Details

sample221.0ms

Algorithm

intervals

Results

96.0ms	44×	body	1280	valid
44.0ms	56×	body	640	valid
30.0ms	163×	body	80	valid
14.0ms	26×	body	320	valid
5.0ms	12×	body	160	valid

simplify84.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	33	11
3	43	11
4	54	11
5	60	11
6	62	11
done	62	11

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
0.2b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
29×	`add-cube-cbrt`
28×	`times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `fma-def` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `sum-log` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `distribute-lft-neg-in` `associate-+l-` `neg-mul-1` `distribute-rgt-neg-in` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 117

Calls

4 calls:

34.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
12.0ms	(/ 1.0 (sin B))
12.0ms	(/ 1.0 (tan B))
36.0ms	(* x (/ 1.0 (tan B)))

series478.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
38.0ms	(/ 1.0 (sin B))
61.0ms	(/ 1.0 (tan B))
182.0ms	(* x (/ 1.0 (tan B)))

simplify1.3s

Counts

129 → 129

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	188	1244
1	462	1184
2	1710	1083
done	5000	1074

prune882.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
0.1b	(* x (cos B))
0.2b	(/ 1.0 (sin B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
13×	`add-exp-log` `add-cbrt-cube`
12×	`times-frac`
8×	`add-log-exp`
6×	`pow1` `fma-def` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `div-inv`
2×	`distribute-rgt-neg-in` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `distribute-lft-neg-in` `associate-+l-` `neg-mul-1` `flip3-+` `associate-r/` `pow-prod-down` `neg-log` `frac-add` `-commutative` `flip-+` `distribute-neg-frac` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

32.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
17.0ms	(* x (cos B))
11.0ms	(/ 1.0 (sin B))
24.0ms	(/ (* x (cos B)) (sin B))

series481.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
64.0ms	(* x (cos B))
42.0ms	(/ 1.0 (sin B))
182.0ms	(/ (* x (cos B)) (sin B))

simplify1.5s

Counts

108 → 108

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	162	1113
1	394	1066
2	1605	956
done	5000	943

prune815.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (sin B))
0.2b	(* (* x (/ 1.0 (sin B))) (cos B))
0.3b	(* x (/ 1.0 (sin B)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
28×	`times-frac`
22×	`add-exp-log` `add-cbrt-cube`
16×	`associate-r`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r` `associate-/l`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`frac-2neg` `associate-r/` `clear-num` `-commutative` `unswap-sqr`
1×	`associate-*l/`

Counts

4 → 115

Calls

4 calls:

12.0ms	(/ 1.0 (sin B))
12.0ms	(/ 1.0 (sin B))
68.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
44.0ms	(* x (/ 1.0 (sin B)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ 1.0 (sin B))
39.0ms	(/ 1.0 (sin B))
215.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
111.0ms	(* x (/ 1.0 (sin B)))

simplify1.7s

Counts

127 → 127

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	140	1194
1	347	1150
2	1633	1022
done	5001	1014

prune962.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin B)) (cbrt (sin B)))
0.6b	(cbrt (sin B))
0.6b	(cbrt (sin B))
0.6b	(cbrt (sin B))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

32.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
3.0ms	(cbrt (sin B))
3.0ms	(cbrt (sin B))
3.0ms	(cbrt (sin B))

series856.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
213.0ms	(cbrt (sin B))
207.0ms	(cbrt (sin B))
201.0ms	(cbrt (sin B))

simplify1.7s

Counts

93 → 93

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	79	750
1	183	664
2	715	564
done	5000	549

prune606.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes222.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify13.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	15
1	18	15
2	22	15
3	28	15
done	28	15

end0.0ms

sample7.8s

Algorithm

intervals

Results

3.1s	1765×	body	1280	valid
2.0s	4931×	body	80	valid
1.4s	1416×	body	640	valid
572.0ms	715×	body	320	valid
241.0ms	350×	body	160	valid