Details

sample150.0ms

Algorithm

intervals

Results

59.0ms	53×	body	1280	valid
28.0ms	39×	body	640	valid
25.0ms	157×	body	80	valid
13.0ms	24×	body	320	valid
3.0ms	10×	body	160	valid

simplify87.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

28.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
7.0ms	(/ 1.0 (tan B))
20.0ms	(/ 1.0 (sin B))
26.0ms	(* x (/ 1.0 (tan B)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
52.0ms	(/ 1.0 (tan B))
25.0ms	(/ 1.0 (sin B))
147.0ms	(* x (/ 1.0 (tan B)))

simplify1.9s

Counts

113 → 113

Iterations

Useful iterations: 2 (201.0ms)

Iter	Nodes	Cost
0	174	1141
1	383	1074
2	966	996
3	2660	996
done	5000	996

prune340.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt` `times-frac`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`add-log-exp`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `div-exp`
2×	`frac-2neg` `clear-num` `div-inv` `difference-of-squares`
1×	`tan-quot` `sub-neg` `flip3--` `diff-log` `prod-exp` `associate-/r/` `frac-sub` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

3 → 65

Calls

3 calls:

45.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
8.0ms	(/ 1.0 (sin B))
21.0ms	(/ (* x 1.0) (tan B))

series376.0ms

Counts

3 → 9

Calls

3 calls:

185.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
27.0ms	(/ 1.0 (sin B))
164.0ms	(/ (* x 1.0) (tan B))

simplify2.2s

Counts

74 → 74

Iterations

Useful iterations: 2 (224.0ms)

Iter	Nodes	Cost
0	143	847
1	316	799
2	870	739
3	3273	739
done	5001	739

prune277.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

53.0ms	(- (/ 1.0 (sin B)) (* (* 1.0 (/ x (sin B))) (cos B)))
9.0ms	(/ 1.0 (sin B))
10.0ms	(/ x (sin B))
39.0ms	(* (* 1.0 (/ x (sin B))) (cos B))

series436.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(- (/ 1.0 (sin B)) (* (* 1.0 (/ x (sin B))) (cos B)))
38.0ms	(/ 1.0 (sin B))
80.0ms	(/ x (sin B))
131.0ms	(* (* 1.0 (/ x (sin B))) (cos B))

simplify1.8s

Counts

101 → 101

Iterations

Useful iterations: 2 (339.0ms)

Iter	Nodes	Cost
0	168	1176
1	378	1109
2	1206	996
done	5000	996

prune350.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 2 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `times-frac` `add-cbrt-cube`
7×	`pow1`
3×	`associate-r` `pow-prod-down` `prod-exp` `associate-/r` `cbrt-unprod` `associate-/l`
2×	`associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `associate-l` `clear-num` `*-commutative` `flip--` `div-inv`

Counts

2 → 48

Calls

2 calls:

22.0ms	(* (* 1.0 x) (cos B))
20.0ms	(/ (- 1.0 (* (* 1.0 x) (cos B))) (sin B))

series177.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(* (* 1.0 x) (cos B))
110.0ms	(/ (- 1.0 (* (* 1.0 x) (cos B))) (sin B))

simplify2.7s

Counts

54 → 54

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	108	789
1	254	764
2	853	676
3	3235	674
done	5000	674

prune167.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes70.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	11	11
done	11	11

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.6s	1741×	body	1280	valid
1.7s	1384×	body	640	valid
1.2s	4950×	body	80	valid
500.0ms	713×	body	320	valid
125.0ms	351×	body	160	valid