Details

sample277.0ms

Algorithm

intervals

Results

66.0ms	57×	body	1280	valid
63.0ms	20×	body	320	valid
38.0ms	48×	body	640	valid
28.0ms	155×	body	80	valid
2.0ms	7×	body	160	valid

simplify111.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	33	11
3	43	11
4	54	11
5	60	11
6	62	11
done	62	11

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
29×	`add-cube-cbrt`
28×	`times-frac`
14×	`associate-r`
13×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
6×	`pow1` `associate-/r` `fma-def` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`clear-num` `sum-log` `frac-2neg` `prod-exp` `tan-quot` `associate-*r/` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`neg-sub0` `distribute-lft-neg-in` `+-commutative` `neg-mul-1` `distribute-rgt-neg-in` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `associate-+l-` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 117

Calls

4 calls:

34.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
8.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))
16.0ms	(* x (/ 1.0 (tan B)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
39.0ms	(/ 1.0 (sin B))
72.0ms	(/ 1.0 (tan B))
174.0ms	(* x (/ 1.0 (tan B)))

simplify1.1s

Counts

129 → 129

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	189	1244
1	464	1184
2	1720	1083
done	5000	1074

prune779.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
107×	`add-sqr-sqrt`
105×	`*-un-lft-identity`
98×	`add-cube-cbrt`
91×	`prod-diff`
28×	`div-inv`
15×	`add-exp-log`
13×	`add-cbrt-cube` `fma-neg`
7×	`pow1`
6×	`associate-/r*` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `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 → 204

Calls

4 calls:

40.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
13.0ms	(* x (cos B))
6.0ms	(/ 1 (sin B))
9.0ms	(/ (* x (cos B)) (sin B))

series377.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
54.0ms	(* x (cos B))
28.0ms	(/ 1 (sin B))
149.0ms	(/ (* x (cos B)) (sin B))

simplify2.0s

Counts

216 → 216

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	265	6388
1	614	4956
2	3128	4056
done	5000	3834

prune696.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 3 expressions with local error:

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

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
23×	`add-cube-cbrt`
20×	`times-frac`
18×	`add-exp-log`
16×	`associate-l`
12×	`add-cbrt-cube`
8×	`pow1`
6×	`associate-r` `prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in` `prod-exp`
4×	`div-exp` `unswap-sqr`
3×	`expm1-log1p-u` `associate-/r` `cbrt-unprod` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`frac-times` `cbrt-undiv` `rec-exp` `sub-neg` `flip3--` `1-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv` `flip--`
1×	`clear-num` `frac-2neg` `associate-*l/` `pow-flip` `inv-pow`

Counts

3 → 104

Calls

3 calls:

6.0ms	(* x (cos B))
41.0ms	(* (/ 1 (sin B)) (- 1 (* x (cos B))))
11.0ms	(/ 1 (sin B))

series159.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(* x (cos B))
97.0ms	(* (/ 1 (sin B)) (- 1 (* x (cos B))))
16.0ms	(/ 1 (sin B))

simplify1.9s

Counts

113 → 113

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	168	1333
1	455	1204
2	2755	1008
done	5001	1002

prune500.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ 1 (sin B)))
0.4b	(cbrt (/ 1 (sin B)))
0.4b	(cbrt (/ 1 (sin B)))
0.5b	(* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B))))

rewrite52.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 161

Calls

4 calls:

2.0ms	(cbrt (/ 1 (sin B)))
8.0ms	(cbrt (/ 1 (sin B)))
2.0ms	(cbrt (/ 1 (sin B)))
33.0ms	(* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B))))

series641.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (/ 1 (sin B)))
146.0ms	(cbrt (/ 1 (sin B)))
176.0ms	(cbrt (/ 1 (sin B)))
172.0ms	(* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B))))

simplify1.1s

Counts

173 → 173

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	159	2443
1	298	2107
2	1045	1888
done	5000	1862

prune815.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes208.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	15	14
done	15	14

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.6s	1690×	body	1280	valid
1.5s	4996×	body	80	valid
1.1s	1437×	body	640	valid
407.0ms	710×	body	320	valid
165.0ms	377×	body	160	valid