Details

sample110.0ms

Algorithm

intervals

Results

36.0ms	86×	body	1280	valid
22.0ms	90×	body	640	valid
14.0ms	261×	body	80	valid
10.0ms	46×	body	320	valid
3.0ms	30×	body	160	valid

simplify15.3s

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: 19.9b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
6.2b	(- (exp l) (exp (- l)))

rewrite125.0ms

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:

48.0ms	(* J (- (exp l) (exp (- l))))
59.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
16.0ms	(- (exp l) (exp (- l)))

series201.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(* J (- (exp l) (exp (- l))))
101.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
39.0ms	(- (exp l) (exp (- l)))

simplify2.5s

Counts

105 → 105

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	168	2051
1	343	1619
2	935	1258
3	4166	1093
done	5000	1093

prune250.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

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	(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)))

rewrite26.0ms

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

Counts

3 → 52

Calls

3 calls:

7.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
0.0ms	(fma 1/60 (pow l 5) (* 2 l))
18.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

series452.0ms

Counts

3 → 9

Calls

3 calls:

138.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
134.0ms	(fma 1/60 (pow l 5) (* 2 l))
179.0ms	(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

simplify2.1s

Counts

61 → 61

Iterations

Useful iterations: 3 (855.0ms)

Iter	Nodes	Cost
0	104	1222
1	222	1205
2	737	1001
3	3988	987
done	5000	987

prune238.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/60 (pow l 5) (* 2 l))
0.1b	(* (+ (* 1/3 (* J (pow l 3))) (* (fma 1/60 (pow l 5) (* 2 l)) J)) (cos (/ K 2.0)))
0.2b	(* 1/3 (* J (pow l 3)))
7.0b	(* J (pow l 3))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
20×	`add-sqr-sqrt`
16×	`associate-r`
13×	`add-cbrt-cube`
11×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp`
9×	`associate-l`
8×	`pow1`
5×	`cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `unpow-prod-down` `cube-prod` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-to-exp` `pow-prod-down` `associate-*l/` `pow-exp` `sqr-pow`
1×	`cube-mult` `flip3-+` `unpow3` `flip-+` `fma-udef`

Counts

4 → 86

Calls

4 calls:

0.0ms	(fma 1/60 (pow l 5) (* 2 l))
62.0ms	(* (+ (* 1/3 (* J (pow l 3))) (* (fma 1/60 (pow l 5) (* 2 l)) J)) (cos (/ K 2.0)))
23.0ms	(* 1/3 (* J (pow l 3)))
13.0ms	(* J (pow l 3))

series430.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(fma 1/60 (pow l 5) (* 2 l))
181.0ms	(* (+ (* 1/3 (* J (pow l 3))) (* (fma 1/60 (pow l 5) (* 2 l)) J)) (cos (/ K 2.0)))
63.0ms	(* 1/3 (* J (pow l 3)))
55.0ms	(* J (pow l 3))

simplify733.0ms

Counts

98 → 98

Iterations

Useful iterations: done (730.0ms)

Iter	Nodes	Cost
0	148	1376
1	342	1267
2	1201	1130
done	5001	1096

prune380.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(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)))

rewrite26.0ms

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

Counts

3 → 50

Calls

3 calls:

0.0ms	(fma 1/60 (pow l 5) (* 2 l))
17.0ms	(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))
8.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

series406.0ms

Counts

3 → 9

Calls

3 calls:

133.0ms	(fma 1/60 (pow l 5) (* 2 l))
180.0ms	(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))
93.0ms	(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

simplify2.1s

Counts

59 → 59

Iterations

Useful iterations: 3 (906.0ms)

Iter	Nodes	Cost
0	101	1269
1	222	1255
2	771	1045
3	4056	1021
done	5000	1021

prune212.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes353.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	25
1	29	25
done	29	25

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.1s	2693×	body	1280	valid
656.0ms	2631×	body	640	valid
465.0ms	8408×	body	80	valid
250.0ms	1454×	body	320	valid
86.0ms	809×	body	160	valid