Details

sample126.0ms

Algorithm

intervals

Results

42.0ms	50×	body	1280	valid
35.0ms	39×	body	640	valid
21.0ms	173×	body	80	valid
11.0ms	26×	body	320	valid
3.0ms	10×	body	160	valid

simplify90.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	10	358
1	18	358
2	33	318
3	43	318
4	54	318
5	60	318
6	62	318
done	62	318

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

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)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
46×	`times-frac`
42×	`*-un-lft-identity` `add-cube-cbrt`
14×	`associate-r`
13×	`add-cbrt-cube` `fma-neg` `prod-diff` `add-exp-log`
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×	`clear-num` `frac-2neg` `prod-exp` `tan-quot` `associate-*r/` `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:

42.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
7.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))
23.0ms	(* x (/ 1.0 (tan B)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
24.0ms	(/ 1.0 (sin B))
38.0ms	(/ 1.0 (tan B))
176.0ms	(* x (/ 1.0 (tan B)))

simplify1.5s

Counts

147 → 147

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	200	45976
1	480	43936
2	1727	42631
done	5001	42414

prune871.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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))
0.2b	(/ (* x (cos B)) (sin B))
0.2b	(* x (cos B))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`add-cbrt-cube` `fma-neg` `prod-diff` `add-exp-log`
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×	`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 → 115

Calls

4 calls:

28.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
8.0ms	(/ 1.0 (sin B))
10.0ms	(/ (* x (cos B)) (sin B))
8.0ms	(* x (cos B))

series369.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
24.0ms	(/ 1.0 (sin B))
142.0ms	(/ (* x (cos B)) (sin B))
48.0ms	(* x (cos B))

simplify1.6s

Counts

127 → 127

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	175	40753
1	421	39193
2	1736	38171
done	5001	37824

prune861.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 2 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

20.0ms	(/ (- 1.0 (* 1.0 (* x (cos B)))) (sin B))
13.0ms	(* x (cos B))

series176.0ms

Counts

2 → 6

Calls

2 calls:

121.0ms	(/ (- 1.0 (* 1.0 (* x (cos B)))) (sin B))
54.0ms	(* x (cos B))

simplify1.3s

Counts

58 → 58

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	107	18422
1	246	17868
2	957	17560
done	5000	17535

prune322.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (sin B))
0.1b	(* (* x (/ 1.0 (sin B))) (cos B))
0.3b	(* x (/ 1.0 (sin B)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`*-un-lft-identity` `add-cube-cbrt`
28×	`times-frac`
22×	`add-cbrt-cube` `add-exp-log`
16×	`associate-r`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r` `associate-/l`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`clear-num` `frac-2neg` `associate-r/` `-commutative` `unswap-sqr`
1×	`associate-*l/`

Counts

4 → 115

Calls

4 calls:

4.0ms	(/ 1.0 (sin B))
4.0ms	(/ 1.0 (sin B))
30.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
26.0ms	(* x (/ 1.0 (sin B)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 1.0 (sin B))
23.0ms	(/ 1.0 (sin B))
160.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
69.0ms	(* x (/ 1.0 (sin B)))

simplify2.0s

Counts

127 → 127

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	140	30577
1	347	28729
2	1641	28165
done	5001	28005

prune640.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes169.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	283
1	11	283
done	11	283

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.3s	1734×	body	1280	valid
1.7s	4856×	body	80	valid
1.1s	1499×	body	640	valid
302.0ms	681×	body	320	valid
158.0ms	379×	body	160	valid