Details

sample83.0ms

Algorithm

intervals

Results

28.0ms	63×	body	1280	valid
15.0ms	157×	body	80	valid
15.0ms	51×	body	640	valid
4.0ms	17×	body	320	valid
2.0ms	13×	body	160	valid

simplify41.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	30	11
3	40	11
4	51	11
5	54	11
done	54	11

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.2b

Counts

2 → 1

localize12.0ms

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)))

rewrite31.0ms

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:

7.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
4.0ms	(/ 1.0 (sin B))
4.0ms	(/ 1.0 (tan B))
10.0ms	(* x (/ 1.0 (tan B)))

series93.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
5.0ms	(/ 1.0 (sin B))
12.0ms	(/ 1.0 (tan B))
44.0ms	(* x (/ 1.0 (tan B)))

simplify947.0ms

Counts

113 → 113

Iterations

Useful iterations: 3 (373.0ms)

Iter	Nodes	Cost
0	175	1141
1	396	1081
2	1110	1009
3	3752	1001
done	5001	1001

prune194.0ms

Filtered

92 candidates to 113 candidates (-22.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	105	8	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	8	114

Merged error: 0.0b

Counts

114 → 8

localize11.0ms

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
12×	`times-frac`
6×	`pow1` `associate-/r*` `add-log-exp`
4×	`associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `div-inv`
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 → 81

Calls

4 calls:

7.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
4.0ms	(/ 1.0 (sin B))
5.0ms	(* x (cos B))
6.0ms	(/ (* x (cos B)) (sin B))

series63.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
5.0ms	(/ 1.0 (sin B))
8.0ms	(* x (cos B))
23.0ms	(/ (* x (cos B)) (sin B))

simplify1.3s

Counts

93 → 93

Iterations

Useful iterations: 3 (375.0ms)

Iter	Nodes	Cost
0	150	1006
1	345	969
2	1041	868
3	4809	864
done	5000	864

prune135.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	92	9	101

Merged error: 0.0b

Counts

101 → 9

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

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:

6.0ms	(/ (- 1.0 (* 1.0 (* x (cos B)))) (sin B))
5.0ms	(* x (cos B))

series26.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(/ (- 1.0 (* 1.0 (* x (cos B)))) (sin B))
7.0ms	(* x (cos B))

simplify596.0ms

Counts

54 → 54

Iterations

Useful iterations: done (595.0ms)

Iter	Nodes	Cost
0	103	734
1	230	712
2	620	651
3	1940	647
done	5000	640

prune94.0ms

Filtered

40 candidates to 54 candidates (-35.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	54	9	63

Merged error: 0.0b

Counts

63 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (sin B))
0.2b	(* (* (/ 1.0 (sin B)) x) (cos B))
0.3b	(* (/ 1.0 (sin B)) x)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

4.0ms	(/ 1.0 (sin B))
4.0ms	(/ 1.0 (sin B))
8.0ms	(* (* (/ 1.0 (sin B)) x) (cos B))
8.0ms	(* (/ 1.0 (sin B)) x)

series44.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (sin B))
5.0ms	(/ 1.0 (sin B))
22.0ms	(* (* (/ 1.0 (sin B)) x) (cos B))
12.0ms	(* (/ 1.0 (sin B)) x)

simplify573.0ms

Counts

119 → 119

Iterations

Useful iterations: done (570.0ms)

Iter	Nodes	Cost
0	134	1122
1	321	1102
2	1213	973
done	5000	952

prune134.0ms

Filtered

89 candidates to 119 candidates (-33.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	119	9	128

Merged error: 0.0b

Counts

128 → 9

regimes126.0ms

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

sample2.3s

Algorithm

intervals

Results

762.0ms	1755×	body	1280	valid
602.0ms	4874×	body	80	valid
423.0ms	1441×	body	640	valid
152.0ms	721×	body	320	valid
58.0ms	367×	body	160	valid

Details

sample83.0ms

simplify41.0ms

prune11.0ms

localize12.0ms

rewrite31.0ms

series93.0ms

simplify947.0ms

prune194.0ms

localize11.0ms

rewrite24.0ms

series63.0ms

simplify1.3s

prune135.0ms

localize13.0ms

rewrite12.0ms

series26.0ms

simplify596.0ms

prune94.0ms

localize10.0ms

rewrite28.0ms

series44.0ms

simplify573.0ms

prune134.0ms

regimes126.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.3s

Profiling