Details

sample81.0ms

Algorithm

intervals

Results

32.0ms	55×	body	1280	valid
16.0ms	169×	body	80	valid
16.0ms	45×	body	640	valid
4.0ms	15×	body	320	valid
2.0ms	10×	body	160	valid

simplify23.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	30	11
3	40	11
4	51	11
5	54	11
done	54	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--`

Counts

4 → 101

Calls

4 calls:

12.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
2.0ms	(/ 1.0 (sin B))
2.0ms	(/ 1.0 (tan B))
11.0ms	(* x (/ 1.0 (tan B)))

series289.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
21.0ms	(/ 1.0 (sin B))
36.0ms	(/ 1.0 (tan B))
110.0ms	(* x (/ 1.0 (tan B)))

simplify2.0s

Counts

113 → 113

Iterations

Useful iterations: 2 (122.0ms)

Iter	Nodes	Cost
0	174	1141
1	387	1074
2	1180	996
3	4783	996
done	5000	996

prune298.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
0.1b	(/ 1.0 (sin B))
0.1b	(/ (* x 1.0) (tan B))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt` `times-frac`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`add-log-exp`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `div-exp`
2×	`frac-2neg` `clear-num` `div-inv` `difference-of-squares`
1×	`tan-quot` `sub-neg` `flip3--` `diff-log` `prod-exp` `associate-/r/` `frac-sub` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

3 → 65

Calls

3 calls:

18.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
2.0ms	(/ 1.0 (sin B))
4.0ms	(/ (* x 1.0) (tan B))

series255.0ms

Counts

3 → 9

Calls

3 calls:

125.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
19.0ms	(/ 1.0 (sin B))
110.0ms	(/ (* x 1.0) (tan B))

simplify1.6s

Counts

74 → 74

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	143	847
1	317	799
2	930	739
3	4176	739
done	5001	739

prune188.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
0.1b	(/ 1 (sin B))
0.1b	(* x (cos B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`add-exp-log` `times-frac`
13×	`add-cbrt-cube`
7×	`pow1` `div-inv`
6×	`associate-/r*` `add-log-exp`
4×	`div-exp` `associate-/l*`
3×	`cbrt-undiv` `distribute-rgt-out--` `associate-r` `associate-l` `difference-of-squares`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `distribute-lft-out--`
1×	`sub-neg` `rec-exp` `flip3--` `pow-flip` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `inv-pow` `sub-div` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

15.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
2.0ms	(/ 1 (sin B))
3.0ms	(* x (cos B))
4.0ms	(/ (* x (cos B)) (sin B))

series245.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
16.0ms	(/ 1 (sin B))
37.0ms	(* x (cos B))
97.0ms	(/ (* x (cos B)) (sin B))

simplify888.0ms

Counts

104 → 104

Iterations

Useful iterations: done (886.0ms)

Iter	Nodes	Cost
0	145	1077
1	310	981
2	1012	904
done	5000	887

prune217.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (sin B))
0.2b	(* (/ 1.0 (sin B)) (cos B))
0.3b	(* x (* (/ 1.0 (sin B)) (cos B)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
28×	`times-frac`
22×	`add-exp-log` `add-cbrt-cube`
16×	`associate-l`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r` `associate-/l`
4×	`cbrt-undiv` `div-exp` `associate-r` `pow-prod-down` `add-log-exp`
3×	`div-inv`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative` `unswap-sqr`
1×	`associate-*r/`

Counts

4 → 107

Calls

4 calls:

2.0ms	(/ 1.0 (sin B))
2.0ms	(/ 1.0 (sin B))
9.0ms	(* (/ 1.0 (sin B)) (cos B))
12.0ms	(* x (* (/ 1.0 (sin B)) (cos B)))

series185.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ 1.0 (sin B))
19.0ms	(/ 1.0 (sin B))
41.0ms	(* (/ 1.0 (sin B)) (cos B))
107.0ms	(* x (* (/ 1.0 (sin B)) (cos B)))

simplify2.2s

Counts

119 → 119

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	136	1167
1	318	1138
2	974	984
3	4905	984
done	5000	984

prune283.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes53.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	12	16
1	17	14
done	17	14

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.0s	1744×	body	1280	valid
605.0ms	4907×	body	80	valid
530.0ms	1436×	body	640	valid
180.0ms	717×	body	320	valid
60.0ms	350×	body	160	valid