Details

sample118.0ms

Algorithm

intervals

Results

45.0ms	49×	body	1280	valid
24.0ms	40×	body	640	valid
17.0ms	140×	body	80	valid
5.0ms	13×	body	320	valid
4.0ms	14×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	19
2	19
1	12
0	8

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 3 expressions with local error:

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

rewrite30.0ms

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×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 48

Calls

3 calls:

13.0ms	(- (* x (cos y)) (* z (sin y)))
7.0ms	(* z (sin y))
8.0ms	(* x (cos y))

series212.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(- (* x (cos y)) (* z (sin y)))
63.0ms	(* z (sin y))
53.0ms	(* x (cos y))

simplify3.6s

Counts

57 → 57

Iterations

Iter	Nodes
done	5021
4	4873
3	1340
2	420
1	178
0	80

prune402.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

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))

rewrite16.0ms

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:

11.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
1.0ms	(cbrt (cos y))
1.0ms	(cbrt (cos y))
1.0ms	(cbrt (cos y))

series638.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
120.0ms	(cbrt (cos y))
129.0ms	(cbrt (cos y))
162.0ms	(cbrt (cos y))

simplify1.9s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
3	1140
2	366
1	144
0	64

prune550.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

26.0ms	(* x (pow (* (cos y) (cos y)) 1/3))
30.0ms	(* (* x (pow (* (cos y) (cos y)) 1/3)) (cbrt (cos y)))
16.0ms	(* (cos y) (cos y))
2.0ms	(cbrt (cos y))

series352.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* x (pow (* (cos y) (cos y)) 1/3))
71.0ms	(* (* x (pow (* (cos y) (cos y)) 1/3)) (cbrt (cos y)))
25.0ms	(* (cos y) (cos y))
136.0ms	(cbrt (cos y))

simplify2.5s

Counts

99 → 99

Iterations

Iter	Nodes
done	5006
3	2818
2	928
1	333
0	127

prune666.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

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

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

122×	`pow1`
37×	`pow-prod-up`
24×	`pow-prod-down`
23×	`pow-sqr`
19×	`pow-plus`
18×	`add-cbrt-cube` `add-exp-log`
17×	`cos-mult`
14×	`pow2`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
7×	`cbrt-div`
6×	`frac-times` `associate-*l/`
4×	`cbrt-prod` `swap-sqr` `associate-r` `associate-l` `associate-*r/` `add-log-exp`
3×	`sqr-cos`
2×	`pow1/3` `*-commutative` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `pow3` `rem-cbrt-cube`

Counts

4 → 123

Calls

4 calls:

15.0ms	(* (cos y) (cos y))
68.0ms	(* (* (cos y) (cos y)) (* (cos y) (cos y)))
2.0ms	(cbrt (cos y))
141.0ms	(cbrt (* (* (* (cos y) (cos y)) (* (cos y) (cos y))) (* (cos y) (cos y))))

series208.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (cos y) (cos y))
40.0ms	(* (* (cos y) (cos y)) (* (cos y) (cos y)))
129.0ms	(cbrt (cos y))
19.0ms	(cbrt (* (* (* (cos y) (cos y)) (* (cos y) (cos y))) (* (cos y) (cos y))))

simplify3.0s

Counts

135 → 135

Iterations

Iter	Nodes
done	5001
2	1956
1	397
0	129

prune694.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes448.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.7s	1491×	body	1280	valid
919.0ms	4233×	body	80	valid
853.0ms	1300×	body	640	valid
294.0ms	643×	body	320	valid
72.0ms	333×	body	160	valid