Details

sample245.0ms

Algorithm

intervals

Results

56.0ms	53×	body	1280	valid
52.0ms	24×	body	320	valid
22.0ms	157×	body	80	valid
21.0ms	39×	body	640	valid
3.0ms	10×	body	160	valid

simplify54.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

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

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

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:

33.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
8.0ms	(/ 1.0 (tan B))
6.0ms	(/ 1.0 (sin B))
28.0ms	(* x (/ 1.0 (tan B)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
51.0ms	(/ 1.0 (tan B))
28.0ms	(/ 1.0 (sin B))
167.0ms	(* x (/ 1.0 (tan B)))

simplify2.3s

Counts

113 → 113

Iterations

Useful iterations: 2 (239.0ms)

Iter	Nodes	Cost
0	174	1141
1	383	1074
2	966	996
3	2660	996
done	5000	996

prune477.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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))
0.1b	(/ (* x 1.0) (tan B))

rewrite85.0ms

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:

63.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
9.0ms	(/ 1.0 (sin B))
11.0ms	(/ (* x 1.0) (tan B))

series391.0ms

Counts

3 → 9

Calls

3 calls:

210.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
31.0ms	(/ 1.0 (sin B))
150.0ms	(/ (* x 1.0) (tan B))

simplify2.4s

Counts

74 → 74

Iterations

Useful iterations: 2 (176.0ms)

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

prune317.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

61.0ms	(- (/ 1.0 (sin B)) (* (/ (* x 1.0) (sin B)) (cos B)))
12.0ms	(/ 1.0 (sin B))
12.0ms	(/ (* x 1.0) (sin B))
43.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

series507.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(- (/ 1.0 (sin B)) (* (/ (* x 1.0) (sin B)) (cos B)))
22.0ms	(/ 1.0 (sin B))
102.0ms	(/ (* x 1.0) (sin B))
165.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

simplify1.5s

Counts

101 → 101

Iterations

Useful iterations: 2 (324.0ms)

Iter	Nodes	Cost
0	160	1221
1	390	1156
2	1338	1021
done	5001	1021

prune412.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 48

Calls

2 calls:

30.0ms	(* (* x 1.0) (cos B))
16.0ms	(/ (- 1.0 (* (* x 1.0) (cos B))) (sin B))

series217.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(* (* x 1.0) (cos B))
139.0ms	(/ (- 1.0 (* (* x 1.0) (cos B))) (sin B))

simplify2.6s

Counts

54 → 54

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	110	789
1	257	764
2	889	676
3	3263	674
done	5000	674

prune192.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes125.0ms

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	9	11
1	11	11
done	11	11

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.6s	1741×	body	1280	valid
1.4s	4950×	body	80	valid
1.1s	1384×	body	640	valid
368.0ms	713×	body	320	valid
177.0ms	351×	body	160	valid