp l) (exp (- l)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U)
88.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
56.0ms	(* J (- (exp l) (exp (- l))))
37.0ms	(- (exp l) (exp (- l)))

simplify58.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	448	1507
1	1734	1074
2	5002	1037

prune269.0ms

Filtered

122 candidates to 73 candidates (59.8%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	1	123

Merged error: 0.3b

Counts

123 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-udef`
2×	`*-commutative`
1×	`+-commutative` `distribute-rgt-in` `fma-def` `distribute-lft-in` `flip3-+` `sum-log` `flip-+` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

5.0ms	(+ (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))) U)
1.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
3.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
5.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

series581.0ms

Counts

4 → 12

Calls

4 calls:

240.0ms	(+ (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))) U)
51.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
131.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
159.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	288	798
1	1356	696
2	5003	696

prune297.0ms

Filtered

78 candidates to 57 candidates (73.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	72	6	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	6	79

Merged error: 0.2b

Counts

79 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
5×	`fma-udef`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 52

Calls

4 calls:

1.0ms	(fma 1/60 (pow l 5) (* 2 l))
1.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
3.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
1.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

series536.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(fma 1/60 (pow l 5) (* 2 l))
56.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
132.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
229.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

simplify115.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	186	510
1	795	442
2	4250	434
3	5001	434

prune235.0ms

Filtered

64 candidates to 49 candidates (76.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	64	6	70

Merged error: 0.2b

Counts

70 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
2×	`*-commutative`
1×	`+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+` `fma-udef` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

5.0ms	(+ (* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))) U)
1.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
5.0ms	(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))
4.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

series546.0ms

Counts

4 → 12

Calls

4 calls:

249.0ms	(+ (* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))) U)
56.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
158.0ms	(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))
83.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	288	841
1	1139	734
2	5002	733

prune228.0ms

Filtered

76 candidates to 56 candidates (73.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	75	7	82

Merged error: 0.2b

Counts

82 → 7

regimes257.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.1s	2659×	body	1280	valid
691.0ms	2582×	body	640	valid
488.0ms	8421×	body	80	valid
263.0ms	1432×	body	320	valid
89.0ms	747×	body	160	valid