Details

sample76.0ms

Algorithm

intervals

Results

31.0ms	55×	body	1280	valid
15.0ms	45×	body	640	valid
13.0ms	165×	body	80	valid
5.0ms	20×	body	320	valid
2.0ms	10×	body	160	valid

simplify27.0ms

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

prune9.0ms

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)))

rewrite28.0ms

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:

11.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
2.0ms	(/ 1.0 (sin B))
2.0ms	(/ 1.0 (tan B))
9.0ms	(* x (/ 1.0 (tan B)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
19.0ms	(/ 1.0 (sin B))
39.0ms	(/ 1.0 (tan B))
113.0ms	(* x (/ 1.0 (tan B)))

simplify1.3s

Counts

113 → 113

Iterations

Useful iterations: 2 (159.0ms)

Iter	Nodes	Cost
0	174	1141
1	387	1074
2	955	996
3	2837	996
done	5000	996

prune292.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

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))
0.2b	(/ (* x 1.0) (tan B))

rewrite25.0ms

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:

15.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
2.0ms	(/ 1.0 (sin B))
4.0ms	(/ (* x 1.0) (tan B))

series249.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
18.0ms	(/ 1.0 (sin B))
110.0ms	(/ (* x 1.0) (tan B))

simplify1.5s

Counts

74 → 74

Iterations

Useful iterations: 2 (142.0ms)

Iter	Nodes	Cost
0	143	847
1	317	799
2	859	739
3	3348	739
done	5000	739

prune193.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (/ 1 (/ (tan B) (* x 1.0))))
0.1b	(/ 1.0 (sin B))
0.1b	(/ (tan B) (* x 1.0))
0.3b	(/ 1 (/ (tan B) (* x 1.0)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
47×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
32×	`add-exp-log`
30×	`add-cube-cbrt`
20×	`add-cbrt-cube`
15×	`div-exp`
11×	`associate-/r*`
9×	`associate-/l*`
8×	`cbrt-undiv` `div-inv`
6×	`add-log-exp` `difference-of-squares`
5×	`pow1`
4×	`prod-exp`
3×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `distribute-lft-out--`
2×	`cbrt-unprod`
1×	`tan-quot` `sub-neg` `flip3--` `pow-flip` `diff-log` `associate-/r/` `frac-sub` `flip--` `associate-/l/` `inv-pow`

Counts

4 → 127

Calls

4 calls:

26.0ms	(- (/ 1.0 (sin B)) (/ 1 (/ (tan B) (* x 1.0))))
2.0ms	(/ 1.0 (sin B))
3.0ms	(/ (tan B) (* x 1.0))
7.0ms	(/ 1 (/ (tan B) (* x 1.0)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(- (/ 1.0 (sin B)) (/ 1 (/ (tan B) (* x 1.0))))
19.0ms	(/ 1.0 (sin B))
53.0ms	(/ (tan B) (* x 1.0))
98.0ms	(/ 1 (/ (tan B) (* x 1.0)))

simplify1.5s

Counts

139 → 139

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	234	1841
1	530	1655
2	1363	1427
done	5000	1417

prune304.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

11.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
2.0ms	(/ 1.0 (sin B))
4.0ms	(* x (cos B))
4.0ms	(/ (* x (cos B)) (sin B))

series276.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
19.0ms	(/ 1.0 (sin B))
41.0ms	(* x (cos B))
99.0ms	(/ (* x (cos B)) (sin B))

simplify2.2s

Counts

93 → 93

Iterations

Useful iterations: 2 (139.0ms)

Iter	Nodes	Cost
0	149	1006
1	334	964
2	949	863
3	4354	863
done	5001	863

prune218.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes56.0ms

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	9	11
1	11	11
done	11	11

end0.0ms

sample2.3s

Algorithm

intervals

Results

986.0ms	1700×	body	1280	valid
510.0ms	1461×	body	640	valid
387.0ms	4889×	body	80	valid
188.0ms	725×	body	320	valid
61.0ms	368×	body	160	valid