Details

sample150.0ms

Algorithm

intervals

Results

46.0ms	44×	body	1280	valid
39.0ms	56×	body	640	valid
25.0ms	163×	body	80	valid
12.0ms	26×	body	320	valid
4.0ms	12×	body	160	valid

simplify111.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	31	11
3	39	11
4	50	11
5	53	11
done	53	11

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite122.0ms

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:

50.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
11.0ms	(/ 1.0 (sin B))
11.0ms	(/ 1.0 (tan B))
44.0ms	(* x (/ 1.0 (tan B)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
33.0ms	(/ 1.0 (sin B))
68.0ms	(/ 1.0 (tan B))
195.0ms	(* x (/ 1.0 (tan B)))

simplify1.6s

Counts

113 → 113

Iterations

Useful iterations: 2 (736.0ms)

Iter	Nodes	Cost
0	174	1141
1	409	1078
2	1459	996
done	5000	996

prune741.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 3 expressions with local error:

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

rewrite99.0ms

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:

64.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
11.0ms	(/ 1.0 (sin B))
21.0ms	(/ (* x 1.0) (tan B))

series433.0ms

Counts

3 → 9

Calls

3 calls:

218.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
31.0ms	(/ 1.0 (sin B))
183.0ms	(/ (* x 1.0) (tan B))

simplify1.2s

Counts

74 → 74

Iterations

Useful iterations: 2 (290.0ms)

Iter	Nodes	Cost
0	143	847
1	337	799
2	1401	739
done	5000	739

prune482.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
15×	`times-frac`
7×	`associate-l`
6×	`pow1` `associate-/r*` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
4×	`associate-/l*`
3×	`associate-r` `associate-*l/` `div-inv`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

53.0ms	(- (/ 1.0 (sin B)) (* (/ (* x 1.0) (sin B)) (cos B)))
17.0ms	(/ (* x 1.0) (sin B))
9.0ms	(/ 1.0 (sin B))
43.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

series551.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(- (/ 1.0 (sin B)) (* (/ (* x 1.0) (sin B)) (cos B)))
103.0ms	(/ (* x 1.0) (sin B))
32.0ms	(/ 1.0 (sin B))
179.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

simplify1.9s

Counts

101 → 101

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	160	1221
1	418	1156
2	2174	1037
done	5001	1031

prune794.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize52.0ms

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))

rewrite41.0ms

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×	`add-cbrt-cube` `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 → 73

Calls

4 calls:

29.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
2.0ms	(cbrt (sin B))
2.0ms	(cbrt (sin B))
3.0ms	(cbrt (sin B))

series847.0ms

Counts

4 → 12

Calls

4 calls:

250.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
197.0ms	(cbrt (sin B))
195.0ms	(cbrt (sin B))
204.0ms	(cbrt (sin B))

simplify1.7s

Counts

85 → 85

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	75	710
1	177	628
2	754	534
done	5000	520

prune607.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes240.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample8.2s

Algorithm

intervals

Results

3.6s	1765×	body	1280	valid
2.1s	1416×	body	640	valid
1.3s	4931×	body	80	valid
563.0ms	715×	body	320	valid
207.0ms	350×	body	160	valid