Details

sample196.0ms

Algorithm

intervals

Results

68.0ms	52×	body	1280	valid
52.0ms	58×	body	640	valid
28.0ms	141×	body	80	valid
16.0ms	27×	body	320	valid
6.0ms	14×	body	160	valid

simplify155.0ms

Counts

1 → 1

Iterations

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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

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))

rewrite148.0ms

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:

108.0ms	(- (/ 1.0 (sin B)) (/ x (/ (tan B) 1.0)))
19.0ms	(/ x (/ (tan B) 1.0))
11.0ms	(/ 1.0 (sin B))

series470.0ms

Counts

3 → 9

Calls

3 calls:

225.0ms	(- (/ 1.0 (sin B)) (/ x (/ (tan B) 1.0)))
199.0ms	(/ x (/ (tan B) 1.0))
46.0ms	(/ 1.0 (sin B))

simplify2.5s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
2	1945
1	596
0	246

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

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:

49.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
18.0ms	(* x (cos B))
11.0ms	(/ 1.0 (sin B))
25.0ms	(/ (* x (cos B)) (sin B))

series501.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
59.0ms	(* x (cos B))
38.0ms	(/ 1.0 (sin B))
183.0ms	(/ (* x (cos B)) (sin B))

simplify2.1s

Counts

93 → 93

Iterations

Iter	Nodes
done	5004
2	1112
1	354
0	149

prune793.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

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	(* x (/ (cos B) (sin B)))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

58.0ms	(- (/ 1.0 (sin B)) (* 1.0 (* x (/ (cos B) (sin B)))))
11.0ms	(/ 1.0 (sin B))
20.0ms	(/ (cos B) (sin B))
40.0ms	(* x (/ (cos B) (sin B)))

series478.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(- (/ 1.0 (sin B)) (* 1.0 (* x (/ (cos B) (sin B)))))
33.0ms	(/ 1.0 (sin B))
41.0ms	(/ (cos B) (sin B))
184.0ms	(* x (/ (cos B) (sin B)))

simplify2.8s

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
2	1381
1	415
0	174

prune959.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize67.0ms

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))

rewrite54.0ms

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:

41.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
3.0ms	(cbrt (sin B))
3.0ms	(cbrt (sin B))
3.0ms	(cbrt (sin B))

series796.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
175.0ms	(cbrt (sin B))
201.0ms	(cbrt (sin B))
204.0ms	(cbrt (sin B))

simplify3.3s

Counts

85 → 85

Iterations

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

prune657.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes219.0ms

Accuracy

0% (0.6b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	15
1	15
0	13

end0.0ms

sample7.8s

Algorithm

intervals

Results

3.3s	1716×	body	1280	valid
1.8s	4859×	body	80	valid
1.4s	1434×	body	640	valid
621.0ms	691×	body	320	valid
149.0ms	352×	body	160	valid