Details

sample168.0ms

Algorithm

intervals

Results

59.0ms	50×	body	1280	valid
46.0ms	45×	body	640	valid
27.0ms	153×	body	80	valid
17.0ms	27×	body	320	valid
6.0ms	16×	body	160	valid

simplify136.0ms

Counts: 1 → 1

prune346.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite33.0ms

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

21.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
5.0ms	(/ 1 (sin B))
5.0ms	(/ x (tan B))

series228.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

114.0ms	(/ x (tan B))
101.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
14.0ms	(/ 1 (sin B))

simplify523.0ms

Counts: 93 → 93

prune834.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

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)))

rewrite76.0ms

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

35.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
22.0ms	(/ (* x (cos B)) (sin B))
10.0ms	(* x (cos B))
8.0ms	(/ 1 (sin B))

series303.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

122.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
120.0ms	(/ (* x (cos B)) (sin B))
44.0ms	(* x (cos B))
18.0ms	(/ 1 (sin B))

simplify1.9s

Counts: 108 → 108

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
36×	`add-exp-log`
34×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `add-cube-cbrt`
22×	`add-cbrt-cube`
16×	`div-exp`
11×	`associate-/r*`
9×	`associate-/l*`
8×	`pow1` `cbrt-undiv`
7×	`div-inv`
5×	`prod-exp`
4×	`rec-exp` `1-exp` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `associate-l` `cbrt-unprod`
2×	`pow-flip` `inv-pow`
1×	`pow-prod-down` `associate-/r/` `*-commutative` `unswap-sqr`

Counts

4 → 130

Calls

4 calls:

Slowest

19.0ms	(/ (sin B) (* x (cos B)))
15.0ms	(/ 1 (/ (sin B) (* x (cos B))))
11.0ms	(/ 1 (sin B))
8.0ms	(* x (cos B))

series233.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

101.0ms	(/ 1 (/ (sin B) (* x (cos B))))
66.0ms	(/ (sin B) (* x (cos B)))
53.0ms	(* x (cos B))
14.0ms	(/ 1 (sin B))

simplify2.1s

Counts: 142 → 142

prune1.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

11.5b	(/ (- (tan B) (* x (sin B))) (* (sin B) (tan B)))
0.1b	(* (sin B) (tan B))
0.1b	(* x (sin B))
0.0b	(- (tan B) (* x (sin B)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

Slowest

38.0ms	(/ (- (tan B) (* x (sin B))) (* (sin B) (tan B)))
23.0ms	(* (sin B) (tan B))
12.0ms	(* x (sin B))
11.0ms	(- (tan B) (* x (sin B)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

200.0ms	(/ (- (tan B) (* x (sin B))) (* (sin B) (tan B)))
117.0ms	(- (tan B) (* x (sin B)))
74.0ms	(* (sin B) (tan B))
70.0ms	(* x (sin B))

simplify1.8s

Counts: 90 → 90

prune1.0s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes111.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample8.9s

Algorithm

intervals

Results

3.7s	1784×	body	1280	valid
2.3s	4931×	body	80	valid
1.7s	1407×	body	640	valid
752.0ms	720×	body	320	valid
180.0ms	348×	body	160	valid