Details

sample138.0ms

Algorithm

intervals

Results

65.0ms	53×	body	1280	valid
21.0ms	147×	body	80	valid
20.0ms	38×	body	640	valid
11.0ms	28×	body	320	valid
4.0ms	17×	body	160	valid

simplify33.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	31	11
3	39	11
4	50	11
5	52	11
done	52	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `associate-/r` `associate-/l`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `sum-log` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

25.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
8.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))
29.0ms	(* x (/ 1.0 (tan B)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
27.0ms	(/ 1.0 (sin B))
65.0ms	(/ 1.0 (tan B))
154.0ms	(* x (/ 1.0 (tan B)))

simplify2.2s

Counts

115 → 115

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	180	1184
1	414	1125
2	1121	1022
3	3390	1017
done	5000	1017

prune431.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-/r*`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `div-exp`
2×	`frac-2neg` `clear-num` `sum-log` `div-inv` `distribute-lft-out`
1×	`tan-quot` `+-commutative` `neg-sub0` `associate-+l-` `distribute-rgt-neg-in` `flip3-+` `neg-log` `frac-add` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `distribute-neg-frac`

Counts

3 → 65

Calls

3 calls:

65.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
17.0ms	(/ (* x 1.0) (tan B))

series405.0ms

Counts

3 → 9

Calls

3 calls:

182.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
44.0ms	(/ 1.0 (sin B))
180.0ms	(/ (* x 1.0) (tan B))

simplify2.0s

Counts

74 → 74

Iterations

Useful iterations: 3 (885.0ms)

Iter	Nodes	Cost
0	144	837
1	334	797
2	988	711
3	3734	706
done	5000	706

prune297.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
21×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
17×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
8×	`add-log-exp`
6×	`associate-/r` `associate-/l`
5×	`prod-exp` `cbrt-unprod`
3×	`cbrt-undiv` `div-exp` `associate-r` `pow-prod-down`
2×	`frac-2neg` `associate-r/` `associate-l/` `clear-num` `sum-log` `div-inv`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `associate-l` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 90

Calls

4 calls:

24.0ms	(+ (- (* (* 1.0 (/ x (sin B))) (cos B))) (/ 1.0 (sin B)))
10.0ms	(/ 1.0 (sin B))
7.0ms	(/ x (sin B))
54.0ms	(* (* 1.0 (/ x (sin B))) (cos B))

series393.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(+ (- (* (* 1.0 (/ x (sin B))) (cos B))) (/ 1.0 (sin B)))
22.0ms	(/ 1.0 (sin B))
66.0ms	(/ x (sin B))
153.0ms	(* (* 1.0 (/ x (sin B))) (cos B))

simplify1.8s

Counts

102 → 102

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	173	1214
1	406	1164
2	1364	1019
done	5001	1012

prune391.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sin B))
0.2b	(/ (sin B) x)
0.2b	(* (* 1.0 (/ 1 (/ (sin B) x))) (cos B))
0.3b	(/ 1 (/ (sin B) x))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

93×	`times-frac`
63×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
47×	`add-exp-log`
27×	`add-cbrt-cube`
19×	`associate-/r*`
16×	`div-exp`
15×	`prod-exp`
10×	`pow1`
9×	`associate-/l*`
8×	`cbrt-undiv`
7×	`cbrt-unprod` `div-inv`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`frac-2neg` `associate-r` `pow-prod-down` `clear-num`
2×	`associate-*l/`
1×	`pow-flip` `associate-r/` `associate-l` `associate-/r/` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 158

Calls

4 calls:

6.0ms	(/ 1.0 (sin B))
11.0ms	(/ (sin B) x)
73.0ms	(* (* 1.0 (/ 1 (/ (sin B) x))) (cos B))
25.0ms	(/ 1 (/ (sin B) x))

series281.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ 1.0 (sin B))
55.0ms	(/ (sin B) x)
138.0ms	(* (* 1.0 (/ 1 (/ (sin B) x))) (cos B))
63.0ms	(/ 1 (/ (sin B) x))

simplify4.1s

Counts

170 → 170

Iterations

Useful iterations: 3 (2.3s)

Iter	Nodes	Cost
0	265	2012
1	571	1705
2	1402	1442
3	4696	1424
done	5000	1424

prune550.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes157.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify15.0ms

Iterations

Useful iterations: 3 (11.0ms)

Iter	Nodes	Cost
0	13	17
1	22	17
2	30	17
3	33	16
done	33	16

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.1s	1654×	body	1280	valid
2.1s	1505×	body	640	valid
940.0ms	4888×	body	80	valid
597.0ms	702×	body	320	valid
184.0ms	344×	body	160	valid