Details

sample227.0ms

Algorithm

intervals

Results

92.0ms	63×	body	1280	valid
50.0ms	46×	body	640	valid
47.0ms	141×	body	80	valid
18.0ms	24×	body	320	valid
5.0ms	10×	body	160	valid

simplify444.0ms

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 1 (sin B)) (/ x (tan B)))
0.2b	(/ x (tan B))
0.2b	(/ 1 (sin B))

rewrite41.0ms

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:

27.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
5.0ms	(/ x (tan B))
6.0ms	(/ 1 (sin B))

series354.0ms

Counts

3 → 9

Calls

3 calls:

146.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
181.0ms	(/ x (tan B))
27.0ms	(/ 1 (sin B))

simplify13.9s

Counts

93 → 93

Iterations

Iter	Nodes
4	3737
3	1682
2	734
1	294
0	153

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 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	(/ (tan B) x)
0.2b	(/ 1 (sin B))
0.3b	(/ 1 (/ (tan B) x))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

127×	`times-frac`
111×	`add-sqr-sqrt`
85×	`*-un-lft-identity`
64×	`add-cube-cbrt`
21×	`add-exp-log`
19×	`associate-/r*`
15×	`difference-of-squares`
13×	`add-cbrt-cube`
11×	`div-inv`
10×	`div-exp`
9×	`associate-/l*`
7×	`distribute-lft-out--`
6×	`pow1` `add-log-exp`
5×	`cbrt-undiv`
4×	`insert-posit16`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
2×	`pow-flip` `inv-pow`
1×	`sub-neg` `flip3--` `diff-log` `tan-quot` `associate-/r/` `frac-sub` `flip--` `associate-/l/`

Counts

4 → 174

Calls

4 calls:

23.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
6.0ms	(/ (tan B) x)
6.0ms	(/ 1 (sin B))
14.0ms	(/ 1 (/ (tan B) x))

series387.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
72.0ms	(/ (tan B) x)
26.0ms	(/ 1 (sin B))
122.0ms	(/ 1 (/ (tan B) x))

simplify1.3m

Counts

186 → 186

Iterations

Iter	Nodes
3	5589
2	1666
1	610
0	271

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite86.0ms

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)))
10.0ms	(/ x (sin B))
11.0ms	(/ 1 (sin B))
31.0ms	(* (/ x (sin B)) (cos B))

series394.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
78.0ms	(/ x (sin B))
26.0ms	(/ 1 (sin B))
154.0ms	(* (/ x (sin B)) (cos B))

simplify18.6s

Counts

120 → 120

Iterations

Iter	Nodes
3	4196
2	1189
1	365
0	166

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 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:

16.0ms	(* x (cos B))
26.0ms	(/ (- 1 (* x (cos B))) (sin B))

series167.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(* x (cos B))
108.0ms	(/ (- 1 (* x (cos B))) (sin B))

simplify3.1m

Counts

56 → 56

Iterations

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

prune333.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes77.0ms

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	10
1	10
0	9

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.0s	1699×	body	1280	valid
1.5s	1465×	body	640	valid
1.4s	4990×	body	80	valid
369.0ms	681×	body	320	valid
157.0ms	344×	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