Details

sample408.0ms

Algorithm

intervals

Results

134.0ms	63×	body	1280	valid
75.0ms	23×	body	320	valid
55.0ms	165×	body	80	valid
45.0ms	32×	body	640	valid
10.0ms	14×	body	160	valid

simplify1.2s

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

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))

rewrite47.0ms

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:

20.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
5.0ms	(/ 1 (sin B))
20.0ms	(/ x (tan B))

series312.0ms

Counts

3 → 9

Calls

3 calls:

131.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
18.0ms	(/ 1 (sin B))
162.0ms	(/ x (tan B))

simplify536.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	2002
2	849
1	300
0	153

prune393.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

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))

rewrite54.0ms

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:

18.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
14.0ms	(* x (cos B))
9.0ms	(/ 1 (sin B))
11.0ms	(/ (* x (cos B)) (sin B))

series331.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
50.0ms	(* x (cos B))
18.0ms	(/ 1 (sin B))
143.0ms	(/ (* x (cos B)) (sin B))

simplify654.0ms

Counts

108 → 108

Iterations

Iter	Nodes
done	2068
2	1063
1	329
0	150

prune499.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

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))

rewrite84.0ms

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:

40.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
10.0ms	(/ 1 (sin B))
9.0ms	(/ x (sin B))
21.0ms	(* (/ x (sin B)) (cos B))

series368.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
14.0ms	(/ 1 (sin B))
79.0ms	(/ x (sin B))
150.0ms	(* (/ x (sin B)) (cos B))

simplify616.0ms

Counts

120 → 120

Iterations

Iter	Nodes
done	2002
2	1312
1	373
0	166

prune459.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

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:

15.0ms	(* (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)))

series572.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B))))
124.0ms	(cbrt (/ 1 (sin B)))
139.0ms	(cbrt (/ 1 (sin B)))
152.0ms	(cbrt (/ 1 (sin B)))

simplify1.5s

Counts

169 → 169

Iterations

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

prune820.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes140.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.7s	1718×	body	1280	valid
1.9s	1427×	body	640	valid
1.8s	4963×	body	80	valid
633.0ms	696×	body	320	valid
257.0ms	352×	body	160	valid