Details

sample130.0ms

Algorithm

intervals

Results

48.0ms	53×	body	1280	valid
34.0ms	147×	body	80	valid
20.0ms	38×	body	640	valid
11.0ms	28×	body	320	valid
5.0ms	17×	body	160	valid

simplify41.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize39.0ms

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)))

rewrite62.0ms

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)))
6.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))
20.0ms	(* x (/ 1.0 (tan B)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
22.0ms	(/ 1.0 (sin B))
72.0ms	(/ 1.0 (tan B))
140.0ms	(* x (/ 1.0 (tan B)))

simplify2.1s

Counts

115 → 115

Iterations

Useful iterations: 3 (992.0ms)

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

prune449.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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))

rewrite110.0ms

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:

83.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
12.0ms	(/ 1.0 (sin B))
13.0ms	(/ (* x 1.0) (tan B))

series354.0ms

Counts

3 → 9

Calls

3 calls:

163.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
20.0ms	(/ 1.0 (sin B))
171.0ms	(/ (* x 1.0) (tan B))

simplify2.5s

Counts

74 → 74

Iterations

Useful iterations: 3 (1.3s)

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

prune270.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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

rewrite86.0ms

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:

27.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
10.0ms	(/ 1.0 (sin B))
19.0ms	(/ (* x 1.0) (sin B))
28.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

series345.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
24.0ms	(/ 1.0 (sin B))
71.0ms	(/ (* x 1.0) (sin B))
126.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

simplify1.3s

Counts

102 → 102

Iterations

Useful iterations: done (1.3s)

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

prune340.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

77×	`times-frac`
64×	`add-exp-log`
52×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
45×	`add-cube-cbrt`
34×	`add-cbrt-cube`
27×	`div-exp`
26×	`associate-l`
17×	`prod-exp`
13×	`cbrt-undiv`
11×	`associate-/r*` `div-inv`
9×	`associate-/l*`
7×	`pow1` `cbrt-unprod`
6×	`rec-exp` `1-exp`
4×	`add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `unswap-sqr`
2×	`associate-/r/`
1×	`pow-flip` `pow-prod-down` `associate-l/` `-commutative` `inv-pow`

Counts

4 → 160

Calls

4 calls:

6.0ms	(/ 1.0 (sin B))
12.0ms	(/ (sin B) (* x 1.0))
53.0ms	(* (/ 1 (/ (sin B) (* x 1.0))) (cos B))
27.0ms	(/ 1 (/ (sin B) (* x 1.0)))

series214.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ 1.0 (sin B))
38.0ms	(/ (sin B) (* x 1.0))
98.0ms	(* (/ 1 (/ (sin B) (* x 1.0))) (cos B))
58.0ms	(/ 1 (/ (sin B) (* x 1.0)))

simplify1.4s

Counts

172 → 172

Iterations

Useful iterations: 2 (355.0ms)

Iter	Nodes	Cost
0	246	2103
1	561	1814
2	1451	1516
done	5000	1516

prune407.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes79.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 2 (3.0ms)

Iter	Nodes	Cost
0	13	17
1	22	17
2	27	16
done	27	16

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.4s	1654×	body	1280	valid
1.5s	1505×	body	640	valid
1.0s	4888×	body	80	valid
843.0ms	702×	body	320	valid
110.0ms	344×	body	160	valid