Details

sample166.0ms

Algorithm

intervals

Results

50.0ms	46×	body	1280	valid
30.0ms	16×	body	2560	valid
21.0ms	29×	body	640	valid
20.0ms	131×	body	80	valid
10.0ms	20×	body	320	valid
6.0ms	14×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune46.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize25.0ms

Local error

Found 3 expressions with local error:

6.0b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
27.4b	(sin (/ x (* y 2.0)))
28.1b	(tan (/ x (* y 2.0)))

rewrite36.0ms

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:

19.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
8.0ms	(sin (/ x (* y 2.0)))
7.0ms	(tan (/ x (* y 2.0)))

series141.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
21.0ms	(sin (/ x (* y 2.0)))
63.0ms	(tan (/ x (* y 2.0)))

simplify2.2s

Counts

58 → 58

Iterations

Useful iterations: 3 (202.0ms)

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

prune278.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 26.0b

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

prune48.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 26.0b

localize13.0ms

Local error

Found 4 expressions with local error:

5.9b	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
27.4b	(sin (/ x (* y 2.0)))
27.4b	(sin (/ x (* y 2.0)))
28.1b	(cos (/ x (* y 2.0)))

rewrite62.0ms

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:

44.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
5.0ms	(sin (/ x (* y 2.0)))
5.0ms	(sin (/ x (* y 2.0)))
6.0ms	(cos (/ x (* y 2.0)))

series93.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
18.0ms	(sin (/ x (* y 2.0)))
13.0ms	(sin (/ x (* y 2.0)))
22.0ms	(cos (/ x (* y 2.0)))

simplify6.8s

Counts

63 → 63

Iterations

Useful iterations: 3 (555.0ms)

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

prune340.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 26.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (/ 1 (cos (/ x (* y 2.0))))) (cbrt (/ 1 (cos (/ x (* y 2.0))))))
28.1b	(cos (/ x (* y 2.0)))
28.1b	(cos (/ x (* y 2.0)))
28.1b	(cos (/ x (* y 2.0)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

80×	`cbrt-prod`
76×	`add-sqr-sqrt`
52×	`times-frac`
46×	`*-un-lft-identity`
36×	`add-cube-cbrt`
18×	`swap-sqr`
16×	`associate-r` `associate-l` `unswap-sqr`
11×	`pow1`
6×	`add-exp-log` `pow1/3` `div-inv`
4×	`expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 116

Calls

4 calls:

52.0ms	(* (cbrt (/ 1 (cos (/ x (* y 2.0))))) (cbrt (/ 1 (cos (/ x (* y 2.0))))))
11.0ms	(cos (/ x (* y 2.0)))
12.0ms	(cos (/ x (* y 2.0)))
11.0ms	(cos (/ x (* y 2.0)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(* (cbrt (/ 1 (cos (/ x (* y 2.0))))) (cbrt (/ 1 (cos (/ x (* y 2.0))))))
16.0ms	(cos (/ x (* y 2.0)))
27.0ms	(cos (/ x (* y 2.0)))
26.0ms	(cos (/ x (* y 2.0)))

simplify5.8s

Counts

128 → 128

Iterations

Useful iterations: 5 (3.2s)

Iter	Nodes	Cost
0	142	2816
1	216	2565
2	400	2451
3	719	2241
4	1384	2219
5	4934	2201
done	5000	2201

prune584.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 25.8b

regimes426.0ms

Accuracy

0% (2.5b remaining)

Error of 28.4b against oracle of 25.9b and baseline of 28.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	33
1	19	33
done	19	33

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.2s	1371×	body	1280	valid
1.4s	642×	body	2560	valid
1.1s	4097×	body	80	valid
823.0ms	1004×	body	640	valid
338.0ms	572×	body	320	valid
111.0ms	314×	body	160	valid