Details

sample138.0ms

Algorithm

intervals

Results

52.0ms	53×	body	1280	valid
33.0ms	20×	body	2560	valid
15.0ms	137×	body	80	valid
13.0ms	23×	body	640	valid
6.0ms	16×	body	320	valid
2.0ms	7×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	278
1	11	278
2	13	278
done	13	278

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize29.0ms

Local error

Found 3 expressions with local error:

8.2b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
26.5b	(sin (/ x (* y 2.0)))
27.0b	(tan (/ x (* y 2.0)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`tan-quot`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv` `associate-/l/`

Counts

3 → 49

Calls

3 calls:

43.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
7.0ms	(sin (/ x (* y 2.0)))
5.0ms	(tan (/ x (* y 2.0)))

series162.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
18.0ms	(sin (/ x (* y 2.0)))
71.0ms	(tan (/ x (* y 2.0)))

simplify1.6s

Counts

58 → 58

Iterations

Useful iterations: 2 (122.0ms)

Iter	Nodes	Cost
0	83	20158
1	152	18581
2	502	18181
3	3100	18181
done	5000	18181

prune420.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 24.9b

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune74.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 24.9b

localize29.0ms

Local error

Found 4 expressions with local error:

8.2b	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
26.5b	(sin (/ x (* y 2.0)))
26.5b	(sin (/ x (* y 2.0)))
26.9b	(cos (/ x (* y 2.0)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cbrt-cube` `add-exp-log`
6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-/l*`
2×	`cbrt-undiv` `div-exp`
1×	`clear-num` `associate-/r*` `frac-2neg` `prod-exp` `associate-/r/` `cbrt-unprod` `div-inv` `sin-cos-mult`

Counts

4 → 51

Calls

4 calls:

39.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
5.0ms	(sin (/ x (* y 2.0)))
6.0ms	(sin (/ x (* y 2.0)))
7.0ms	(cos (/ x (* y 2.0)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
17.0ms	(sin (/ x (* y 2.0)))
17.0ms	(sin (/ x (* y 2.0)))
21.0ms	(cos (/ x (* y 2.0)))

simplify2.9s

Counts

63 → 63

Iterations

Useful iterations: 3 (993.0ms)

Iter	Nodes	Cost
0	77	17463
1	152	14539
2	489	13779
3	3634	13697
done	5000	13697

prune398.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 24.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (cos (/ x (* y 2.0))))
0.6b	(log1p (expm1 (/ 1 (cos (/ x (* y 2.0))))))
0.7b	(expm1 (/ 1 (cos (/ x (* y 2.0)))))
26.9b	(cos (/ x (* y 2.0)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
8×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`pow1` `log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`div-exp`
1×	`cbrt-undiv` `rec-exp` `log1p-udef` `expm1-log1p` `clear-num` `frac-2neg` `1-exp` `log1p-expm1` `div-inv` `pow-flip` `inv-pow` `expm1-udef`

Counts

4 → 64

Calls

4 calls:

5.0ms	(/ 1 (cos (/ x (* y 2.0))))
0.0ms	(log1p (expm1 (/ 1 (cos (/ x (* y 2.0))))))
0.0ms	(expm1 (/ 1 (cos (/ x (* y 2.0)))))
4.0ms	(cos (/ x (* y 2.0)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ 1 (cos (/ x (* y 2.0))))
117.0ms	(log1p (expm1 (/ 1 (cos (/ x (* y 2.0))))))
79.0ms	(expm1 (/ 1 (cos (/ x (* y 2.0)))))
15.0ms	(cos (/ x (* y 2.0)))

simplify3.6s

Counts

76 → 76

Iterations

Useful iterations: 2 (129.0ms)

Iter	Nodes	Cost
0	91	23692
1	164	17746
2	570	17376
3	3175	17376
done	5001	17376

prune442.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 24.8b

regimes653.0ms

Accuracy

0% (2.4b remaining)

Error of 28.4b against oracle of 26.0b and baseline of 28.4b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	13	504
1	17	504
done	17	504

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.7s	1429×	body	1280	valid
1.5s	645×	body	2560	valid
750.0ms	971×	body	640	valid
701.0ms	4118×	body	80	valid
238.0ms	559×	body	320	valid
89.0ms	278×	body	160	valid