Details

sample244.0ms

Algorithm

intervals

Results

76.0ms	102×	body	640	valid
73.0ms	85×	body	1280	valid
29.0ms	243×	body	80	valid
15.0ms	44×	body	320	valid
6.0ms	24×	body	160	valid

simplify25.0s

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	14	15
1	24	14
2	45	14
3	90	14
4	189	14
5	281	14
6	358	14
7	493	14
8	646	14
9	1031	14
10	1800	14
11	2586	14
12	3243	14
13	3564	14
14	3648	14
done	3648	14

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize41.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
0.2b	(* J (- (exp l) (exp (- l))))
7.5b	(- (exp l) (exp (- l)))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 96

Calls

3 calls:

68.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
61.0ms	(* J (- (exp l) (exp (- l))))
34.0ms	(- (exp l) (exp (- l)))

series284.0ms

Counts

3 → 9

Calls

3 calls:

149.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
92.0ms	(* J (- (exp l) (exp (- l))))
42.0ms	(- (exp l) (exp (- l)))

simplify3.8s

Counts

105 → 105

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	168	2051
1	343	1619
2	933	1258
3	4210	1093
done	5000	1093

prune332.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (* 2 (* J l)) (cos (/ K 2.0))) U)
0.0b	(* 2 (* J l))
0.1b	(* (* 2 (* J l)) (cos (/ K 2.0)))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 57

Calls

3 calls:

89.0ms	(+ (* (* 2 (* J l)) (cos (/ K 2.0))) U)
33.0ms	(* 2 (* J l))
106.0ms	(* (* 2 (* J l)) (cos (/ K 2.0)))

series273.0ms

Counts

3 → 9

Calls

3 calls:

159.0ms	(+ (* (* 2 (* J l)) (cos (/ K 2.0))) U)
22.0ms	(* 2 (* J l))
92.0ms	(* (* 2 (* J l)) (cos (/ K 2.0)))

simplify5.5s

Counts

66 → 66

Iterations

Useful iterations: 3 (3.0s)

Iter	Nodes	Cost
0	99	823
1	253	758
2	971	656
3	4802	648
done	5000	648

prune249.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 2 (* J (* (cos (* 0.5 K)) l))) U)
0.0b	(* 2 (* J (* (cos (* 0.5 K)) l)))
0.1b	(* (cos (* 0.5 K)) l)
0.1b	(* J (* (cos (* 0.5 K)) l))

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

75.0ms	(+ (* 2 (* J (* (cos (* 0.5 K)) l))) U)
92.0ms	(* 2 (* J (* (cos (* 0.5 K)) l)))
26.0ms	(* (cos (* 0.5 K)) l)
47.0ms	(* J (* (cos (* 0.5 K)) l))

series385.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(+ (* 2 (* J (* (cos (* 0.5 K)) l))) U)
102.0ms	(* 2 (* J (* (cos (* 0.5 K)) l)))
65.0ms	(* (cos (* 0.5 K)) l)
76.0ms	(* J (* (cos (* 0.5 K)) l))

simplify4.3s

Counts

89 → 89

Iterations

Useful iterations: 3 (2.3s)

Iter	Nodes	Cost
0	115	1089
1	277	1023
2	959	878
3	4457	871
done	5000	871

prune236.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (cos (* 0.5 K))) (cbrt (cos (* 0.5 K))))
0.3b	(cbrt (cos (* 0.5 K)))
0.3b	(cbrt (cos (* 0.5 K)))
0.3b	(cbrt (cos (* 0.5 K)))

rewrite46.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 81

Calls

4 calls:

34.0ms	(* (cbrt (cos (* 0.5 K))) (cbrt (cos (* 0.5 K))))
3.0ms	(cbrt (cos (* 0.5 K)))
3.0ms	(cbrt (cos (* 0.5 K)))
3.0ms	(cbrt (cos (* 0.5 K)))

series988.0ms

Counts

4 → 12

Calls

4 calls:

419.0ms	(* (cbrt (cos (* 0.5 K))) (cbrt (cos (* 0.5 K))))
225.0ms	(cbrt (cos (* 0.5 K)))
181.0ms	(cbrt (cos (* 0.5 K)))
161.0ms	(cbrt (cos (* 0.5 K)))

simplify2.5s

Counts

93 → 93

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	71	1042
1	133	947
2	355	783
3	1178	753
done	5000	746

prune357.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.2b

regimes337.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	12
1	17	12
done	17	12

end0.0ms

sample7.8s

Algorithm

intervals

Results

2.8s	2781×	body	1280	valid
1.7s	8234×	body	80	valid
1.6s	2644×	body	640	valid
566.0ms	1396×	body	320	valid
152.0ms	769×	body	160	valid