Details

sample346.0ms

Algorithm

intervals

Results

132.0ms	53×	body	1280	valid
69.0ms	55×	body	640	valid
40.0ms	153×	body	80	valid
16.0ms	19×	body	320	valid
6.0ms	10×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
32	435
31	435
30	432
29	414
28	400
27	390
26	385
25	377
24	363
23	351
22	342
21	337
20	328
19	314
18	304
17	297
16	278
15	265
14	256
13	250
12	241
11	234
10	224
9	203
8	191
7	179
6	159
5	97
4	71
3	42
2	34
1	20
0	10

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

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))

rewrite60.0ms

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:

27.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
5.0ms	(/ x (tan B))
7.0ms	(/ 1 (sin B))

series377.0ms

Counts

3 → 9

Calls

3 calls:

179.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
173.0ms	(/ x (tan B))
25.0ms	(/ 1 (sin B))

simplify2.3s

Counts

294 → 294

Iterations

Iter	Nodes
3	4697
2	1876
1	835
0	381

prune3.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

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))

rewrite77.0ms

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:

25.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
7.0ms	(* x (cos B))
10.0ms	(/ 1 (sin B))
28.0ms	(/ (* x (cos B)) (sin B))

series832.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
67.0ms	(* x (cos B))
31.0ms	(/ 1 (sin B))
586.0ms	(/ (* x (cos B)) (sin B))

simplify3.5s

Counts

220 → 220

Iterations

Iter	Nodes
3	6615
2	1586
1	606
0	269

prune2.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

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)))

rewrite65.0ms

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:

45.0ms	(* (cbrt (/ x (tan B))) (cbrt (/ x (tan B))))
5.0ms	(cbrt (/ x (tan B)))
5.0ms	(cbrt (/ x (tan B)))
5.0ms	(cbrt (/ x (tan B)))

series1.1s

Counts

4 → 12

Calls

4 calls:

316.0ms	(* (cbrt (/ x (tan B))) (cbrt (/ x (tan B))))
269.0ms	(cbrt (/ x (tan B)))
259.0ms	(cbrt (/ x (tan B)))
258.0ms	(cbrt (/ x (tan B)))

simplify2.6s

Counts

174 → 174

Iterations

Iter	Nodes
4	4952
3	1736
2	753
1	339
0	191

prune2.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize88.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
29×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`times-frac` `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` `cbrt-div` `pow-plus` `prod-exp` `tan-quot` `associate-/r/` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 97

Calls

4 calls:

15.0ms	(* (cbrt x) (cbrt x))
12.0ms	(cbrt (/ x (tan B)))
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.1s

Counts

4 → 12

Calls

4 calls:

304.0ms	(* (cbrt x) (cbrt x))
274.0ms	(cbrt (/ x (tan B)))
266.0ms	(cbrt x)
301.0ms	(cbrt x)

simplify3.9s

Counts

109 → 109

Iterations

Iter	Nodes
4	8334
3	1720
2	581
1	272
0	148

prune1.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes134.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	20
1	20
0	16

end0.0ms

sample8.8s

Algorithm

intervals

Results

3.5s	1746×	body	1280	valid
2.2s	1360×	body	640	valid
1.4s	4906×	body	80	valid
814.0ms	759×	body	320	valid
640.0ms	380×	body	160	valid

Iter	Nodes
32	435
31	435
30	432
29	414
28	400
27	390
26	385
25	377
24	363
23	351
22	342
21	337
20	328
19	314
18	304
17	297
16	278
15	265
14	256
13	250
12	241
11	234
10	224
9	203
8	191
7	179
6	159
5	97
4	71
3	42
2	34
1	20
0	10

Iter	Nodes
32	435
31	435
30	432
29	414
28	400
27	390
26	385
25	377
24	363
23	351
22	342
21	337
20	328
19	314
18	304
17	297
16	278
15	265
14	256
13	250
12	241
11	234
10	224
9	203
8	191
7	179
6	159
5	97
4	71
3	42
2	34
1	20
0	10

Iter	Nodes
32	435
31	435
30	432
29	414
28	400
27	390
26	385
25	377
24	363
23	351
22	342
21	337
20	328
19	314
18	304
17	297
16	278
15	265
14	256
13	250
12	241
11	234
10	224
9	203
8	191
7	179
6	159
5	97
4	71
3	42
2	34
1	20
0	10