Details

sample239.0ms

Algorithm

intervals

Results

117.0ms	63×	body	1280	valid
43.0ms	165×	body	80	valid
37.0ms	32×	body	640	valid
19.0ms	23×	body	320	valid
8.0ms	14×	body	160	valid

simplify992.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
17	1964
16	1837
15	1728
14	1603
13	1490
12	1330
11	1186
10	1061
9	917
8	762
7	635
6	430
5	255
4	161
3	80
2	43
1	20
0	10

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 1 (sin B)) (/ x (tan B)))
0.1b	(/ 1 (sin B))
0.1b	(/ x (tan B))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`times-frac`
19×	`add-cube-cbrt`
9×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/r` `associate-/l` `difference-of-squares`
5×	`add-log-exp`
4×	`pow1`
3×	`div-exp` `insert-posit16` `div-inv` `distribute-lft-out--`
2×	`cbrt-undiv` `clear-num` `frac-2neg`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `tan-quot` `associate-/r/` `frac-sub` `pow-flip` `flip--` `inv-pow`

Counts

3 → 84

Calls

3 calls:

23.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
13.0ms	(/ 1 (sin B))
7.0ms	(/ x (tan B))

series278.0ms

Counts

3 → 9

Calls

3 calls:

123.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
21.0ms	(/ 1 (sin B))
133.0ms	(/ x (tan B))

simplify513.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	2002
2	849
1	300
0	153

prune311.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
0.1b	(* x (cos B))
0.1b	(/ 1 (sin B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`times-frac` `add-exp-log`
13×	`add-cbrt-cube`
7×	`pow1` `div-inv`
6×	`associate-/r*` `add-log-exp`
4×	`div-exp` `insert-posit16` `associate-/l*`
3×	`cbrt-undiv` `distribute-rgt-out--` `associate-r` `associate-l` `difference-of-squares`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `frac-sub` `pow-flip` `flip--` `inv-pow` `sub-div` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

23.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
8.0ms	(* x (cos B))
6.0ms	(/ 1 (sin B))
11.0ms	(/ (* x (cos B)) (sin B))

series294.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
53.0ms	(* x (cos B))
14.0ms	(/ 1 (sin B))
102.0ms	(/ (* x (cos B)) (sin B))

simplify449.0ms

Counts

108 → 108

Iterations

Iter	Nodes
done	2068
2	1063
1	329
0	150

prune356.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
0.1b	(/ 1 (sin B))
0.1b	(/ x (sin B))
0.2b	(* (/ x (sin B)) (cos B))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
15×	`add-exp-log`
13×	`add-cbrt-cube` `associate-l`
7×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
4×	`div-exp` `insert-posit16`
3×	`cbrt-undiv` `associate-r` `associate-*l/` `div-inv`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `frac-sub` `pow-flip` `flip--` `inv-pow` `sub-div`

Counts

4 → 108

Calls

4 calls:

33.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
6.0ms	(/ 1 (sin B))
4.0ms	(/ x (sin B))
19.0ms	(* (/ x (sin B)) (cos B))

series318.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
20.0ms	(/ 1 (sin B))
70.0ms	(/ x (sin B))
126.0ms	(* (/ x (sin B)) (cos B))

simplify580.0ms

Counts

120 → 120

Iterations

Iter	Nodes
done	2002
2	1312
1	373
0	166

prune441.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B))))
0.5b	(cbrt (/ 1 (sin B)))
0.5b	(cbrt (/ 1 (sin B)))
0.5b	(cbrt (/ 1 (sin B)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

119×	`cbrt-prod`
97×	`add-sqr-sqrt`
79×	`times-frac`
67×	`*-un-lft-identity`
57×	`add-cube-cbrt`
18×	`swap-sqr`
16×	`associate-r` `associate-l` `unswap-sqr`
11×	`pow1`
9×	`pow1/3` `div-inv`
7×	`cbrt-div`
6×	`add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 157

Calls

4 calls:

16.0ms	(* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B))))
2.0ms	(cbrt (/ 1 (sin B)))
2.0ms	(cbrt (/ 1 (sin B)))
2.0ms	(cbrt (/ 1 (sin B)))

series585.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B))))
130.0ms	(cbrt (/ 1 (sin B)))
139.0ms	(cbrt (/ 1 (sin B)))
177.0ms	(cbrt (/ 1 (sin B)))

simplify817.0ms

Counts

169 → 169

Iterations

Iter	Nodes
done	2001
3	1544
2	629
1	291
0	157

prune630.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes110.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample8.8s

Algorithm

intervals

Results

3.6s	1718×	body	1280	valid
2.3s	1427×	body	640	valid
1.5s	4963×	body	80	valid
952.0ms	696×	body	320	valid
225.0ms	352×	body	160	valid