Details

sample397.0ms

Algorithm

intervals

Results

50.0ms	51×	body	1280	valid
18.0ms	51×	body	640	valid
13.0ms	157×	body	80	valid
6.0ms	19×	body	320	valid
2.0ms	10×	body	160	valid

simplify45.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	31	11
3	39	11
4	50	11
5	52	11
done	52	11

prune7.0ms

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

rewrite64.0ms

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:

24.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
5.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))
25.0ms	(* x (/ 1.0 (tan B)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
19.0ms	(/ 1.0 (sin B))
36.0ms	(/ 1.0 (tan B))
128.0ms	(* x (/ 1.0 (tan B)))

simplify1.4s

Counts

113 → 113

Iterations

Useful iterations: 2 (160.0ms)

Iter	Nodes	Cost
0	174	1141
1	383	1074
2	964	996
3	2656	996
done	5000	996

prune280.0ms

Pruning

9 alts after pruning (9 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))

rewrite49.0ms

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:

32.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
5.0ms	(/ 1.0 (sin B))
10.0ms	(/ (* x 1.0) (tan B))

series262.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
19.0ms	(/ 1.0 (sin B))
113.0ms	(/ (* x 1.0) (tan B))

simplify1.6s

Counts

74 → 74

Iterations

Useful iterations: 2 (140.0ms)

Iter	Nodes	Cost
0	143	847
1	316	799
2	870	739
3	3273	739
done	5001	739

prune181.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

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:

26.0ms	(- (/ 1.0 (sin B)) (* (/ (* x 1.0) (sin B)) (cos B)))
6.0ms	(/ 1.0 (sin B))
10.0ms	(/ (* x 1.0) (sin B))
26.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

series308.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (/ 1.0 (sin B)) (* (/ (* x 1.0) (sin B)) (cos B)))
19.0ms	(/ 1.0 (sin B))
60.0ms	(/ (* x 1.0) (sin B))
106.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

simplify985.0ms

Counts

101 → 101

Iterations

Useful iterations: 2 (209.0ms)

Iter	Nodes	Cost
0	160	1221
1	390	1156
2	1338	1021
done	5001	1021

prune238.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

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))

rewrite21.0ms

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:

15.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
1.0ms	(cbrt (sin B))
1.0ms	(cbrt (sin B))
2.0ms	(cbrt (sin B))

series415.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
99.0ms	(cbrt (sin B))
98.0ms	(cbrt (sin B))
105.0ms	(cbrt (sin B))

simplify1.9s

Counts

85 → 85

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	75	710
1	156	628
2	405	534
3	1260	512
done	5001	507

prune216.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes57.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.0s	1726×	body	1280	valid
506.0ms	1395×	body	640	valid
417.0ms	4997×	body	80	valid
182.0ms	715×	body	320	valid
62.0ms	354×	body	160	valid