Details

sample180.0ms

Algorithm

intervals

Results

86.0ms	90×	body	1280	valid
34.0ms	96×	body	640	valid
21.0ms	257×	body	80	valid
11.0ms	45×	body	320	valid
4.0ms	24×	body	160	valid

simplify26.0s

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize31.0ms

Local error

Found 3 expressions with local error:

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

rewrite239.0ms

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:

91.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
111.0ms	(* J (- (exp l) (exp (- l))))
34.0ms	(- (exp l) (exp (- l)))

series322.0ms

Counts

3 → 9

Calls

3 calls:

166.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
96.0ms	(* J (- (exp l) (exp (- l))))
60.0ms	(- (exp l) (exp (- l)))

simplify4.0s

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

prune512.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

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

rewrite75.0ms

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:

20.0ms	(+ (* (* 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)))
15.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
38.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

series1.0s

Counts

4 → 12

Calls

4 calls:

442.0ms	(+ (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))) U)
122.0ms	(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))))
285.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

simplify896.0ms

Counts

78 → 78

Iterations

Useful iterations: done (892.0ms)

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

prune559.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize42.0ms

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)))
12.0ms	(* 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)

series857.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(fma 1/60 (pow l 5) (* 2 l))
86.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
194.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
397.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

simplify2.3s

Counts

64 → 64

Iterations

Useful iterations: 3 (828.0ms)

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

prune472.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize20.0ms

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)))

rewrite85.0ms

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:

27.0ms	(+ (* 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)))
46.0ms	(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))
10.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

series862.0ms

Counts

4 → 12

Calls

4 calls:

367.0ms	(+ (* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))) U)
89.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
267.0ms	(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))
140.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

simplify1.4s

Counts

76 → 76

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	120	1865
1	288	1788
2	1044	1565
done	5001	1508

prune430.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes434.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	21
1	21	21
done	21	21

end0.0ms

sample7.9s

Algorithm

intervals

Results

3.4s	2675×	body	1280	valid
1.6s	2587×	body	640	valid
1.2s	8311×	body	80	valid
652.0ms	1476×	body	320	valid
232.0ms	748×	body	160	valid