Details

sample146.0ms

Algorithm

intervals

Results

75.0ms	59×	body	1280	valid
24.0ms	43×	body	640	valid
19.0ms	146×	body	80	valid
8.0ms	22×	body	320	valid
2.0ms	9×	body	160	valid

simplify46.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
0.1b	(/ 1.0 (tan B))
0.1b	(/ 1.0 (sin B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite413.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
46×	`times-frac`
42×	`add-cube-cbrt` `*-un-lft-identity`
14×	`associate-r`
13×	`add-exp-log` `fma-neg` `prod-diff` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-l`
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 → 135

Calls

4 calls:

361.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
9.0ms	(/ 1.0 (tan B))
8.0ms	(/ 1.0 (sin B))
27.0ms	(* x (/ 1.0 (tan B)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
53.0ms	(/ 1.0 (tan B))
21.0ms	(/ 1.0 (sin B))
178.0ms	(* x (/ 1.0 (tan B)))

simplify1.1s

Counts

147 → 147

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	199	1713
1	478	1639
2	1725	1528
done	5001	1459

prune530.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

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))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

133×	`times-frac`
107×	`add-sqr-sqrt`
104×	`*-un-lft-identity` `prod-diff`
102×	`add-cube-cbrt`
24×	`div-inv`
14×	`tan-quot` `associate-/r/`
13×	`fma-neg`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`add-log-exp`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
2×	`frac-2neg` `clear-num` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `prod-exp` `frac-sub` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

3 → 188

Calls

3 calls:

64.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
9.0ms	(/ 1.0 (sin B))
18.0ms	(/ (* x 1.0) (tan B))

series389.0ms

Counts

3 → 9

Calls

3 calls:

195.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
21.0ms	(/ 1.0 (sin B))
173.0ms	(/ (* x 1.0) (tan B))

simplify1.6s

Counts

197 → 197

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	284	6281
1	678	5154
2	2704	4201
done	5000	3986

prune574.0ms

Pruning

9 alts after pruning (9 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	(/ 1 (sin B))
0.1b	(* x (cos B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite123.0ms

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×	`fma-neg` `add-cbrt-cube`
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×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `distribute-lft-out--`
1×	`sub-neg` `rec-exp` `flip3--` `pow-flip` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `inv-pow` `sub-div` `unswap-sqr`

Counts

4 → 204

Calls

4 calls:

41.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
12.0ms	(/ 1 (sin B))
25.0ms	(* x (cos B))
24.0ms	(/ (* x (cos B)) (sin B))

series365.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
15.0ms	(/ 1 (sin B))
42.0ms	(* x (cos B))
140.0ms	(/ (* x (cos B)) (sin B))

simplify2.1s

Counts

216 → 216

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	264	6388
1	612	4957
2	3119	4056
done	5000	3834

prune530.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 2 expressions with local error:

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

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1`
3×	`associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

2 → 52

Calls

2 calls:

17.0ms	(* x (cos B))
38.0ms	(/ (- 1 (* x (cos B))) (sin B))

series160.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(* x (cos B))
96.0ms	(/ (- 1 (* x (cos B))) (sin B))

simplify907.0ms

Counts

58 → 58

Iterations

Useful iterations: done (905.0ms)

Iter	Nodes	Cost
0	98	662
1	215	637
2	1003	585
done	5000	582

prune222.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes106.0ms

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	11
1	14	11
done	14	11

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.1s	1742×	body	1280	valid
1.4s	1462×	body	640	valid
856.0ms	4957×	body	80	valid
453.0ms	647×	body	320	valid
114.0ms	365×	body	160	valid