Details

sample310.0ms

Algorithm

intervals

Results

129.0ms	99×	body	1280	valid
79.0ms	100×	body	640	valid
40.0ms	252×	body	80	valid
26.0ms	54×	body	320	valid
6.0ms	18×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
7	2000
6	1004
5	361
4	183
3	80
2	41
1	23
0	14

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(* J (exp l))
0.0b	(* (cos (/ K 2)) (- (* J (exp l)) (/ J (exp l))))
0.0b	(/ J (exp l))
6.6b	(- (* J (exp l)) (/ J (exp l)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
10×	`add-cbrt-cube`
9×	`times-frac`
8×	`pow1` `add-exp-log`
7×	`associate-r`
6×	`associate-l` `add-log-exp`
4×	`insert-posit16`
3×	`associate-/r` `sub-neg` `div-inv` `associate-/l`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `flip--` `distribute-lft-out--` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `diff-log` `div-exp`

Counts

4 → 87

Calls

4 calls:

18.0ms	(* J (exp l))
62.0ms	(* (cos (/ K 2)) (- (* J (exp l)) (/ J (exp l))))
11.0ms	(/ J (exp l))
25.0ms	(- (* J (exp l)) (/ J (exp l)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* J (exp l))
98.0ms	(* (cos (/ K 2)) (- (* J (exp l)) (/ J (exp l))))
40.0ms	(/ J (exp l))
65.0ms	(- (* J (exp l)) (/ J (exp l)))

simplify1.1s

Counts

99 → 99

Iterations

Iter	Nodes
done	2001
3	2001
2	919
1	326
0	143

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ U (* (cos (/ K 2)) (* 2 (* J l))))
0.0b	(* 2 (* J l))
0.2b	(* (cos (/ K 2)) (* 2 (* J l)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

9.0ms	(+ U (* (cos (/ K 2)) (* 2 (* J l))))
13.0ms	(* 2 (* J l))
74.0ms	(* (cos (/ K 2)) (* 2 (* J l)))

series309.0ms

Counts

3 → 9

Calls

3 calls:

166.0ms	(+ U (* (cos (/ K 2)) (* 2 (* J l))))
35.0ms	(* 2 (* J l))
107.0ms	(* (cos (/ K 2)) (* 2 (* J l)))

simplify1.1s

Counts

62 → 62

Iterations

Iter	Nodes
done	2004
3	2004
2	790
1	230
0	91

prune802.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 77

Calls

4 calls:

25.0ms	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
2.0ms	(cbrt (cos (/ K 2)))
2.0ms	(cbrt (cos (/ K 2)))
2.0ms	(cbrt (cos (/ K 2)))

series615.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
152.0ms	(cbrt (cos (/ K 2)))
124.0ms	(cbrt (cos (/ K 2)))
118.0ms	(cbrt (cos (/ K 2)))

simplify1.3s

Counts

89 → 89

Iterations

Iter	Nodes
done	2000
4	2000
3	795
2	342
1	154
0	71

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt (cos (/ K 2))) (* 2 (* J l)))
0.1b	(* (pow (* (cos (/ K 2)) (cos (/ K 2))) 1/3) (* (cbrt (cos (/ K 2))) (* 2 (* J l))))
0.3b	(* (cos (/ K 2)) (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-exp-log`
51×	`prod-exp`
30×	`add-cbrt-cube`
27×	`cbrt-unprod`
20×	`pow1`
14×	`add-sqr-sqrt` `associate-l`
12×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow-exp`
7×	`pow-prod-down`
6×	`cbrt-prod`
5×	`associate-r`
4×	`pow-to-exp` `unpow1/3` `insert-posit16` `add-log-exp`
3×	`swap-sqr` `*-commutative`
1×	`pow2` `sqr-cos` `unpow-prod-down` `pow-plus` `pow1/3` `pow-sqr` `cos-mult` `pow-prod-up` `unswap-sqr` `sqr-pow`

Counts

4 → 104

Calls

4 calls:

58.0ms	(* (cbrt (cos (/ K 2))) (* 2 (* J l)))
120.0ms	(* (pow (* (cos (/ K 2)) (cos (/ K 2))) 1/3) (* (cbrt (cos (/ K 2))) (* 2 (* J l))))
8.0ms	(* (cos (/ K 2)) (cos (/ K 2)))
2.0ms	(cbrt (cos (/ K 2)))

series483.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(* (cbrt (cos (/ K 2))) (* 2 (* J l)))
89.0ms	(* (pow (* (cos (/ K 2)) (cos (/ K 2))) 1/3) (* (cbrt (cos (/ K 2))) (* 2 (* J l))))
25.0ms	(* (cos (/ K 2)) (cos (/ K 2)))
178.0ms	(cbrt (cos (/ K 2)))

simplify1.3s

Counts

116 → 116

Iterations

Iter	Nodes
done	2005
3	2005
2	1629
1	441
0	164

prune1.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes621.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	15
1	15
0	11

end0.0ms

sample9.9s

Algorithm

intervals

Results

3.5s	2747×	body	1280	valid
2.4s	8326×	body	80	valid
2.2s	2572×	body	640	valid
929.0ms	1360×	body	320	valid
286.0ms	730×	body	160	valid