Details

sample158.0ms

Algorithm

intervals

Results

65.0ms	57×	body	1280	valid
35.0ms	48×	body	640	valid
27.0ms	155×	body	80	valid
10.0ms	20×	body	320	valid
2.0ms	7×	body	160	valid

simplify47.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	53
5	53
4	50
3	39
2	31
1	18
0	10

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
14×	`associate-l`
13×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-r` `div-inv`
2×	`clear-num` `frac-2neg` `associate-*l/` `prod-exp` `tan-quot` `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:

24.0ms	(- (/ 1.0 (sin B)) (* (/ 1.0 (tan B)) x))
4.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))
27.0ms	(* (/ 1.0 (tan B)) x)

series406.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(- (/ 1.0 (sin B)) (* (/ 1.0 (tan B)) x))
29.0ms	(/ 1.0 (sin B))
55.0ms	(/ 1.0 (tan B))
145.0ms	(* (/ 1.0 (tan B)) x)

simplify1.1s

Counts

113 → 113

Iterations

Iter	Nodes
done	5001
2	1607
1	406
0	176

prune628.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 3 expressions with local error:

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

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

29×	`times-frac`
28×	`*-un-lft-identity`
22×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`associate-/l*`
7×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*`
5×	`add-log-exp`
4×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in`
3×	`pow1` `distribute-frac-neg`
2×	`neg-sub0` `cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv` `distribute-lft-out`
1×	`+-commutative` `associate-+r-` `sum-log` `flip3-+` `unsub-neg` `frac-add` `tan-quot` `associate-/r/` `flip-+`

Counts

3 → 86

Calls

3 calls:

37.0ms	(+ (/ 1.0 (sin B)) (/ (- (* x 1.0)) (tan B)))
13.0ms	(/ (- (* x 1.0)) (tan B))
8.0ms	(/ 1.0 (sin B))

series412.0ms

Counts

3 → 9

Calls

3 calls:

167.0ms	(+ (/ 1.0 (sin B)) (/ (- (* x 1.0)) (tan B)))
212.0ms	(/ (- (* x 1.0)) (tan B))
33.0ms	(/ 1.0 (sin B))

simplify920.0ms

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
2	1596
1	389
0	173

prune555.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (cos B))
0.2b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (sin B))
0.3b	(* (/ 1.0 (sin B)) (* x (cos B)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

18.0ms	(* x (cos B))
8.0ms	(/ 1.0 (sin B))
9.0ms	(/ 1.0 (sin B))
47.0ms	(* (/ 1.0 (sin B)) (* x (cos B)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* x (cos B))
36.0ms	(/ 1.0 (sin B))
23.0ms	(/ 1.0 (sin B))
135.0ms	(* (/ 1.0 (sin B)) (* x (cos B)))

simplify850.0ms

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	1265
1	321
0	126

prune638.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ 1.0 (sin B)))
0.4b	(cbrt (/ 1.0 (sin B)))
0.4b	(cbrt (/ 1.0 (sin B)))
0.5b	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`*-un-lft-identity` `add-cube-cbrt`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 144

Calls

4 calls:

4.0ms	(cbrt (/ 1.0 (sin B)))
5.0ms	(cbrt (/ 1.0 (sin B)))
11.0ms	(cbrt (/ 1.0 (sin B)))
29.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

series847.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(cbrt (/ 1.0 (sin B)))
192.0ms	(cbrt (/ 1.0 (sin B)))
190.0ms	(cbrt (/ 1.0 (sin B)))
263.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

simplify1.1s

Counts

156 → 156

Iterations

Iter	Nodes
done	5000
2	1533
1	336
0	170

prune1.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes191.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.6s	1690×	body	1280	valid
1.7s	1437×	body	640	valid
881.0ms	4996×	body	80	valid
424.0ms	710×	body	320	valid
125.0ms	377×	body	160	valid