Details

sample96.0ms

Algorithm

intervals

Results

39.0ms	46×	body	1280	valid
21.0ms	45×	body	640	valid
14.0ms	144×	body	80	valid
4.0ms	15×	body	320	valid
1.0ms	6×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	243
1	11	243
done	11	243

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x (cos y)) (* z (sin y)))
0.1b	(* x (cos y))
0.1b	(* z (sin y))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
7×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+`

Counts

3 → 47

Calls

3 calls:

22.0ms	(+ (* x (cos y)) (* z (sin y)))
7.0ms	(* x (cos y))
14.0ms	(* z (sin y))

series181.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(+ (* x (cos y)) (* z (sin y)))
56.0ms	(* x (cos y))
43.0ms	(* z (sin y))

simplify2.1s

Counts

56 → 56

Iterations

Useful iterations: 2 (144.0ms)

Iter	Nodes	Cost
0	80	11187
1	192	10594
2	684	10434
3	3228	10434
done	5001	10434

prune336.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (cos y)) (cbrt (cos y)))
0.3b	(cbrt (cos y))
0.3b	(cbrt (cos y))
0.3b	(cbrt (cos y))

rewrite15.0ms

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` `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 → 73

Calls

4 calls:

10.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
1.0ms	(cbrt (cos y))
1.0ms	(cbrt (cos y))
1.0ms	(cbrt (cos y))

series626.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
133.0ms	(cbrt (cos y))
116.0ms	(cbrt (cos y))
143.0ms	(cbrt (cos y))

simplify1.1s

Counts

85 → 85

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	64	22963
1	146	19212
2	622	18886
done	5000	18006

prune500.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* z (sin y))
0.2b	(* (* x (pow (* (cos y) (cos y)) 1/3)) (cbrt (cos y)))
0.3b	(cbrt (cos y))
0.3b	(* (cos y) (cos y))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
17×	`add-sqr-sqrt`
15×	`pow1`
13×	`*-un-lft-identity` `add-cube-cbrt`
12×	`add-cbrt-cube` `associate-r` `prod-exp`
7×	`associate-l` `cbrt-unprod`
6×	`cbrt-prod`
4×	`add-log-exp`
3×	`swap-sqr` `pow-prod-down` `*-commutative`
2×	`pow-exp` `unswap-sqr`
1×	`pow2` `pow-to-exp` `sqr-cos` `pow-plus` `unpow1/3` `pow1/3` `pow-sqr` `cos-mult` `pow-prod-up`

Counts

4 → 80

Calls

4 calls:

12.0ms	(* z (sin y))
61.0ms	(* (* x (pow (* (cos y) (cos y)) 1/3)) (cbrt (cos y)))
7.0ms	(cbrt (cos y))
8.0ms	(* (cos y) (cos y))

series265.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* z (sin y))
41.0ms	(* (* x (pow (* (cos y) (cos y)) 1/3)) (cbrt (cos y)))
151.0ms	(cbrt (cos y))
18.0ms	(* (cos y) (cos y))

simplify2.1s

Counts

92 → 92

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	134	24321
1	349	18976
2	2177	18569
done	5002	17969

prune646.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos y) (cos y))
0.3b	(* (cos y) (cos y))
0.3b	(* (* (cos y) (cos y)) (* (cos y) (cos y)))
0.4b	(cbrt (* (* (* (cos y) (cos y)) (* (cos y) (cos y))) (* (cos y) (cos y))))

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

129×	`pow1`
38×	`pow-prod-up`
25×	`pow-prod-down`
24×	`pow-sqr`
20×	`pow-plus` `add-cbrt-cube` `add-exp-log`
18×	`cos-mult`
16×	`add-sqr-sqrt`
15×	`pow2`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`prod-exp` `cbrt-unprod`
7×	`cbrt-div` `swap-sqr` `associate-r` `associate-l`
6×	`frac-times` `associate-*l/`
4×	`sqr-cos` `associate-*r/` `add-log-exp`
3×	`*-commutative` `unswap-sqr`
1×	`cbrt-prod` `distribute-rgt-in` `distribute-lft-in` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 139

Calls

4 calls:

16.0ms	(* (cos y) (cos y))
16.0ms	(* (cos y) (cos y))
68.0ms	(* (* (cos y) (cos y)) (* (cos y) (cos y)))
158.0ms	(cbrt (* (* (* (cos y) (cos y)) (* (cos y) (cos y))) (* (cos y) (cos y))))

series130.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (cos y) (cos y))
25.0ms	(* (cos y) (cos y))
43.0ms	(* (* (cos y) (cos y)) (* (cos y) (cos y)))
32.0ms	(cbrt (* (* (* (cos y) (cos y)) (* (cos y) (cos y))) (* (cos y) (cos y))))

simplify4.5s

Counts

151 → 151

Iterations

Useful iterations: done (4.5s)

Iter	Nodes	Cost
0	113	29302
1	364	21673
2	3069	21012
done	5001	20971

prune788.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes353.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	243
1	11	243
done	11	243

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.3s	1527×	body	1280	valid
1.0s	4233×	body	80	valid
781.0ms	1289×	body	640	valid
257.0ms	628×	body	320	valid
81.0ms	323×	body	160	valid