Details

sample172.0ms

Algorithm

intervals

Results

48.0ms	269×	body	80	valid
44.0ms	87×	body	1280	valid
32.0ms	89×	body	640	valid
15.0ms	65×	body	320	valid
3.0ms	20×	body	160	valid

simplify25.1s

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.9b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
4.6b	(- (exp l) (exp (- l)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 74

Calls

2 calls:

50.0ms	(* J (- (exp l) (exp (- l))))
24.0ms	(- (exp l) (exp (- l)))

series133.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(* J (- (exp l) (exp (- l))))
61.0ms	(- (exp l) (exp (- l)))

simplify2.2s

Counts

80 → 80

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	131	1620
1	259	1196
2	605	915
3	2360	751
done	5000	724

prune227.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 2 expressions with local error:

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)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

13.0ms	(* 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)

series590.0ms

Counts

2 → 6

Calls

2 calls:

189.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
401.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

simplify1.3s

Counts

38 → 38

Iterations

Useful iterations: 3 (506.0ms)

Iter	Nodes	Cost
0	82	824
1	168	815
2	453	704
3	1917	690
done	5001	690

prune244.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/3 (* J (pow l 3))) (* J (fma 1/60 (pow l 5) (* 2 l))))
0.0b	(fma (+ (* 1/3 (* J (pow l 3))) (* J (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)
0.2b	(* 1/3 (* J (pow l 3)))
4.3b	(* J (pow l 3))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
16×	`add-sqr-sqrt`
13×	`associate-r`
11×	`add-cbrt-cube`
10×	`prod-exp`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `cube-prod` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
3×	`fma-udef`
2×	`pow-to-exp` `associate-+r+` `pow-exp` `*-commutative` `sqr-pow`
1×	`+-commutative` `distribute-rgt-in` `cube-mult` `fma-def` `distribute-lft-in` `flip3-+` `unpow3` `pow-prod-down` `sum-log` `flip-+`

Counts

4 → 80

Calls

4 calls:

25.0ms	(+ (* 1/3 (* J (pow l 3))) (* J (fma 1/60 (pow l 5) (* 2 l))))
1.0ms	(fma (+ (* 1/3 (* J (pow l 3))) (* J (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)
51.0ms	(* 1/3 (* J (pow l 3)))
13.0ms	(* J (pow l 3))

series709.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(+ (* 1/3 (* J (pow l 3))) (* J (fma 1/60 (pow l 5) (* 2 l))))
366.0ms	(fma (+ (* 1/3 (* J (pow l 3))) (* J (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)
87.0ms	(* 1/3 (* J (pow l 3)))
76.0ms	(* J (pow l 3))

simplify1.1s

Counts

92 → 92

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	143	1348
1	347	1220
2	1130	1101
done	5000	1058

prune504.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b

(* J (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)))) (cos (/ K 2.0))) U)

0.1b

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 56

Calls

3 calls:

9.0ms

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

23.0ms

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

22.0ms

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

series817.0ms

Counts

3 → 9

Calls

3 calls:

188.0ms

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

369.0ms

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

260.0ms

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

simplify4.1s

Counts

65 → 65

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	116	1600
1	279	1526
2	919	1335
3	4884	1288
done	5000	1288

prune404.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes259.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	24
1	26	24
done	26	24

end0.0ms

sample8.4s

Algorithm

intervals

Results

2.5s	2682×	body	1280	valid
1.9s	8289×	body	80	valid
1.7s	2606×	body	640	valid
698.0ms	1444×	body	320	valid
622.0ms	785×	body	160	valid