Details

sample99.0ms

Algorithm

intervals

Results

42.0ms	53×	body	1280	valid
17.0ms	38×	body	640	valid
15.0ms	147×	body	80	valid
9.0ms	28×	body	320	valid
4.0ms	17×	body	160	valid

simplify73.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	33	11
3	43	11
4	54	11
5	59	11
6	61	11
done	61	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
46×	`times-frac`
42×	`add-cube-cbrt` `*-un-lft-identity`
14×	`associate-r`
13×	`add-exp-log` `fma-neg` `prod-diff` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-l`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--`

Counts

4 → 135

Calls

4 calls:

31.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
12.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))
19.0ms	(* x (/ 1.0 (tan B)))

series331.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
21.0ms	(/ 1.0 (sin B))
44.0ms	(/ 1.0 (tan B))
127.0ms	(* x (/ 1.0 (tan B)))

simplify2.1s

Counts

147 → 147

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	199	1713
1	446	1635
2	1139	1489
3	3298	1451
done	5000	1440

prune437.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
0.1b	(/ 1.0 (sin B))
0.1b	(/ (* x 1.0) (tan B))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

133×	`times-frac`
107×	`add-sqr-sqrt`
104×	`*-un-lft-identity` `prod-diff`
102×	`add-cube-cbrt`
24×	`div-inv`
14×	`tan-quot` `associate-/r/`
13×	`fma-neg`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`add-log-exp`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
2×	`frac-2neg` `clear-num` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `prod-exp` `frac-sub` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

3 → 188

Calls

3 calls:

58.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
6.0ms	(/ 1.0 (sin B))
13.0ms	(/ (* x 1.0) (tan B))

series324.0ms

Counts

3 → 9

Calls

3 calls:

157.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
30.0ms	(/ 1.0 (sin B))
137.0ms	(/ (* x 1.0) (tan B))

simplify1.7s

Counts

197 → 197

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	284	6281
1	640	5115
2	1655	4181
done	5001	3472

prune632.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
17×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-r`
9×	`times-frac`
8×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `associate-l` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l` `unswap-sqr`
1×	`associate-*r/`

Counts

4 → 95

Calls

4 calls:

18.0ms	(/ (* x 1.0) (sin B))
15.0ms	(* x (cos B))
21.0ms	(/ (* x (cos B)) (sin B))
49.0ms	(* (cos B) (/ (* x 1.0) (sin B)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (* x 1.0) (sin B))
49.0ms	(* x (cos B))
142.0ms	(/ (* x (cos B)) (sin B))
118.0ms	(* (cos B) (/ (* x 1.0) (sin B)))

simplify1.8s

Counts

107 → 107

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	142	1045
1	338	1017
2	1305	851
done	5000	850

prune504.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin B) (* x 1.0))
0.2b	(/ (* x (cos B)) (sin B))
0.2b	(* (cos B) (/ 1 (/ (sin B) (* x 1.0))))
0.3b	(/ 1 (/ (sin B) (* x 1.0)))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

71×	`times-frac`
67×	`add-exp-log`
46×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
39×	`add-cube-cbrt`
37×	`add-cbrt-cube`
28×	`div-exp`
26×	`associate-r`
18×	`prod-exp`
14×	`cbrt-undiv`
11×	`associate-/r*` `div-inv`
8×	`cbrt-unprod`
7×	`pow1` `associate-/l*`
6×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-l` `clear-num` `unswap-sqr`
2×	`associate-/r/`
1×	`pow-flip` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 163

Calls

4 calls:

16.0ms	(/ (sin B) (* x 1.0))
17.0ms	(/ (* x (cos B)) (sin B))
51.0ms	(* (cos B) (/ 1 (/ (sin B) (* x 1.0))))
26.0ms	(/ 1 (/ (sin B) (* x 1.0)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (sin B) (* x 1.0))
146.0ms	(/ (* x (cos B)) (sin B))
127.0ms	(* (cos B) (/ 1 (/ (sin B) (* x 1.0))))
92.0ms	(/ 1 (/ (sin B) (* x 1.0)))

simplify1.7s

Counts

175 → 175

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	243	2200
1	582	1882
2	1702	1570
done	5001	1551

prune844.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes125.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	21	36
1	33	36
2	38	35
done	38	35

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.7s	1654×	body	1280	valid
1.6s	1505×	body	640	valid
1.1s	4888×	body	80	valid
464.0ms	702×	body	320	valid
112.0ms	344×	body	160	valid