Details

sample219.0ms

Algorithm

intervals

Results

108.0ms	53×	body	1280	valid
38.0ms	41×	body	640	valid
35.0ms	166×	body	80	valid
14.0ms	20×	body	320	valid
8.0ms	18×	body	160	valid

simplify164.0ms

Counts: 1 → 1

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

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)))

rewrite51.0ms

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

26.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
8.0ms	(/ x (tan B))
7.0ms	(/ 1 (sin B))

series253.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

127.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
109.0ms	(/ x (tan B))
17.0ms	(/ 1 (sin B))

simplify725.0ms

Counts: 294 → 294

prune2.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

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)))

rewrite82.0ms

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

41.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
22.0ms	(* (/ x (sin B)) (cos B))
9.0ms	(/ 1 (sin B))
8.0ms	(/ x (sin B))

series309.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

144.0ms	(* (/ x (sin B)) (cos B))
98.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
53.0ms	(/ x (sin B))
14.0ms	(/ 1 (sin B))

simplify1.8s

Counts: 154 → 154

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

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

23.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
13.0ms	(/ 1 (/ (tan B) x))
5.0ms	(/ (tan B) x)
5.0ms	(/ 1 (sin B))

series275.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

108.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
96.0ms	(/ 1 (/ (tan B) x))
54.0ms	(/ (tan B) x)
16.0ms	(/ 1 (sin B))

simplify1.4s

Counts: 779 → 779

prune10.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
107×	`add-sqr-sqrt`
105×	`*-un-lft-identity`
98×	`add-cube-cbrt`
91×	`prod-diff`
28×	`div-inv`
15×	`add-exp-log`
13×	`add-cbrt-cube` `fma-neg`
7×	`pow1`
6×	`associate-/r*` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u` `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 → 208

Calls

4 calls:

Slowest

29.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
11.0ms	(/ (* x (cos B)) (sin B))
7.0ms	(* x (cos B))
5.0ms	(/ 1 (sin B))

series327.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

150.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
114.0ms	(/ (* x (cos B)) (sin B))
49.0ms	(* x (cos B))
15.0ms	(/ 1 (sin B))

simplify634.0ms

Counts: 220 → 220

prune2.4s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes95.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample9.1s

Algorithm

intervals

Results

4.1s	1719×	body	1280	valid
1.9s	1423×	body	640	valid
1.9s	4915×	body	80	valid
570.0ms	715×	body	320	valid
268.0ms	382×	body	160	valid