Details

sample90.0ms

Algorithm

intervals

Results

37.0ms	64×	body	1280	valid
19.0ms	55×	body	640	valid
12.0ms	136×	body	80	valid
8.0ms	20×	body	320	valid
2.0ms	13×	body	160	valid

simplify26.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	30	11
3	40	11
4	51	11
5	54	11
done	54	11

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

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:

8.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (tan B))
2.0ms	(/ 1.0 (sin B))
8.0ms	(* x (/ 1.0 (tan B)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
40.0ms	(/ 1.0 (tan B))
20.0ms	(/ 1.0 (sin B))
116.0ms	(* x (/ 1.0 (tan B)))

simplify1.9s

Counts

115 → 115

Iterations

Useful iterations: 3 (867.0ms)

Iter	Nodes	Cost
0	180	1184
1	419	1125
2	1077	1022
3	3593	1017
done	5000	1017

prune311.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

8.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
3.0ms	(* x (cos B))
2.0ms	(/ 1.0 (sin B))
4.0ms	(/ (* x (cos B)) (sin B))

series264.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
40.0ms	(* x (cos B))
19.0ms	(/ 1.0 (sin B))
100.0ms	(/ (* x (cos B)) (sin B))

simplify2.3s

Counts

94 → 94

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	154	1045
1	360	1002
2	1017	886
3	4766	879
done	5000	879

prune251.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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))

rewrite10.0ms

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:

6.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
1.0ms	(cbrt (sin B))
1.0ms	(cbrt (sin B))
1.0ms	(cbrt (sin B))

series429.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
101.0ms	(cbrt (sin B))
102.0ms	(cbrt (sin B))
104.0ms	(cbrt (sin B))

simplify3.8s

Counts

85 → 85

Iterations

Useful iterations: 4 (2.1s)

Iter	Nodes	Cost
0	75	710
1	156	632
2	401	534
3	1302	512
4	4214	505
done	5001	505

prune249.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (tan B) (* x (sin B)))
0.2b	(* x (sin B))
0.2b	(* (tan B) (sin B))
9.4b	(/ (* 1.0 (- (tan B) (* x (sin B)))) (* (tan B) (sin B)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `associate-l` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`cbrt-undiv` `div-exp`
2×	`tan-quot` `flip3--` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `associate-/l/` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `associate-/r/` `div-inv` `associate-/l`

Counts

4 → 73

Calls

4 calls:

3.0ms	(- (tan B) (* x (sin B)))
3.0ms	(* x (sin B))
4.0ms	(* (tan B) (sin B))
10.0ms	(/ (* 1.0 (- (tan B) (* x (sin B)))) (* (tan B) (sin B)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (tan B) (* x (sin B)))
39.0ms	(* x (sin B))
47.0ms	(* (tan B) (sin B))
160.0ms	(/ (* 1.0 (- (tan B) (* x (sin B)))) (* (tan B) (sin B)))

simplify1.2s

Counts

85 → 85

Iterations

Useful iterations: 2 (180.0ms)

Iter	Nodes	Cost
0	147	1089
1	394	1030
2	1596	855
done	5001	855

prune181.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes69.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	15	14
done	15	14

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	1724×	body	1280	valid
527.0ms	1455×	body	640	valid
392.0ms	4904×	body	80	valid
186.0ms	727×	body	320	valid
63.0ms	367×	body	160	valid