Details

sample219.0ms

Algorithm

intervals

Results

52.0ms	52×	body	1280	valid
46.0ms	23×	body	320	valid
35.0ms	54×	body	640	valid
23.0ms	148×	body	80	valid
4.0ms	13×	body	160	valid

simplify97.0ms

Counts

1 → 1

Iterations

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

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

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))

rewrite130.0ms

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:

94.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
9.0ms	(/ 1.0 (sin B))
20.0ms	(/ (* x 1.0) (tan B))

series797.0ms

Counts

3 → 9

Calls

3 calls:

405.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
68.0ms	(/ 1.0 (sin B))
324.0ms	(/ (* x 1.0) (tan B))

simplify1.5s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
2	1078
1	338
0	144

prune483.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

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)))

rewrite101.0ms

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:

51.0ms	(- (/ 1.0 (sin B)) (/ 1 (/ (tan B) (* x 1.0))))
5.0ms	(/ 1.0 (sin B))
14.0ms	(/ (tan B) (* x 1.0))
24.0ms	(/ 1 (/ (tan B) (* x 1.0)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(- (/ 1.0 (sin B)) (/ 1 (/ (tan B) (* x 1.0))))
38.0ms	(/ 1.0 (sin B))
93.0ms	(/ (tan B) (* x 1.0))
141.0ms	(/ 1 (/ (tan B) (* x 1.0)))

simplify1.8s

Counts

139 → 139

Iterations

Iter	Nodes
done	5001
2	1989
1	562
0	234

prune672.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
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×	`clear-num` `frac-2neg` `prod-exp` `associate-*r/` `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:

40.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
7.0ms	(* x (cos B))
4.0ms	(/ 1.0 (sin B))
9.0ms	(/ (* x (cos B)) (sin B))

series434.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
44.0ms	(* x (cos B))
36.0ms	(/ 1.0 (sin B))
181.0ms	(/ (* x (cos B)) (sin B))

simplify1.3s

Counts

93 → 93

Iterations

Iter	Nodes
done	5003
2	1155
1	355
0	150

prune463.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (cos B))
0.1b	(/ 1.0 (sin B))
0.1b	(/ 1 (sin B))
0.3b	(* (* x (cos B)) (/ 1 (sin B)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

7.0ms	(* x (cos B))
4.0ms	(/ 1.0 (sin B))
5.0ms	(/ 1 (sin B))
22.0ms	(* (* x (cos B)) (/ 1 (sin B)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* x (cos B))
21.0ms	(/ 1.0 (sin B))
26.0ms	(/ 1 (sin B))
163.0ms	(* (* x (cos B)) (/ 1 (sin B)))

simplify3.3s

Counts

126 → 126

Iterations

Iter	Nodes
done	5008
3	3683
2	1184
1	399
0	168

prune668.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes184.0ms

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	14
1	14
0	11

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.1s	1710×	body	1280	valid
1.3s	4905×	body	80	valid
1.1s	1422×	body	640	valid
584.0ms	379×	body	160	valid
362.0ms	700×	body	320	valid