Details

sample80.0ms

Algorithm

intervals

Results

32.0ms	54×	body	1280	valid
16.0ms	44×	body	640	valid
12.0ms	151×	body	80	valid
7.0ms	29×	body	320	valid
2.0ms	15×	body	160	valid

simplify31.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

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	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `associate-/r` `associate-/l`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `sum-log` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

8.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
2.0ms	(/ 1.0 (tan B))
8.0ms	(* x (/ 1.0 (tan B)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
18.0ms	(/ 1.0 (sin B))
35.0ms	(/ 1.0 (tan B))
116.0ms	(* x (/ 1.0 (tan B)))

simplify1.6s

Counts

115 → 115

Iterations

Useful iterations: 3 (823.0ms)

Iter	Nodes	Cost
0	180	1184
1	419	1125
2	1075	1022
3	3577	1017
done	5000	1017

prune308.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ (* x 1.0) (tan B))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-/r*`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `div-exp`
2×	`frac-2neg` `clear-num` `sum-log` `div-inv` `distribute-lft-out`
1×	`tan-quot` `+-commutative` `neg-sub0` `associate-+l-` `distribute-rgt-neg-in` `flip3-+` `neg-log` `frac-add` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `distribute-neg-frac`

Counts

3 → 65

Calls

3 calls:

29.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
3.0ms	(/ (* x 1.0) (tan B))

series235.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
18.0ms	(/ 1.0 (sin B))
106.0ms	(/ (* x 1.0) (tan B))

simplify1.9s

Counts

74 → 74

Iterations

Useful iterations: 3 (916.0ms)

Iter	Nodes	Cost
0	144	837
1	336	797
2	945	711
3	3838	706
done	5000	706

prune180.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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:

17.0ms	(- (/ 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))

series235.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
13.0ms	(/ 1 (sin B))
35.0ms	(* x (cos B))
97.0ms	(/ (* x (cos B)) (sin B))

simplify2.3s

Counts

104 → 104

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	145	1077
1	310	981
2	853	904
3	4188	887
done	5000	887

prune212.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 48

Calls

2 calls:

3.0ms	(* x (cos B))
6.0ms	(/ (- 1 (* x (cos B))) (sin B))

series104.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(* x (cos B))
66.0ms	(/ (- 1 (* x (cos B))) (sin B))

simplify1.6s

Counts

54 → 54

Iterations

Useful iterations: 3 (437.0ms)

Iter	Nodes	Cost
0	94	632
1	195	607
2	519	555
3	1749	554
done	5000	554

prune119.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes52.0ms

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: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	14	11
done	14	11

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	1749×	body	1280	valid
510.0ms	1427×	body	640	valid
379.0ms	4866×	body	80	valid
179.0ms	718×	body	320	valid
60.0ms	364×	body	160	valid