Details

sample398.0ms

Algorithm

intervals

Results

36.0ms	63×	body	1280	valid
25.0ms	18×	body	320	valid
14.0ms	166×	body	80	valid
13.0ms	39×	body	640	valid
2.0ms	11×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	18	7
1	31	6
2	39	6
3	50	6
4	53	6
5	53	6
done	53	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

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)))

rewrite65.0ms

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:

29.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
5.0ms	(/ 1.0 (tan B))
6.0ms	(/ 1.0 (sin B))
20.0ms	(* x (/ 1.0 (tan B)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
39.0ms	(/ 1.0 (tan B))
20.0ms	(/ 1.0 (sin B))
127.0ms	(* x (/ 1.0 (tan B)))

simplify44.0ms

Counts

113 → 113

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	386	627
1	1479	584
2	5001	584
done	5001	584

prune289.0ms

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))
0.2b	(/ (* x 1.0) (tan B))

rewrite49.0ms

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:

29.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
5.0ms	(/ 1.0 (sin B))
13.0ms	(/ (* x 1.0) (tan B))

series263.0ms

Counts

3 → 9

Calls

3 calls:

126.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
23.0ms	(/ 1.0 (sin B))
113.0ms	(/ (* x 1.0) (tan B))

simplify33.0ms

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	316	461
1	1175	428
2	5001	428
done	5001	428

prune182.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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))

rewrite59.0ms

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:

28.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
8.0ms	(* x (cos B))
6.0ms	(/ 1 (sin B))
14.0ms	(/ (* x (cos B)) (sin B))

series250.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
37.0ms	(* x (cos B))
17.0ms	(/ 1 (sin B))
98.0ms	(/ (* x (cos B)) (sin B))

simplify42.0ms

Counts

104 → 104

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	309	612
1	1342	540
2	5002	535
done	5002	535

prune214.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 48

Calls

2 calls:

8.0ms	(* x (cos B))
15.0ms	(/ (- 1 (* x (cos B))) (sin B))

series110.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(* x (cos B))
70.0ms	(/ (- 1 (* x (cos B))) (sin B))

simplify73.0ms

Counts

54 → 54

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	195	361
1	793	329
2	3167	329
3	5001	329
done	5001	329

prune117.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes58.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	6
1	14	6
done	14	6

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	1795×	body	1280	valid
527.0ms	1458×	body	640	valid
378.0ms	4839×	body	80	valid
167.0ms	698×	body	320	valid
67.0ms	358×	body	160	valid