Details

sample172.0ms

Algorithm

intervals

Results

65.0ms	55×	body	1280	valid
48.0ms	180×	body	80	valid
33.0ms	43×	body	640	valid
11.0ms	19×	body	320	valid
4.0ms	9×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
29	4790
28	4572
27	4388
26	4180
25	3967
24	3753
23	3564
22	3407
21	3205
20	3006
19	2833
18	2631
17	2458
16	2289
15	2130
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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

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))

rewrite49.0ms

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:

25.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
7.0ms	(/ 1 (sin B))
5.0ms	(/ x (tan B))

series274.0ms

Counts

3 → 9

Calls

3 calls:

126.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
16.0ms	(/ 1 (sin B))
131.0ms	(/ x (tan B))

simplify1.4s

Counts

294 → 294

Iterations

Iter	Nodes
done	5001
2	1990
1	848
0	381

prune800.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

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))

rewrite65.0ms

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-l` `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-r` `associate-*l/`
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:

28.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
12.0ms	(/ 1 (sin B))
8.0ms	(/ x (sin B))
15.0ms	(* (/ x (sin B)) (cos B))

series353.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
22.0ms	(/ 1 (sin B))
79.0ms	(/ x (sin B))
126.0ms	(* (/ x (sin B)) (cos B))

simplify1.5s

Counts

154 → 154

Iterations

Iter	Nodes
done	5008
2	1482
1	433
0	190

prune717.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 75

Calls

3 calls:

5.0ms	(- 1 (* x (cos B)))
9.0ms	(* x (cos B))
16.0ms	(/ (- 1 (* x (cos B))) (sin B))

series189.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(- 1 (* x (cos B)))
49.0ms	(* x (cos B))
92.0ms	(/ (- 1 (* x (cos B))) (sin B))

simplify2.2s

Counts

84 → 84

Iterations

Iter	Nodes
done	5005
3	3066
2	804
1	276
0	123

prune311.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin B)) (cbrt (sin B)))
0.6b	(cbrt (sin B))
0.6b	(cbrt (sin B))
0.6b	(cbrt (sin B))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 85

Calls

4 calls:

31.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
3.0ms	(cbrt (sin B))
3.0ms	(cbrt (sin B))
3.0ms	(cbrt (sin B))

series600.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
143.0ms	(cbrt (sin B))
115.0ms	(cbrt (sin B))
141.0ms	(cbrt (sin B))

simplify2.4s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
3	1352
2	474
1	182
0	81

prune506.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes118.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample8.4s

Algorithm

intervals

Results

3.9s	1662×	body	1280	valid
1.7s	1353×	body	640	valid
1.6s	5090×	body	80	valid
670.0ms	715×	body	320	valid
231.0ms	376×	body	160	valid