Details

sample348.0ms

Algorithm

intervals

Results

112.0ms	58×	body	1280	valid
41.0ms	172×	body	80	valid
38.0ms	41×	body	640	valid
19.0ms	27×	body	320	valid
7.0ms	8×	body	160	valid

simplify361.0ms

Counts

1 → 1

Iterations

Iter	Nodes
19	264
18	264
17	260
16	251
15	247
14	243
13	240
12	236
11	224
10	211
9	198
8	188
7	178
6	149
5	98
4	65
3	36
2	30
1	18
0	10

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

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))

rewrite80.0ms

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:

41.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
11.0ms	(/ 1 (sin B))
24.0ms	(/ x (tan B))

series387.0ms

Counts

3 → 9

Calls

3 calls:

175.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
29.0ms	(/ 1 (sin B))
183.0ms	(/ x (tan B))

simplify15.1s

Counts

93 → 93

Iterations

Iter	Nodes
4	4201
3	1747
2	741
1	294
0	153

prune960.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`times-frac` `add-exp-log`
13×	`add-cbrt-cube`
7×	`pow1` `div-inv`
6×	`associate-/r*` `add-log-exp`
4×	`div-exp` `insert-posit16` `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 → 96

Calls

4 calls:

40.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
10.0ms	(/ 1 (sin B))
14.0ms	(* x (cos B))
21.0ms	(/ (* x (cos B)) (sin B))

series349.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
16.0ms	(/ 1 (sin B))
43.0ms	(* x (cos B))
167.0ms	(/ (* x (cos B)) (sin B))

simplify7.1s

Counts

108 → 108

Iterations

Iter	Nodes
3	4490
2	1032
1	322
0	150

prune992.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`pow1`
3×	`associate-/r` `associate-r` `associate-l` `associate-/l`
2×	`insert-posit16` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `flip--` `unswap-sqr`

Counts

2 → 50

Calls

2 calls:

14.0ms	(* x (cos B))
24.0ms	(/ (- 1 (* x (cos B))) (sin B))

series156.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(* x (cos B))
90.0ms	(/ (- 1 (* x (cos B))) (sin B))

simplify3.2m

Counts

56 → 56

Iterations

Iter	Nodes
4	8611
3	1973
2	603
1	204
0	96

prune488.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 3 expressions with local error:

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
59×	`add-sqr-sqrt`
57×	`*-un-lft-identity` `add-cube-cbrt`
18×	`associate-/r*` `add-exp-log`
12×	`add-cbrt-cube`
11×	`associate-/r/`
8×	`div-exp`
6×	`pow1` `div-inv` `associate-/l*`
5×	`flip3--` `flip--`
4×	`cbrt-undiv`
3×	`associate-r` `associate-l` `insert-posit16` `add-log-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `pow-flip` `inv-pow` `unswap-sqr`

Counts

3 → 134

Calls

3 calls:

23.0ms	(/ (sin B) (- 1 (* x (cos B))))
15.0ms	(* x (cos B))
24.0ms	(/ 1 (/ (sin B) (- 1 (* x (cos B)))))

series223.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(/ (sin B) (- 1 (* x (cos B))))
62.0ms	(* x (cos B))
91.0ms	(/ 1 (/ (sin B) (- 1 (* x (cos B)))))

simplify11.5s

Counts

143 → 143

Iterations

Iter	Nodes
3	4314
2	1257
1	542
0	228

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes136.0ms

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
2	9
1	9
0	8

end0.0ms

sample8.8s

Algorithm

intervals

Results

3.9s	1709×	body	1280	valid
2.3s	1441×	body	640	valid
1.4s	4952×	body	80	valid
706.0ms	703×	body	320	valid
215.0ms	345×	body	160	valid

Iter	Nodes
19	264
18	264
17	260
16	251
15	247
14	243
13	240
12	236
11	224
10	211
9	198
8	188
7	178
6	149
5	98
4	65
3	36
2	30
1	18
0	10

Iter	Nodes
19	264
18	264
17	260
16	251
15	247
14	243
13	240
12	236
11	224
10	211
9	198
8	188
7	178
6	149
5	98
4	65
3	36
2	30
1	18
0	10

Iter	Nodes
19	264
18	264
17	260
16	251
15	247
14	243
13	240
12	236
11	224
10	211
9	198
8	188
7	178
6	149
5	98
4	65
3	36
2	30
1	18
0	10