Details

sample400.0ms

Algorithm

intervals

Results

96.0ms	56×	body	1280	valid
33.0ms	47×	body	640	valid
30.0ms	150×	body	80	valid
15.0ms	29×	body	320	valid
4.0ms	10×	body	160	valid

simplify3.2s

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

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))

rewrite147.0ms

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:

95.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
12.0ms	(/ 1 (sin B))
13.0ms	(/ x (tan B))

series338.0ms

Counts

3 → 9

Calls

3 calls:

131.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
15.0ms	(/ 1 (sin B))
191.0ms	(/ x (tan B))

simplify1.8s

Counts

294 → 294

Iterations

Iter	Nodes
done	5001
2	1990
1	848
0	381

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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))

rewrite111.0ms

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:

37.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
13.0ms	(/ 1 (sin B))
12.0ms	(/ x (sin B))
46.0ms	(* (/ x (sin B)) (cos B))

series376.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
22.0ms	(/ 1 (sin B))
92.0ms	(/ x (sin B))
141.0ms	(* (/ x (sin B)) (cos B))

simplify1.6s

Counts

154 → 154

Iterations

Iter	Nodes
done	5008
2	1482
1	433
0	190

prune838.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

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))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

1390×	`times-frac`
881×	`add-sqr-sqrt`
855×	`*-un-lft-identity`
834×	`add-cube-cbrt`
572×	`prod-diff`
108×	`div-inv`
21×	`add-exp-log`
19×	`associate-/r*`
15×	`difference-of-squares`
14×	`associate-/r/`
13×	`add-cbrt-cube` `fma-neg`
10×	`div-exp`
9×	`associate-/l*`
7×	`distribute-lft-out--`
6×	`pow1` `add-log-exp`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
2×	`pow-flip` `inv-pow`
1×	`sub-neg` `flip3--` `diff-log` `tan-quot` `frac-sub` `flip--` `associate-/l/`

Counts

4 → 767

Calls

4 calls:

104.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
6.0ms	(/ 1 (sin B))
6.0ms	(/ (tan B) x)
14.0ms	(/ 1 (/ (tan B) x))

series361.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
27.0ms	(/ 1 (sin B))
82.0ms	(/ (tan B) x)
105.0ms	(/ 1 (/ (tan B) x))

simplify2.4s

Counts

779 → 779

Iterations

Iter	Nodes
done	5000
2	4208
1	2254
0	961

prune3.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ x (tan B))) (cbrt (/ x (tan B))))
0.6b	(cbrt (/ x (tan B)))
0.6b	(cbrt (/ x (tan B)))
0.6b	(cbrt (/ x (tan B)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

110×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`*-un-lft-identity` `add-cube-cbrt`
17×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `tan-quot` `associate-/r/` `div-inv`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `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 → 162

Calls

4 calls:

61.0ms	(* (cbrt (/ x (tan B))) (cbrt (/ x (tan B))))
3.0ms	(cbrt (/ x (tan B)))
3.0ms	(cbrt (/ x (tan B)))
3.0ms	(cbrt (/ x (tan B)))

series1.5s

Counts

4 → 12

Calls

4 calls:

297.0ms	(* (cbrt (/ x (tan B))) (cbrt (/ x (tan B))))
282.0ms	(cbrt (/ x (tan B)))
261.0ms	(cbrt (/ x (tan B)))
631.0ms	(cbrt (/ x (tan B)))

simplify1.8s

Counts

174 → 174

Iterations

Iter	Nodes
done	5001
3	1937
2	795
1	350
0	191

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes132.0ms

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

sample6.6s

Algorithm

intervals

Results

3.4s	1737×	body	1280	valid
1.3s	1386×	body	640	valid
964.0ms	4891×	body	80	valid
420.0ms	691×	body	320	valid
251.0ms	409×	body	160	valid