Details

sample124.0ms

Algorithm

intervals

Results

36.0ms	46×	body	1280	valid
29.0ms	18×	body	2560	valid
17.0ms	35×	body	640	valid
14.0ms	131×	body	80	valid
7.0ms	18×	body	320	valid
2.0ms	8×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.1b

localize24.0ms

Local error

Found 3 expressions with local error:

9.0b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
28.5b	(sin (/ x (* y 2.0)))
28.8b	(tan (/ x (* y 2.0)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

16.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
9.0ms	(sin (/ x (* y 2.0)))
7.0ms	(tan (/ x (* y 2.0)))

series120.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
12.0ms	(sin (/ x (* y 2.0)))
53.0ms	(tan (/ x (* y 2.0)))

simplify2.1s

Counts

58 → 58

Iterations

Useful iterations: 3 (171.0ms)

Iter	Nodes	Cost
0	83	878
1	147	865
2	330	789
3	814	785
4	2543	785
done	5001	785

prune368.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 26.3b

localize0.0ms

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

prune46.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 26.3b

localize23.0ms

Local error

Found 4 expressions with local error:

8.9b	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
28.5b	(sin (/ x (* y 2.0)))
28.5b	(sin (/ x (* y 2.0)))
29.0b	(cos (/ x (* y 2.0)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

64.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
10.0ms	(sin (/ x (* y 2.0)))
10.0ms	(sin (/ x (* y 2.0)))
11.0ms	(cos (/ x (* y 2.0)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
13.0ms	(sin (/ x (* y 2.0)))
20.0ms	(sin (/ x (* y 2.0)))
28.0ms	(cos (/ x (* y 2.0)))

simplify6.5s

Counts

63 → 63

Iterations

Useful iterations: 3 (602.0ms)

Iter	Nodes	Cost
0	77	989
1	152	777
2	416	604
3	1226	600
done	5000	600

prune316.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 26.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (/ 1 (cos (/ x (* y 2.0)))))
29.0b	(cos (/ x (* y 2.0)))
29.0b	(cos (/ x (* y 2.0)))
29.0b	(cos (/ x (* y 2.0)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

13×	`cbrt-prod`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 51

Calls

4 calls:

3.0ms	(cbrt (/ 1 (cos (/ x (* y 2.0)))))
5.0ms	(cos (/ x (* y 2.0)))
11.0ms	(cos (/ x (* y 2.0)))
12.0ms	(cos (/ x (* y 2.0)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(cbrt (/ 1 (cos (/ x (* y 2.0)))))
17.0ms	(cos (/ x (* y 2.0)))
27.0ms	(cos (/ x (* y 2.0)))
17.0ms	(cos (/ x (* y 2.0)))

simplify3.3s

Counts

63 → 63

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	73	749
1	108	714
2	163	660
3	287	657
4	526	657
5	770	657
6	893	657
7	1167	657
8	2324	657
done	5000	657

prune317.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 26.2b

regimes612.0ms

Accuracy

22.4% (1.9b remaining)

Error of 28.1b against oracle of 26.2b and baseline of 28.6b

bsearch2.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	60
1	23	60
done	23	60

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.3s	1418×	body	1280	valid
1.3s	679×	body	2560	valid
563.0ms	993×	body	640	valid
493.0ms	4088×	body	80	valid
215.0ms	539×	body	320	valid
83.0ms	283×	body	160	valid