Details

sample144.0ms

Algorithm

intervals

Results

47.0ms	96×	body	1280	valid
30.0ms	85×	body	640	valid
17.0ms	259×	body	80	valid
11.0ms	52×	body	320	valid
3.0ms	23×	body	160	valid

simplify23.7s

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.6b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
4.8b	(- (exp l) (exp (- l)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 84

Calls

3 calls:

105.0ms	(* J (- (exp l) (exp (- l))))
1.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
33.0ms	(- (exp l) (exp (- l)))

series372.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(* J (- (exp l) (exp (- l))))
225.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
63.0ms	(- (exp l) (exp (- l)))

simplify3.0s

Counts

93 → 93

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	162	1865
1	314	1440
2	737	1116
3	2893	950
done	5001	923

prune273.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

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

rewrite14.0ms

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:

0.0ms	(fma 1/60 (pow l 5) (* 2 l))
0.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
11.0ms	(* 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)

series771.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(fma 1/60 (pow l 5) (* 2 l))
100.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
196.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
331.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

simplify2.1s

Counts

64 → 64

Iterations

Useful iterations: 3 (789.0ms)

Iter	Nodes	Cost
0	97	1182
1	186	1164
2	565	1011
3	2815	997
done	5000	997

prune398.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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)))

rewrite86.0ms

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:

39.0ms	(+ (* (* 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)))
15.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
29.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

series845.0ms

Counts

4 → 12

Calls

4 calls:

360.0ms	(+ (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))) U)
79.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
170.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
236.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

simplify1.1s

Counts

78 → 78

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	122	1818
1	288	1738
2	1014	1521
done	5000	1474

prune447.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

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

rewrite73.0ms

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:

19.0ms	(+ (* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))) U)
0.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
14.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))
39.0ms	(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))

series829.0ms

Counts

4 → 12

Calls

4 calls:

360.0ms	(+ (* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))) U)
97.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
133.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))
239.0ms	(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))

simplify1.0s

Counts

76 → 76

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	120	1865
1	288	1788
2	1045	1565
done	5000	1508

prune348.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes485.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	22
1	24	22
done	24	22

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.7s	2716×	body	1280	valid
1.0s	2614×	body	640	valid
692.0ms	8498×	body	80	valid
370.0ms	1428×	body	320	valid
138.0ms	778×	body	160	valid