Details

sample322.0ms

Algorithm

intervals

Results

85.0ms	56×	body	1280	valid
70.0ms	61×	body	640	valid
44.0ms	8×	body	160	valid
38.0ms	153×	body	80	valid
11.0ms	15×	body	320	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
15	2000
14	1959
13	1787
12	1570
11	1347
10	1172
9	1050
8	909
7	752
6	541
5	310
4	185
3	85
2	45
1	20
0	10

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 3 expressions with local error:

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

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

279×	`times-frac`
232×	`add-sqr-sqrt`
224×	`*-un-lft-identity`
215×	`add-cube-cbrt`
182×	`prod-diff`
31×	`div-inv`
14×	`tan-quot` `associate-/r/`
13×	`fma-neg`
9×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/r` `associate-/l` `difference-of-squares`
5×	`add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
2×	`cbrt-undiv` `clear-num` `frac-2neg`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `frac-sub` `pow-flip` `flip--` `inv-pow`

Counts

3 → 285

Calls

3 calls:

48.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
11.0ms	(/ x (tan B))
14.0ms	(/ 1 (sin B))

series302.0ms

Counts

3 → 9

Calls

3 calls:

134.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
135.0ms	(/ x (tan B))
33.0ms	(/ 1 (sin B))

simplify976.0ms

Counts

294 → 294

Iterations

Iter	Nodes
done	2000
2	2000
1	848
0	381

prune3.2s

Pruning

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

rewrite72.0ms

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` `insert-posit16` `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 → 208

Calls

4 calls:

38.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
11.0ms	(* x (cos B))
5.0ms	(/ 1 (sin B))
14.0ms	(/ (* x (cos B)) (sin B))

series362.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
55.0ms	(* x (cos B))
25.0ms	(/ 1 (sin B))
125.0ms	(/ (* x (cos B)) (sin B))

simplify1.3s

Counts

220 → 220

Iterations

Iter	Nodes
done	2000
3	2000
2	1634
1	613
0	269

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`pow1`
3×	`associate-/r` `associate-r` `associate-l` `associate-/l`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `flip--` `unswap-sqr`

Counts

2 → 54

Calls

2 calls:

8.0ms	(* x (cos B))
13.0ms	(/ (- 1 (* x (cos B))) (sin B))

series153.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(* x (cos B))
100.0ms	(/ (- 1 (* x (cos B))) (sin B))

simplify985.0ms

Counts

60 → 60

Iterations

Iter	Nodes
done	2002
3	2002
2	656
1	218
0	100

prune663.0ms

Pruning

7 alts after pruning (6 fresh and 1 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))))
0.2b	(/ (cos B) (sin B))
0.2b	(/ 1 (sin B))
0.2b	(* x (/ (cos B) (sin B)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
46×	`times-frac`
42×	`*-un-lft-identity` `add-cube-cbrt`
15×	`add-exp-log`
13×	`add-cbrt-cube` `fma-neg` `associate-r` `prod-diff`
7×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-l` `associate-*r/`
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 → 142

Calls

4 calls:

39.0ms	(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
19.0ms	(/ (cos B) (sin B))
11.0ms	(/ 1 (sin B))
18.0ms	(* x (/ (cos B) (sin B)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
35.0ms	(/ (cos B) (sin B))
14.0ms	(/ 1 (sin B))
128.0ms	(* x (/ (cos B) (sin B)))

simplify1.6s

Counts

154 → 154

Iterations

Iter	Nodes
done	2000
3	2000
2	1521
1	436
0	192

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes109.0ms

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	11
1	11
0	8

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.6s	1783×	body	1280	valid
1.8s	1431×	body	640	valid
1.6s	4927×	body	80	valid
1.1s	702×	body	320	valid
172.0ms	332×	body	160	valid