Details

sample115.0ms

Algorithm

intervals

Results

47.0ms	62×	body	1280	valid
23.0ms	169×	body	80	valid
19.0ms	42×	body	640	valid
6.0ms	22×	body	320	valid
2.0ms	11×	body	160	valid

simplify45.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

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

localize11.0ms

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))
0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite71.0ms

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:

24.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
8.0ms	(/ 1.0 (sin B))
9.0ms	(/ 1.0 (tan B))
25.0ms	(* x (/ 1.0 (tan B)))

series373.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
28.0ms	(/ 1.0 (sin B))
52.0ms	(/ 1.0 (tan B))
145.0ms	(* x (/ 1.0 (tan B)))

simplify2.1s

Counts

115 → 115

Iterations

Useful iterations: 3 (1.0s)

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

prune396.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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))

rewrite126.0ms

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:

95.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
11.0ms	(/ 1.0 (sin B))
19.0ms	(/ (* x 1.0) (tan B))

series382.0ms

Counts

3 → 9

Calls

3 calls:

200.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
31.0ms	(/ 1.0 (sin B))
151.0ms	(/ (* x 1.0) (tan B))

simplify2.5s

Counts

74 → 74

Iterations

Useful iterations: 3 (1.1s)

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

prune285.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

30.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
12.0ms	(/ (* x 1.0) (sin B))
33.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

series437.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
21.0ms	(/ 1.0 (sin B))
88.0ms	(/ (* x 1.0) (sin B))
146.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

simplify1.6s

Counts

102 → 102

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	165	1259
1	417	1211
2	1482	1044
done	5000	1037

prune360.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* (* x 1.0) (/ (cos B) (sin B)))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ (cos B) (sin B))
0.3b	(* (* x 1.0) (/ (cos B) (sin B)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

39.0ms	(+ (- (* (* x 1.0) (/ (cos B) (sin B)))) (/ 1.0 (sin B)))
11.0ms	(/ 1.0 (sin B))
20.0ms	(/ (cos B) (sin B))
26.0ms	(* (* x 1.0) (/ (cos B) (sin B)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(+ (- (* (* x 1.0) (/ (cos B) (sin B)))) (/ 1.0 (sin B)))
34.0ms	(/ 1.0 (sin B))
21.0ms	(/ (cos B) (sin B))
150.0ms	(* (* x 1.0) (/ (cos B) (sin B)))

simplify1.6s

Counts

114 → 114

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	181	1418
1	450	1354
2	1662	1187
done	5001	1180

prune404.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes69.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	18	15
2	28	15
done	28	15

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.5s	1746×	body	1280	valid
769.0ms	1395×	body	640	valid
587.0ms	4973×	body	80	valid
265.0ms	743×	body	320	valid
88.0ms	348×	body	160	valid