Details

sample246.0ms

Algorithm

intervals

Results

125.0ms	61×	body	1280	valid
52.0ms	45×	body	640	valid
34.0ms	147×	body	80	valid
16.0ms	22×	body	320	valid
5.0ms	11×	body	160	valid

simplify389.0ms

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

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))

rewrite28.0ms

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` `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 → 81

Calls

3 calls:

17.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
5.0ms	(/ 1 (sin B))
5.0ms	(/ x (tan B))

series276.0ms

Counts

3 → 9

Calls

3 calls:

139.0ms	(- (/ 1 (sin B)) (/ x (tan B)))
17.0ms	(/ 1 (sin B))
119.0ms	(/ x (tan B))

simplify7.7s

Counts

90 → 90

Iterations

Iter	Nodes
4	3960
3	1760
2	744
1	291
0	150

prune820.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

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`
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 → 104

Calls

4 calls:

28.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
10.0ms	(/ 1 (sin B))
8.0ms	(/ x (sin B))
12.0ms	(* (/ x (sin B)) (cos B))

series373.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
24.0ms	(/ 1 (sin B))
91.0ms	(/ x (sin B))
134.0ms	(* (/ x (sin B)) (cos B))

simplify17.9s

Counts

116 → 116

Iterations

Iter	Nodes
3	4094
2	1168
1	361
0	162

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite24.0ms

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×	`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 → 48

Calls

2 calls:

17.0ms	(/ (- 1 (* x (cos B))) (sin B))
6.0ms	(* x (cos B))

series145.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(/ (- 1 (* x (cos B))) (sin B))
66.0ms	(* x (cos B))

simplify1.1s

Counts

54 → 54

Iterations

Iter	Nodes
3	2036
2	590
1	200
0	94

prune517.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

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)
0.3b	(/ 1 (/ (tan B) x))

rewrite56.0ms

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`
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 → 170

Calls

4 calls:

33.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
10.0ms	(/ 1 (sin B))
5.0ms	(/ (tan B) x)
6.0ms	(/ 1 (/ (tan B) x))

series314.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
20.0ms	(/ 1 (sin B))
49.0ms	(/ (tan B) x)
116.0ms	(/ 1 (/ (tan B) x))

simplify55.9s

Counts

182 → 182

Iterations

Iter	Nodes
3	5377
2	1696
1	606
0	267

prune1.8s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

regimes162.0ms

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
2	10
1	10
0	9

end0.0ms

sample8.9s

Algorithm

intervals

Results

3.3s	1761×	body	1280	valid
2.4s	1412×	body	640	valid
2.1s	4888×	body	80	valid
677.0ms	726×	body	320	valid
243.0ms	363×	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