Details

sample321.0ms

Algorithm

intervals

Results

59.0ms	134×	body	80	valid
53.0ms	62×	body	1280	valid
31.0ms	50×	body	640	valid
9.0ms	21×	body	320	valid
3.0ms	11×	body	160	valid

simplify67.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	53
5	53
4	50
3	39
2	31
1	18
0	10

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize67.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* (/ 1.0 (tan B)) x))
0.1b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (tan B))
0.2b	(* (/ 1.0 (tan B)) x)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
14×	`associate-l`
13×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-r` `div-inv`
2×	`clear-num` `frac-2neg` `associate-*l/` `prod-exp` `tan-quot` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--`

Counts

4 → 101

Calls

4 calls:

19.0ms	(- (/ 1.0 (sin B)) (* (/ 1.0 (tan B)) x))
4.0ms	(/ 1.0 (sin B))
4.0ms	(/ 1.0 (tan B))
27.0ms	(* (/ 1.0 (tan B)) x)

series393.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(- (/ 1.0 (sin B)) (* (/ 1.0 (tan B)) x))
32.0ms	(/ 1.0 (sin B))
42.0ms	(/ 1.0 (tan B))
111.0ms	(* (/ 1.0 (tan B)) x)

simplify1.4s

Counts

113 → 113

Iterations

Iter	Nodes
done	5001
2	1607
1	406
0	176

prune770.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* 1.0 (/ x (tan B))))
0.1b	(/ 1.0 (sin B))
0.2b	(/ x (tan B))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
7×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r` `associate-/l`
5×	`add-log-exp`
3×	`pow1` `div-inv`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`sub-neg` `flip3--` `diff-log` `tan-quot` `associate-*r/` `associate-/r/` `frac-sub` `flip--` `distribute-lft-out--`

Counts

3 → 69

Calls

3 calls:

21.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ x (tan B))))
4.0ms	(/ 1.0 (sin B))
4.0ms	(/ x (tan B))

series347.0ms

Counts

3 → 9

Calls

3 calls:

180.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ x (tan B))))
21.0ms	(/ 1.0 (sin B))
146.0ms	(/ x (tan B))

simplify980.0ms

Counts

78 → 78

Iterations

Iter	Nodes
done	5001
2	1005
1	317
0	149

prune423.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
0.1b	(/ 1.0 (sin B))
0.1b	(* x (cos B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

37.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
8.0ms	(/ 1.0 (sin B))
17.0ms	(* x (cos B))
19.0ms	(/ (* x (cos B)) (sin B))

series424.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
34.0ms	(/ 1.0 (sin B))
54.0ms	(* x (cos B))
158.0ms	(/ (* x (cos B)) (sin B))

simplify1.3s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	1464
1	355
0	150

prune553.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* 1.0 (/ 1 (/ (tan B) x))))
0.1b	(/ 1.0 (sin B))
0.2b	(/ (tan B) x)
0.3b	(/ 1 (/ (tan B) x))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

93×	`times-frac`
62×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
19×	`associate-/r*` `add-exp-log`
13×	`add-cbrt-cube`
9×	`div-exp` `associate-/l*`
8×	`div-inv`
6×	`add-log-exp`
5×	`pow1` `cbrt-undiv`
3×	`clear-num` `frac-2neg`
2×	`rec-exp` `1-exp` `frac-sub`
1×	`sub-neg` `flip3--` `diff-log` `tan-quot` `associate-*r/` `associate-/r/` `un-div-inv` `pow-flip` `flip--` `distribute-lft-out--` `inv-pow` `associate-/l/`

Counts

4 → 146

Calls

4 calls:

37.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ 1 (/ (tan B) x))))
9.0ms	(/ 1.0 (sin B))
16.0ms	(/ (tan B) x)
15.0ms	(/ 1 (/ (tan B) x))

series383.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ 1 (/ (tan B) x))))
24.0ms	(/ 1.0 (sin B))
60.0ms	(/ (tan B) x)
142.0ms	(/ 1 (/ (tan B) x))

simplify1.7s

Counts

158 → 158

Iterations

Iter	Nodes
done	5001
2	2693
1	618
0	258

prune760.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes150.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	12
1	12
0	10

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.5s	1746×	body	1280	valid
1.6s	1449×	body	640	valid
1.0s	4902×	body	80	valid
504.0ms	688×	body	320	valid
116.0ms	353×	body	160	valid