Details

sample149.0ms

Algorithm

intervals

Results

63.0ms	65×	body	1280	valid
38.0ms	171×	body	80	valid
22.0ms	33×	body	640	valid
8.0ms	17×	body	320	valid
3.0ms	9×	body	160	valid

simplify2.7s

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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

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))

rewrite38.0ms

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:

21.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
5.0ms	(/ 1 (sin B))
10.0ms	(/ x (tan B))

series315.0ms

Counts

3 → 9

Calls

3 calls:

155.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
25.0ms	(/ 1 (sin B))
134.0ms	(/ x (tan B))

simplify1.6s

Counts

93 → 93

Iterations

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

prune446.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

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:

33.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
5.0ms	(/ x (sin B))
6.0ms	(/ 1 (sin B))
23.0ms	(* (/ x (sin B)) (cos B))

series365.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
93.0ms	(/ x (sin B))
14.0ms	(/ 1 (sin B))
137.0ms	(* (/ x (sin B)) (cos B))

simplify2.4s

Counts

120 → 120

Iterations

Iter	Nodes
done	5001
3	4603
2	1301
1	373
0	166

prune627.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `add-log-exp`
3×	`associate-/r` `associate-r` `associate-l` `insert-posit16` `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 → 63

Calls

3 calls:

14.0ms	(- 1 (* x (cos B)))
23.0ms	(/ (- 1 (* x (cos B))) (sin B))
13.0ms	(* x (cos B))

series221.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(- 1 (* x (cos B)))
104.0ms	(/ (- 1 (* x (cos B))) (sin B))
47.0ms	(* x (cos B))

simplify2.4s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
3	3388
2	718
1	248
0	107

prune402.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
21×	`cbrt-prod`
18×	`times-frac`
8×	`cbrt-div`
6×	`add-exp-log` `associate-/l*`
5×	`add-cbrt-cube`
4×	`pow1` `flip3--` `insert-posit16` `flip--` `add-log-exp`
3×	`associate-/r*` `pow1/3`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 84

Calls

4 calls:

3.0ms	(cbrt (- 1 (* x (cos B))))
2.0ms	(cbrt (- 1 (* x (cos B))))
2.0ms	(cbrt (- 1 (* x (cos B))))
10.0ms	(/ (cbrt (- 1 (* x (cos B)))) (sin B))

series405.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(cbrt (- 1 (* x (cos B))))
85.0ms	(cbrt (- 1 (* x (cos B))))
92.0ms	(cbrt (- 1 (* x (cos B))))
157.0ms	(/ (cbrt (- 1 (* x (cos B)))) (sin B))

simplify2.9s

Counts

96 → 96

Iterations

Iter	Nodes
done	5017
3	3833
2	933
1	327
0	151

prune536.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes157.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.6s	1706×	body	1280	valid
1.4s	4957×	body	80	valid
1.1s	1398×	body	640	valid
586.0ms	389×	body	160	valid
536.0ms	738×	body	320	valid