Details

sample449.0ms

Algorithm

intervals

Results

110.0ms	27×	body	320	valid
73.0ms	52×	body	1280	valid
62.0ms	58×	body	640	valid
28.0ms	141×	body	80	valid
6.0ms	14×	body	160	valid

simplify201.0ms

Counts

1 → 1

Iterations

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

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 3 expressions with local error:

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

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

95×	`times-frac`
74×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
53×	`add-cube-cbrt`
16×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
6×	`div-inv` `associate-/l*` `difference-of-squares`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1`
2×	`frac-2neg` `clear-num` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `associate-/r/` `frac-sub` `flip--`

Counts

3 → 118

Calls

3 calls:

128.0ms	(- (/ 1.0 (sin B)) (/ x (/ (tan B) 1.0)))
22.0ms	(/ x (/ (tan B) 1.0))
16.0ms	(/ 1.0 (sin B))

series523.0ms

Counts

3 → 9

Calls

3 calls:

231.0ms	(- (/ 1.0 (sin B)) (/ x (/ (tan B) 1.0)))
233.0ms	(/ x (/ (tan B) 1.0))
59.0ms	(/ 1.0 (sin B))

simplify2.7s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
2	1945
1	596
0	246

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

60.0ms	(- (/ 1.0 (sin B)) (/ (* (* 1.0 x) (cos B)) (sin B)))
38.0ms	(* (* 1.0 x) (cos B))
11.0ms	(/ 1.0 (sin B))
53.0ms	(/ (* (* 1.0 x) (cos B)) (sin B))

series577.0ms

Counts

4 → 12

Calls

4 calls:

240.0ms	(- (/ 1.0 (sin B)) (/ (* (* 1.0 x) (cos B)) (sin B)))
86.0ms	(* (* 1.0 x) (cos B))
39.0ms	(/ 1.0 (sin B))
213.0ms	(/ (* (* 1.0 x) (cos B)) (sin B))

simplify3.4s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	1464
1	398
0	157

prune736.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* (* 1.0 x) (/ (cos B) (sin B))))
0.2b	(/ 1.0 (sin B))
0.2b	(/ (cos B) (sin B))
0.3b	(* (* 1.0 x) (/ (cos B) (sin B)))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

67.0ms	(- (/ 1.0 (sin B)) (* (* 1.0 x) (/ (cos B) (sin B))))
11.0ms	(/ 1.0 (sin B))
21.0ms	(/ (cos B) (sin B))
51.0ms	(* (* 1.0 x) (/ (cos B) (sin B)))

series517.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(- (/ 1.0 (sin B)) (* (* 1.0 x) (/ (cos B) (sin B))))
44.0ms	(/ 1.0 (sin B))
42.0ms	(/ (cos B) (sin B))
203.0ms	(* (* 1.0 x) (/ (cos B) (sin B)))

simplify3.3s

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
2	1614
1	455
0	176

prune935.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize71.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin B)) (cbrt (sin B)))
0.6b	(cbrt (sin B))
0.6b	(cbrt (sin B))
0.6b	(cbrt (sin B))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

28.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
3.0ms	(cbrt (sin B))
3.0ms	(cbrt (sin B))
3.0ms	(cbrt (sin B))

series766.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
196.0ms	(cbrt (sin B))
167.0ms	(cbrt (sin B))
184.0ms	(cbrt (sin B))

simplify3.4s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
3	1329
2	468
1	175
0	75

prune730.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes271.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	15
1	15
0	13

end0.0ms

sample8.2s

Algorithm

intervals

Results

2.9s	1716×	body	1280	valid
2.2s	1434×	body	640	valid
1.9s	4859×	body	80	valid
575.0ms	691×	body	320	valid
226.0ms	352×	body	160	valid