Details

sample96.0ms

Algorithm

intervals

Results

31.0ms	24×	body	2560	valid
25.0ms	42×	body	1280	valid
13.0ms	34×	body	640	valid
10.0ms	127×	body	80	valid
4.0ms	16×	body	320	valid
2.0ms	13×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 37.0b

localize17.0ms

Local error

Found 3 expressions with local error:

7.2b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
28.6b	(sin (/ x (* y 2.0)))
29.9b	(tan (/ x (* y 2.0)))

rewrite9.0ms

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:

4.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
2.0ms	(sin (/ x (* y 2.0)))
1.0ms	(tan (/ x (* y 2.0)))

series95.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
10.0ms	(sin (/ x (* y 2.0)))
40.0ms	(tan (/ x (* y 2.0)))

simplify795.0ms

Counts

58 → 58

Iterations

Useful iterations: 3 (180.0ms)

Iter	Nodes	Cost
0	83	878
1	150	865
2	436	789
3	1883	785
done	5001	785

prune219.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 27.3b

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune35.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 27.3b

localize12.0ms

Local error

Found 4 expressions with local error:

7.2b	(/ (/ (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))) (sin (/ x (* y 2.0))))
28.6b	(sin (/ x (* y 2.0)))
28.6b	(sin (/ x (* y 2.0)))
29.6b	(cos (/ x (* y 2.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

13.0ms	(/ (/ (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))) (sin (/ x (* y 2.0))))
2.0ms	(sin (/ x (* y 2.0)))
2.0ms	(sin (/ x (* y 2.0)))
2.0ms	(cos (/ x (* y 2.0)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (/ (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))) (sin (/ x (* y 2.0))))
9.0ms	(sin (/ x (* y 2.0)))
9.0ms	(sin (/ x (* y 2.0)))
12.0ms	(cos (/ x (* y 2.0)))

simplify654.0ms

Counts

111 → 111

Iterations

Useful iterations: 2 (120.0ms)

Iter	Nodes	Cost
0	167	2899
1	364	2846
2	1511	2406
done	5000	2406

prune394.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 27.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (cos (/ x (* y 2.0))))
0.7b	(log1p (expm1 (/ 1 (cos (/ x (* y 2.0))))))
0.8b	(expm1 (/ 1 (cos (/ x (* y 2.0)))))
29.6b	(cos (/ x (* y 2.0)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
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` `pow-flip` `frac-2neg` `1-exp` `log1p-expm1` `clear-num` `div-inv` `inv-pow` `expm1-udef`

Counts

4 → 64

Calls

4 calls:

2.0ms	(/ 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)))))
2.0ms	(cos (/ x (* y 2.0)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1 (cos (/ x (* y 2.0))))
72.0ms	(log1p (expm1 (/ 1 (cos (/ x (* y 2.0))))))
61.0ms	(expm1 (/ 1 (cos (/ x (* y 2.0)))))
12.0ms	(cos (/ x (* y 2.0)))

simplify1.1s

Counts

76 → 76

Iterations

Useful iterations: 3 (238.0ms)

Iter	Nodes	Cost
0	91	887
1	157	817
2	440	730
3	1600	728
done	5000	728

prune182.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 27.2b

regimes446.0ms

Accuracy

29.9% (1.7b remaining)

Error of 27.9b against oracle of 26.2b and baseline of 28.6b

bsearch2.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	30
1	23	30
done	23	30

end0.0ms

sample3.1s

Algorithm

intervals

Results

887.0ms	1403×	body	1280	valid
882.0ms	657×	body	2560	valid
592.0ms	4077×	body	80	valid
368.0ms	990×	body	640	valid
137.0ms	521×	body	320	valid
69.0ms	352×	body	160	valid