Details

sample326.0ms

Algorithm

intervals

Results

30.0ms	54×	body	1280	valid
15.0ms	44×	body	640	valid
13.0ms	151×	body	80	valid
7.0ms	29×	body	320	valid
2.0ms	15×	body	160	valid

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	32	11
3	44	11
4	55	11
5	60	11
6	62	11
done	62	11

prune8.0ms

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 (sin B))
0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
46×	`times-frac`
42×	`add-cube-cbrt` `*-un-lft-identity`
14×	`associate-r`
13×	`add-exp-log` `fma-neg` `prod-diff` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-l`
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 → 135

Calls

4 calls:

14.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
2.0ms	(/ 1.0 (sin B))
2.0ms	(/ 1.0 (tan B))
10.0ms	(* x (/ 1.0 (tan B)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
18.0ms	(/ 1.0 (sin B))
35.0ms	(/ 1.0 (tan B))
129.0ms	(* x (/ 1.0 (tan B)))

simplify1.6s

Counts

147 → 147

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	199	1713
1	447	1635
2	1134	1489
3	3479	1451
done	5000	1438

prune401.0ms

Pruning

7 alts after pruning (7 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))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

133×	`times-frac`
107×	`add-sqr-sqrt`
104×	`*-un-lft-identity` `prod-diff`
102×	`add-cube-cbrt`
24×	`div-inv`
14×	`tan-quot` `associate-/r/`
13×	`fma-neg`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`add-log-exp`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
2×	`frac-2neg` `clear-num` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `prod-exp` `frac-sub` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

3 → 188

Calls

3 calls:

21.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
2.0ms	(/ 1.0 (sin B))
4.0ms	(/ (* x 1.0) (tan B))

series250.0ms

Counts

3 → 9

Calls

3 calls:

119.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
21.0ms	(/ 1.0 (sin B))
110.0ms	(/ (* x 1.0) (tan B))

simplify1.1s

Counts

197 → 197

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	284	6281
1	609	5115
2	1675	4181
done	5001	4149

prune415.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`add-exp-log` `fma-neg` `prod-diff` `add-cbrt-cube`
6×	`pow1` `associate-/r*` `add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`frac-2neg` `associate-*r/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `distribute-lft-out--` `sub-div` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

14.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
2.0ms	(/ 1.0 (sin B))
3.0ms	(* x (cos B))
4.0ms	(/ (* x (cos B)) (sin B))

series269.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
19.0ms	(/ 1.0 (sin B))
39.0ms	(* x (cos B))
96.0ms	(/ (* x (cos B)) (sin B))

simplify2.2s

Counts

127 → 127

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	174	1742
1	389	1688
2	1113	1482
3	4978	1443
done	5000	1443

prune329.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 52

Calls

2 calls:

3.0ms	(* x (cos B))
7.0ms	(/ (- 1.0 (* 1.0 (* x (cos B)))) (sin B))

series117.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(* x (cos B))
80.0ms	(/ (- 1.0 (* 1.0 (* x (cos B)))) (sin B))

simplify1.1s

Counts

58 → 58

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	107	768
1	236	743
2	621	673
3	1991	673
done	5001	672

prune132.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes63.0ms

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	9	11
1	11	11
done	11	11

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	1749×	body	1280	valid
517.0ms	1427×	body	640	valid
380.0ms	4866×	body	80	valid
170.0ms	718×	body	320	valid
61.0ms	364×	body	160	valid