Details

sample155.0ms

Algorithm

intervals

Results

55.0ms	46×	body	1280	valid
37.0ms	169×	body	80	valid
32.0ms	38×	body	640	valid
11.0ms	19×	body	320	valid
8.0ms	18×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2005
18	2005
17	1964
16	1837
15	1728
14	1603
13	1490
12	1330
11	1186
10	1061
9	917
8	762
7	635
6	430
5	255
4	161
3	80
2	43
1	20
0	10

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 1 (sin B)) (/ x (tan B)))
0.1b	(/ 1 (sin B))
0.1b	(/ x (tan B))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`times-frac`
19×	`add-cube-cbrt`
9×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/r` `associate-/l` `difference-of-squares`
5×	`add-log-exp`
4×	`pow1`
3×	`div-exp` `insert-posit16` `div-inv` `distribute-lft-out--`
2×	`cbrt-undiv` `clear-num` `frac-2neg`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `tan-quot` `associate-/r/` `frac-sub` `pow-flip` `flip--` `inv-pow`

Counts

3 → 84

Calls

3 calls:

28.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
7.0ms	(/ 1 (sin B))
7.0ms	(/ x (tan B))

series270.0ms

Counts

3 → 9

Calls

3 calls:

117.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
17.0ms	(/ 1 (sin B))
135.0ms	(/ x (tan B))

simplify798.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	2006
3	2006
2	849
1	300
0	153

prune360.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
0.1b	(* x (cos B))
0.1b	(/ 1 (sin B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`times-frac` `add-exp-log`
13×	`add-cbrt-cube`
7×	`pow1` `div-inv`
6×	`associate-/r*` `add-log-exp`
4×	`div-exp` `insert-posit16` `associate-/l*`
3×	`cbrt-undiv` `distribute-rgt-out--` `associate-r` `associate-l` `difference-of-squares`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `frac-sub` `pow-flip` `flip--` `inv-pow` `sub-div` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

25.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
10.0ms	(* x (cos B))
7.0ms	(/ 1 (sin B))
19.0ms	(/ (* x (cos B)) (sin B))

series338.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
56.0ms	(* x (cos B))
18.0ms	(/ 1 (sin B))
121.0ms	(/ (* x (cos B)) (sin B))

simplify1.0s

Counts

108 → 108

Iterations

Iter	Nodes
done	2542
3	2542
2	1063
1	329
0	150

prune427.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 2 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`pow1`
3×	`associate-/r` `associate-r` `associate-l` `associate-/l`
2×	`insert-posit16` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `flip--` `unswap-sqr`

Counts

2 → 50

Calls

2 calls:

11.0ms	(* x (cos B))
15.0ms	(/ (- 1 (* x (cos B))) (sin B))

series124.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(* x (cos B))
80.0ms	(/ (- 1 (* x (cos B))) (sin B))

simplify1.1s

Counts

56 → 56

Iterations

Iter	Nodes
done	2001
3	2001
2	625
1	211
0	96

prune219.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
0.1b	(/ 1 (sin B))
0.1b	(/ (cos B) (sin B))
0.3b	(* x (/ (cos B) (sin B)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
15×	`add-exp-log`
13×	`add-cbrt-cube` `associate-r`
7×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
4×	`div-exp` `insert-posit16`
3×	`cbrt-undiv` `associate-l` `associate-*r/` `div-inv`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `frac-sub` `pow-flip` `flip--` `inv-pow` `sub-div`

Counts

4 → 108

Calls

4 calls:

17.0ms	(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
7.0ms	(/ 1 (sin B))
13.0ms	(/ (cos B) (sin B))
14.0ms	(* x (/ (cos B) (sin B)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
14.0ms	(/ 1 (sin B))
33.0ms	(/ (cos B) (sin B))
111.0ms	(* x (/ (cos B) (sin B)))

simplify1.1s

Counts

120 → 120

Iterations

Iter	Nodes
done	2013
3	2013
2	1299
1	373
0	168

prune414.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes90.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
1	11
0	8

end0.0ms

sample8.4s

Algorithm

intervals

Results

3.0s	1721×	body	1280	valid
2.4s	1432×	body	640	valid
1.4s	4925×	body	80	valid
1.2s	709×	body	320	valid
235.0ms	375×	body	160	valid