Details

sample109.0ms

Algorithm

intervals

Results

35.0ms	87×	body	1280	valid
24.0ms	95×	body	640	valid
19.0ms	291×	body	80	valid
8.0ms	47×	body	320	valid
3.0ms	23×	body	160	valid

simplify15.6s

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	14	15
1	24	14
2	44	14
3	80	14
4	141	14
5	236	14
6	334	14
7	467	14
8	645	14
9	1090	14
10	2486	14
11	3254	14
12	3676	14
13	4546	14
14	4827	14
done	4827	14

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
0.0b	(* J (- (exp l) (exp (- l))))
7.0b	(- (exp l) (exp (- l)))

rewrite37.0ms

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:

0.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
26.0ms	(* J (- (exp l) (exp (- l))))
7.0ms	(- (exp l) (exp (- l)))

series258.0ms

Counts

3 → 9

Calls

3 calls:

166.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
56.0ms	(* J (- (exp l) (exp (- l))))
35.0ms	(- (exp l) (exp (- l)))

simplify1.5s

Counts

93 → 93

Iterations

Useful iterations: 3 (557.0ms)

Iter	Nodes	Cost
0	162	1865
1	314	1440
2	763	1116
3	2931	950
done	5000	950

prune247.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

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)

rewrite5.0ms

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)))
3.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
0.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

series569.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(fma 1/60 (pow l 5) (* 2 l))
54.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
141.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
246.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

simplify981.0ms

Counts

64 → 64

Iterations

Useful iterations: 3 (233.0ms)

Iter	Nodes	Cost
0	97	1182
1	186	1164
2	532	1011
3	2291	997
done	5000	997

prune271.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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

rewrite12.0ms

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`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `fma-udef` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`

Counts

4 → 62

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)))
3.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
7.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

series489.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(fma 1/60 (pow l 5) (* 2 l))
60.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
133.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
173.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

simplify2.1s

Counts

74 → 74

Iterations

Useful iterations: 3 (695.0ms)

Iter	Nodes	Cost
0	108	1440
1	229	1417
2	797	1187
3	4264	1173
done	5000	1173

prune511.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

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)))
0.1b	(* 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)))

rewrite11.0ms

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`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `fma-udef`
1×	`unswap-sqr`

Counts

4 → 60

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)))
6.0ms	(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))
3.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(fma 1/60 (pow l 5) (* 2 l))
53.0ms	(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))))
86.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

simplify930.0ms

Counts

72 → 72

Iterations

Useful iterations: done (928.0ms)

Iter	Nodes	Cost
0	106	1487
1	229	1467
2	844	1231
done	5000	1207

prune251.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes339.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.2s	2729×	body	1280	valid
692.0ms	2575×	body	640	valid
480.0ms	8426×	body	80	valid
263.0ms	1423×	body	320	valid
89.0ms	718×	body	160	valid