Details

sample266.0ms

Algorithm

intervals

Results

68.0ms	154×	body	80	valid
56.0ms	55×	body	1280	valid
39.0ms	53×	body	640	valid
11.0ms	21×	body	320	valid
4.0ms	10×	body	160	valid

simplify88.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	31	11
3	39	11
4	50	11
5	52	11
done	52	11

prune41.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `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:

61.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
11.0ms	(/ 1.0 (sin B))
12.0ms	(/ 1.0 (tan B))
39.0ms	(* x (/ 1.0 (tan B)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
40.0ms	(/ 1.0 (sin B))
78.0ms	(/ 1.0 (tan B))
162.0ms	(* x (/ 1.0 (tan B)))

simplify2.5s

Counts

113 → 113

Iterations

Useful iterations: 2 (263.0ms)

Iter	Nodes	Cost
0	174	1141
1	383	1074
2	964	996
3	2656	996
done	5000	996

prune455.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt` `times-frac`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`add-log-exp`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `div-exp`
2×	`frac-2neg` `clear-num` `div-inv` `difference-of-squares`
1×	`tan-quot` `sub-neg` `flip3--` `diff-log` `prod-exp` `associate-/r/` `frac-sub` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

3 → 65

Calls

3 calls:

56.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
12.0ms	(/ 1.0 (sin B))
14.0ms	(/ (* x 1.0) (tan B))

series356.0ms

Counts

3 → 9

Calls

3 calls:

149.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
33.0ms	(/ 1.0 (sin B))
174.0ms	(/ (* x 1.0) (tan B))

simplify2.7s

Counts

74 → 74

Iterations

Useful iterations: 2 (212.0ms)

Iter	Nodes	Cost
0	143	847
1	316	799
2	870	739
3	3273	739
done	5001	739

prune301.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

32.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
14.0ms	(* x (cos B))
7.0ms	(/ 1 (sin B))
15.0ms	(/ (* x (cos B)) (sin B))

series377.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
59.0ms	(* x (cos B))
22.0ms	(/ 1 (sin B))
139.0ms	(/ (* x (cos B)) (sin B))

simplify3.9s

Counts

104 → 104

Iterations

Useful iterations: 3 (1.9s)

Iter	Nodes	Cost
0	145	1077
1	307	981
2	857	905
3	4209	887
done	5000	887

prune331.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
17×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
3×	`cbrt-undiv` `associate-r/` `div-exp` `associate-r` `pow-prod-down` `associate-l/`
2×	`frac-2neg` `clear-num` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `associate-l` `*-commutative` `frac-sub` `flip--` `sub-div`

Counts

4 → 89

Calls

4 calls:

38.0ms	(- (/ 1.0 (sin B)) (* (* 1.0 (/ x (sin B))) (cos B)))
9.0ms	(/ 1.0 (sin B))
13.0ms	(/ x (sin B))
61.0ms	(* (* 1.0 (/ x (sin B))) (cos B))

series458.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(- (/ 1.0 (sin B)) (* (* 1.0 (/ x (sin B))) (cos B)))
21.0ms	(/ 1.0 (sin B))
70.0ms	(/ x (sin B))
142.0ms	(* (* 1.0 (/ x (sin B))) (cos B))

simplify2.3s

Counts

101 → 101

Iterations

Useful iterations: 2 (372.0ms)

Iter	Nodes	Cost
0	168	1176
1	378	1109
2	1206	996
done	5000	996

prune411.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes130.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	12	14
done	12	14

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.7s	1706×	body	1280	valid
1.8s	4938×	body	80	valid
1.1s	1451×	body	640	valid
347.0ms	726×	body	320	valid
174.0ms	334×	body	160	valid