Details

sample360.0ms

Algorithm

intervals

Results

107.0ms	47×	body	640	valid
70.0ms	56×	body	1280	valid
29.0ms	150×	body	80	valid
21.0ms	29×	body	320	valid
4.0ms	10×	body	160	valid

simplify3.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
35	4970
34	4828
33	4665
32	4493
31	4330
30	4139
29	3972
28	3794
27	3608
26	3434
25	3297
24	3150
23	2978
22	2834
21	2632
20	2448
19	2290
18	2119
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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite97.0ms

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:

76.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
7.0ms	(/ 1 (sin B))
9.0ms	(/ x (tan B))

series353.0ms

Counts

3 → 9

Calls

3 calls:

138.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
32.0ms	(/ 1 (sin B))
183.0ms	(/ x (tan B))

simplify1.8s

Counts

93 → 93

Iterations

Iter	Nodes
done	5049
3	2697
2	849
1	300
0	153

prune468.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

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:

27.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
8.0ms	(/ 1 (sin B))
11.0ms	(/ x (sin B))
30.0ms	(* (/ x (sin B)) (cos B))

series336.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
14.0ms	(/ 1 (sin B))
69.0ms	(/ x (sin B))
134.0ms	(* (/ x (sin B)) (cos B))

simplify1.4s

Counts

120 → 120

Iterations

Iter	Nodes
done	5001
2	1312
1	373
0	166

prune548.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 174

Calls

4 calls:

63.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
14.0ms	(/ 1 (sin B))
7.0ms	(/ (tan B) x)
10.0ms	(/ 1 (/ (tan B) x))

series375.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
24.0ms	(/ 1 (sin B))
79.0ms	(/ (tan B) x)
111.0ms	(/ 1 (/ (tan B) x))

simplify3.4s

Counts

186 → 186

Iterations

Iter	Nodes
done	5008
3	4478
2	1538
1	615
0	271

prune759.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
36×	`add-exp-log`
34×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `add-cube-cbrt`
22×	`add-cbrt-cube`
16×	`div-exp`
11×	`associate-/r*`
9×	`associate-/l*`
8×	`pow1` `cbrt-undiv`
7×	`div-inv`
5×	`prod-exp`
4×	`rec-exp` `1-exp` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `associate-l` `cbrt-unprod`
2×	`pow-flip` `inv-pow`
1×	`pow-prod-down` `associate-/r/` `*-commutative` `unswap-sqr`

Counts

4 → 130

Calls

4 calls:

7.0ms	(/ 1 (sin B))
9.0ms	(* x (cos B))
27.0ms	(/ (sin B) (* x (cos B)))
26.0ms	(/ 1 (/ (sin B) (* x (cos B))))

series247.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ 1 (sin B))
45.0ms	(* x (cos B))
82.0ms	(/ (sin B) (* x (cos B)))
106.0ms	(/ 1 (/ (sin B) (* x (cos B))))

simplify1.9s

Counts

142 → 142

Iterations

Iter	Nodes
done	5000
2	1370
1	412
0	187

prune565.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes124.0ms

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

sample6.5s

Algorithm

intervals

Results

2.8s	1737×	body	1280	valid
1.6s	4891×	body	80	valid
1.4s	1386×	body	640	valid
354.0ms	691×	body	320	valid
147.0ms	409×	body	160	valid