Details

sample311.0ms

Algorithm

intervals

Results

94.0ms	90×	body	1280	valid
71.0ms	91×	body	640	valid
66.0ms	57×	body	320	valid
41.0ms	247×	body	80	valid
6.0ms	19×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	2016
7	2016
6	1067
5	416
4	202
3	85
2	44
1	24
0	14

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.3b

localize51.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
0.0b	(* J (- (exp l) (exp (- l))))
5.6b	(- (exp l) (exp (- l)))

rewrite190.0ms

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-cbrt-cube` `add-exp-log`
8×	`associate-r`
5×	`add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`
3×	`expm1-log1p-u` `sub-neg` `flip3--` `fma-neg` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`associate-l/` `-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `unswap-sqr`

Counts

3 → 99

Calls

3 calls:

94.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
70.0ms	(* J (- (exp l) (exp (- l))))
23.0ms	(- (exp l) (exp (- l)))

series315.0ms

Counts

3 → 9

Calls

3 calls:

169.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
76.0ms	(* J (- (exp l) (exp (- l))))
70.0ms	(- (exp l) (exp (- l)))

simplify1.4s

Counts

108 → 108

Iterations

Iter	Nodes
done	2003
3	2003
2	976
1	376
0	168

prune768.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (* 2 (* J l)) (cos (/ K 2))) U)
0.0b	(* 2 (* J l))
0.1b	(* (* 2 (* J l)) (cos (/ K 2)))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`associate-r` `associate-l`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`*-commutative`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+`

Counts

3 → 60

Calls

3 calls:

77.0ms	(+ (* (* 2 (* J l)) (cos (/ K 2))) U)
28.0ms	(* 2 (* J l))
86.0ms	(* (* 2 (* J l)) (cos (/ K 2)))

series289.0ms

Counts

3 → 9

Calls

3 calls:

151.0ms	(+ (* (* 2 (* J l)) (cos (/ K 2))) U)
34.0ms	(* 2 (* J l))
104.0ms	(* (* 2 (* J l)) (cos (/ K 2)))

simplify1.5s

Counts

69 → 69

Iterations

Iter	Nodes
done	2012
3	2012
2	894
1	258
0	100

prune382.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* (sqrt 2) (* (sqrt 2) (* J l))) (cos (/ K 2))) U)
0.1b	(* (* (sqrt 2) (* (sqrt 2) (* J l))) (cos (/ K 2)))
0.3b	(* (sqrt 2) (* (sqrt 2) (* J l)))
0.4b	(* (sqrt 2) (* J l))

rewrite445.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-cbrt-cube` `add-exp-log`
19×	`pow-prod-down` `prod-exp` `cbrt-unprod`
13×	`associate-l`
9×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-prod` `add-log-exp`
5×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`*-commutative`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+`

Counts

4 → 93

Calls

4 calls:

187.0ms	(+ (* (* (sqrt 2) (* (sqrt 2) (* J l))) (cos (/ K 2))) U)
167.0ms	(* (* (sqrt 2) (* (sqrt 2) (* J l))) (cos (/ K 2)))
67.0ms	(* (sqrt 2) (* (sqrt 2) (* J l)))
22.0ms	(* (sqrt 2) (* J l))

series675.0ms

Counts

4 → 12

Calls

4 calls:

322.0ms	(+ (* (* (sqrt 2) (* (sqrt 2) (* J l))) (cos (/ K 2))) U)
205.0ms	(* (* (sqrt 2) (* (sqrt 2) (* J l))) (cos (/ K 2)))
102.0ms	(* (sqrt 2) (* (sqrt 2) (* J l)))
46.0ms	(* (sqrt 2) (* J l))

simplify2.2s

Counts

105 → 105

Iterations

Iter	Nodes
done	2013
3	2013
2	1327
1	337
0	127

prune460.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (sqrt 2) (* (* (sqrt 2) (* J l)) (cos (/ K 2)))) U)
0.1b	(* (* (sqrt 2) (* J l)) (cos (/ K 2)))
0.4b	(* (sqrt 2) (* J l))
0.4b	(* (sqrt 2) (* (* (sqrt 2) (* J l)) (cos (/ K 2))))

rewrite455.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-cbrt-cube` `add-exp-log`
19×	`pow-prod-down` `prod-exp` `cbrt-unprod`
13×	`associate-l`
9×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-prod` `add-log-exp`
5×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`*-commutative`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+`

Counts

4 → 93

Calls

4 calls:

180.0ms	(+ (* (sqrt 2) (* (* (sqrt 2) (* J l)) (cos (/ K 2)))) U)
44.0ms	(* (* (sqrt 2) (* J l)) (cos (/ K 2)))
21.0ms	(* (sqrt 2) (* J l))
207.0ms	(* (sqrt 2) (* (* (sqrt 2) (* J l)) (cos (/ K 2))))

series666.0ms

Counts

4 → 12

Calls

4 calls:

290.0ms	(+ (* (sqrt 2) (* (* (sqrt 2) (* J l)) (cos (/ K 2)))) U)
128.0ms	(* (* (sqrt 2) (* J l)) (cos (/ K 2)))
68.0ms	(* (sqrt 2) (* J l))
179.0ms	(* (sqrt 2) (* (* (sqrt 2) (* J l)) (cos (/ K 2))))

simplify1.5s

Counts

105 → 105

Iterations

Iter	Nodes
done	2001
3	2001
2	1329
1	344
0	129

prune679.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes580.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	15
1	15
0	11

end0.0ms

sample11.1s

Algorithm

intervals

Results

4.0s	2701×	body	1280	valid
2.8s	2471×	body	640	valid
2.4s	8376×	body	80	valid
958.0ms	1437×	body	320	valid
310.0ms	742×	body	160	valid