Details

sample579.0ms

Algorithm

intervals

Results

399.0ms	134×	body	80	valid
47.0ms	62×	body	1280	valid
23.0ms	50×	body	640	valid
7.0ms	21×	body	320	valid
3.0ms	11×	body	160	valid

simplify61.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	52
6	52
5	50
4	44
3	37
2	31
1	18
0	10

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize124.0ms

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))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 65

Calls

3 calls:

130.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
7.0ms	(/ 1.0 (sin B))
51.0ms	(/ (* x 1.0) (tan B))

series694.0ms

Counts

3 → 9

Calls

3 calls:

304.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
77.0ms	(/ 1.0 (sin B))
312.0ms	(/ (* x 1.0) (tan B))

simplify1.8s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
2	1078
1	338
0	144

prune460.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

31.0ms	(- (/ 1.0 (sin B)) (* (/ (* 1.0 x) (sin B)) (cos B)))
4.0ms	(/ 1.0 (sin B))
8.0ms	(/ (* 1.0 x) (sin B))
20.0ms	(* (/ (* 1.0 x) (sin B)) (cos B))

series438.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(- (/ 1.0 (sin B)) (* (/ (* 1.0 x) (sin B)) (cos B)))
30.0ms	(/ 1.0 (sin B))
66.0ms	(/ (* 1.0 x) (sin B))
160.0ms	(* (/ (* 1.0 x) (sin B)) (cos B))

simplify1.6s

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
2	1464
1	405
0	161

prune725.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 2 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 48

Calls

2 calls:

20.0ms	(* (* 1.0 x) (cos B))
12.0ms	(/ (- 1.0 (* (* 1.0 x) (cos B))) (sin B))

series220.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(* (* 1.0 x) (cos B))
144.0ms	(/ (- 1.0 (* (* 1.0 x) (cos B))) (sin B))

simplify2.6s

Counts

54 → 54

Iterations

Iter	Nodes
done	5008
3	3702
2	862
1	263
0	108

prune271.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

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))
0.2b	(/ (tan B) (* x 1.0))
0.3b	(/ 1 (/ (tan B) (* x 1.0)))

rewrite79.0ms

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` `clear-num` `frac-2neg` `1-exp` `distribute-lft-out--`
2×	`cbrt-unprod`
1×	`sub-neg` `flip3--` `diff-log` `tan-quot` `associate-/r/` `frac-sub` `pow-flip` `flip--` `inv-pow` `associate-/l/`

Counts

4 → 127

Calls

4 calls:

46.0ms	(- (/ 1.0 (sin B)) (/ 1 (/ (tan B) (* x 1.0))))
5.0ms	(/ 1.0 (sin B))
7.0ms	(/ (tan B) (* x 1.0))
17.0ms	(/ 1 (/ (tan B) (* x 1.0)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(- (/ 1.0 (sin B)) (/ 1 (/ (tan B) (* x 1.0))))
23.0ms	(/ 1.0 (sin B))
64.0ms	(/ (tan B) (* x 1.0))
116.0ms	(/ 1 (/ (tan B) (* x 1.0)))

simplify1.9s

Counts

139 → 139

Iterations

Iter	Nodes
done	5001
2	1989
1	562
0	234

prune630.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes166.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.2s	1449×	body	640	valid
2.1s	1746×	body	1280	valid
914.0ms	4902×	body	80	valid
451.0ms	688×	body	320	valid
114.0ms	353×	body	160	valid