Details

sample263.0ms

Algorithm

intervals

Results

75.0ms	82×	body	1280	valid
75.0ms	92×	body	640	valid
33.0ms	270×	body	80	valid
20.0ms	52×	body	320	valid
10.0ms	37×	body	160	valid

simplify24.8s

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U)
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
6.9b	(- (exp l) (exp (- l)))

rewrite285.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

71.0ms	(* J (- (exp l) (exp (- l))))
98.0ms	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U)
82.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
26.0ms	(- (exp l) (exp (- l)))

series712.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* J (- (exp l) (exp (- l))))
381.0ms	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U)
158.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
70.0ms	(- (exp l) (exp (- l)))

simplify1.4s

Counts

122 → 122

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	202	2424
1	441	1947
2	1226	1569
done	5001	1393

prune567.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

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)))

rewrite89.0ms

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:

14.0ms

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

36.0ms

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

37.0ms

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

series773.0ms

Counts

3 → 9

Calls

3 calls:

217.0ms

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

343.0ms

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

212.0ms

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

simplify4.2s

Counts

65 → 65

Iterations

Useful iterations: 3 (1.6s)

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

prune387.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

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))) (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))))

0.1b

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

rewrite72.0ms

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-l*`
5×	`add-log-exp`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`*-commutative`
1×	`+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+` `unswap-sqr`

Counts

3 → 54

Calls

3 calls:

39.0ms

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

18.0ms

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

13.0ms

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

series752.0ms

Counts

3 → 9

Calls

3 calls:

391.0ms

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

237.0ms

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

124.0ms

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

simplify4.1s

Counts

63 → 63

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	113	1647
1	279	1576
2	938	1379
3	4795	1322
done	5000	1322

prune374.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))) U)
0.1b	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

rewrite14.0ms

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

Counts

2 → 30

Calls

2 calls:

0.0ms	(fma J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))) U)
13.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

series506.0ms

Counts

2 → 6

Calls

2 calls:

351.0ms	(fma J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))) U)
155.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

simplify2.0s

Counts

36 → 36

Iterations

Useful iterations: 3 (633.0ms)

Iter	Nodes	Cost
0	81	877
1	174	869
2	538	752
3	2250	728
done	5000	728

prune243.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes279.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample8.1s

Algorithm

intervals

Results

2.5s	2599×	body	640	valid
2.5s	2590×	body	1280	valid
1.2s	8345×	body	80	valid
651.0ms	1501×	body	320	valid
251.0ms	762×	body	160	valid