Details

sample399.0ms

Algorithm

intervals

Results

94.0ms	57×	body	1280	valid
79.0ms	49×	body	640	valid
37.0ms	156×	body	80	valid
17.0ms	21×	body	320	valid
6.0ms	11×	body	160	valid

simplify132.0ms

Counts: 1 → 1

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

279×	`times-frac`
232×	`add-sqr-sqrt`
224×	`*-un-lft-identity`
215×	`add-cube-cbrt`
182×	`prod-diff`
31×	`div-inv`
14×	`tan-quot` `associate-/r/`
13×	`fma-neg`
9×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/r` `associate-/l` `difference-of-squares`
5×	`add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
2×	`cbrt-undiv` `clear-num` `frac-2neg`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `frac-sub` `pow-flip` `flip--` `inv-pow`

Counts

3 → 285

Calls

3 calls:

Slowest

25.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
6.0ms	(/ x (tan B))
5.0ms	(/ 1 (sin B))

series397.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

204.0ms	(/ x (tan B))
165.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
27.0ms	(/ 1 (sin B))

simplify925.0ms

Counts: 294 → 294

prune3.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
46×	`times-frac`
42×	`*-un-lft-identity` `add-cube-cbrt`
15×	`add-exp-log`
13×	`add-cbrt-cube` `fma-neg` `associate-l` `prod-diff`
7×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-r` `associate-*l/`
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 → 142

Calls

4 calls:

Slowest

29.0ms	(* (/ x (sin B)) (cos B))
23.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
15.0ms	(/ x (sin B))
10.0ms	(/ 1 (sin B))

series396.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

151.0ms	(* (/ x (sin B)) (cos B))
141.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
77.0ms	(/ x (sin B))
28.0ms	(/ 1 (sin B))

simplify2.1s

Counts: 154 → 154

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

1390×	`times-frac`
881×	`add-sqr-sqrt`
855×	`*-un-lft-identity`
834×	`add-cube-cbrt`
572×	`prod-diff`
108×	`div-inv`
21×	`add-exp-log`
19×	`associate-/r*`
15×	`difference-of-squares`
14×	`associate-/r/`
13×	`add-cbrt-cube` `fma-neg`
10×	`div-exp`
9×	`associate-/l*`
7×	`distribute-lft-out--`
6×	`pow1` `add-log-exp`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
2×	`pow-flip` `inv-pow`
1×	`sub-neg` `flip3--` `diff-log` `tan-quot` `frac-sub` `flip--` `associate-/l/`

Counts

4 → 767

Calls

4 calls:

Slowest

24.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
9.0ms	(/ 1 (sin B))
6.0ms	(/ 1 (/ (tan B) x))
6.0ms	(/ (tan B) x)

series391.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

169.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
131.0ms	(/ 1 (/ (tan B) x))
66.0ms	(/ (tan B) x)
24.0ms	(/ 1 (sin B))

simplify1.8s

Counts: 779 → 779

prune11.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

8.7b	(/ (- (/ (tan B) x) (sin B)) (* (sin B) (/ (tan B) x)))
0.2b	(* (sin B) (/ (tan B) x))
0.2b	(/ (tan B) x)
0.2b	(/ (tan B) x)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
36×	`times-frac`
34×	`*-un-lft-identity`
30×	`add-cube-cbrt`
22×	`add-cbrt-cube` `add-exp-log`
13×	`associate-r`
12×	`associate-/l*`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`pow1`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp` `difference-of-squares` `associate-/l/`
3×	`clear-num` `frac-2neg` `associate-l`
2×	`tan-quot` `associate-*r/` `distribute-lft-out--` `unswap-sqr`
1×	`flip3--` `div-sub` `pow-prod-down` `associate-/r/` `*-commutative` `flip--`

Counts

4 → 133

Calls

4 calls:

Slowest

41.0ms	(/ (- (/ (tan B) x) (sin B)) (* (sin B) (/ (tan B) x)))
15.0ms	(* (sin B) (/ (tan B) x))
12.0ms	(/ (tan B) x)
10.0ms	(/ (tan B) x)

series591.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

317.0ms	(/ (- (/ (tan B) x) (sin B)) (* (sin B) (/ (tan B) x)))
113.0ms	(* (sin B) (/ (tan B) x))
91.0ms	(/ (tan B) x)
69.0ms	(/ (tan B) x)

simplify665.0ms

Counts: 145 → 145

prune1.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes120.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample8.6s

Algorithm

intervals

Results

3.1s	1769×	body	1280	valid
1.8s	1369×	body	640	valid
1.6s	4874×	body	80	valid
1.6s	747×	body	320	valid
228.0ms	353×	body	160	valid