Details

sample324.0ms

Algorithm

intervals

Results

35.0ms	60×	body	1280	valid
14.0ms	41×	body	640	valid
13.0ms	169×	body	80	valid
4.0ms	17×	body	320	valid
1.0ms	7×	body	160	valid

simplify38.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	30	11
3	40	11
4	51	11
5	54	11
done	54	11

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

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))
0.2b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
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 → 101

Calls

4 calls:

11.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
2.0ms	(/ 1.0 (sin B))
2.0ms	(/ 1.0 (tan B))
11.0ms	(* x (/ 1.0 (tan B)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
19.0ms	(/ 1.0 (sin B))
40.0ms	(/ 1.0 (tan B))
122.0ms	(* x (/ 1.0 (tan B)))

simplify1.1s

Counts

113 → 113

Iterations

Useful iterations: 2 (149.0ms)

Iter	Nodes	Cost
0	174	1141
1	387	1074
2	955	996
3	2837	996
done	5000	996

prune299.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

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))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 65

Calls

3 calls:

16.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
2.0ms	(/ 1.0 (sin B))
4.0ms	(/ (* x 1.0) (tan B))

series252.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
18.0ms	(/ 1.0 (sin B))
113.0ms	(/ (* x 1.0) (tan B))

simplify1.2s

Counts

74 → 74

Iterations

Useful iterations: 2 (130.0ms)

Iter	Nodes	Cost
0	143	847
1	317	799
2	859	739
3	3348	739
done	5001	739

prune190.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
12×	`times-frac`
6×	`pow1` `associate-/r*` `add-log-exp`
4×	`associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `div-inv`
2×	`frac-2neg` `associate-*r/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `distribute-lft-out--` `sub-div` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

11.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
2.0ms	(/ 1.0 (sin B))
3.0ms	(* x (cos B))
4.0ms	(/ (* x (cos B)) (sin B))

series266.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
18.0ms	(/ 1.0 (sin B))
40.0ms	(* x (cos B))
95.0ms	(/ (* x (cos B)) (sin B))

simplify1.7s

Counts

93 → 93

Iterations

Useful iterations: 2 (123.0ms)

Iter	Nodes	Cost
0	149	1006
1	334	964
2	949	863
3	4352	863
done	5001	863

prune222.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ 1.0 (sin B)))
0.5b	(cbrt (/ 1.0 (sin B)))
0.5b	(cbrt (/ 1.0 (sin B)))
0.5b	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 144

Calls

4 calls:

2.0ms	(cbrt (/ 1.0 (sin B)))
2.0ms	(cbrt (/ 1.0 (sin B)))
2.0ms	(cbrt (/ 1.0 (sin B)))
19.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

series592.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (/ 1.0 (sin B)))
139.0ms	(cbrt (/ 1.0 (sin B)))
133.0ms	(cbrt (/ 1.0 (sin B)))
180.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

simplify1.3s

Counts

156 → 156

Iterations

Useful iterations: 3 (687.0ms)

Iter	Nodes	Cost
0	170	2245
1	303	2082
2	884	1991
3	2636	1888
done	5001	1888

prune492.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes58.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	12	14
done	12	14

end0.0ms

sample2.3s

Algorithm

intervals

Results

981.0ms	1689×	body	1280	valid
514.0ms	1426×	body	640	valid
388.0ms	4929×	body	80	valid
181.0ms	743×	body	320	valid
63.0ms	352×	body	160	valid