Details

sample356.0ms

Algorithm

intervals

Results

92.0ms	65×	body	1280	valid
67.0ms	145×	body	80	valid
51.0ms	46×	body	640	valid
17.0ms	19×	body	320	valid
8.0ms	16×	body	160	valid

simplify128.0ms

Counts: 1 → 1

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite54.0ms

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:

Slowest

38.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
6.0ms	(/ x (tan B))
5.0ms	(/ 1 (sin B))

series338.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

164.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
159.0ms	(/ x (tan B))
15.0ms	(/ 1 (sin B))

simplify1.9s

Counts: 93 → 93

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

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:

Slowest

24.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
11.0ms	(/ (* x (cos B)) (sin B))
10.0ms	(/ 1 (sin B))
7.0ms	(* x (cos B))

series404.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

165.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
160.0ms	(/ (* x (cos B)) (sin B))
59.0ms	(* x (cos B))
19.0ms	(/ 1 (sin B))

simplify2.3s

Counts: 108 → 108

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 2 expressions with local error:

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

rewrite19.0ms

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:

Slowest

11.0ms	(/ (- 1 (* x (cos B))) (sin B))
7.0ms	(* x (cos B))

series142.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

94.0ms	(/ (- 1 (* x (cos B))) (sin B))
47.0ms	(* x (cos B))

simplify2.9s

Counts: 56 → 56

prune674.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x (/ (cos B) (sin B)))
0.2b	(/ (cos B) (sin B))
0.1b	(/ 1 (sin B))
0.0b	(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))

rewrite52.0ms

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:

Slowest

22.0ms	(* x (/ (cos B) (sin B)))
16.0ms	(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
9.0ms	(/ (cos B) (sin B))
5.0ms	(/ 1 (sin B))

series326.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

138.0ms	(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
129.0ms	(* x (/ (cos B) (sin B)))
44.0ms	(/ (cos B) (sin B))
15.0ms	(/ 1 (sin B))

simplify1.6s

Counts: 120 → 120

prune1.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes147.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.2s	1672×	body	1280	valid
2.6s	1410×	body	640	valid
1.6s	4983×	body	80	valid
671.0ms	720×	body	320	valid
201.0ms	370×	body	160	valid