Details

sample141.0ms

Algorithm

intervals

Results

36.0ms	41×	body	1280	valid
30.0ms	17×	body	2560	valid
27.0ms	32×	body	640	valid
17.0ms	135×	body	80	valid
6.0ms	18×	body	320	valid
4.0ms	13×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize14.0ms

Local error

Found 3 expressions with local error:

5.7b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
27.2b	(sin (/ x (* y 2.0)))
27.8b	(tan (/ x (* y 2.0)))

rewrite55.0ms

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:

42.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
5.0ms	(sin (/ x (* y 2.0)))
6.0ms	(tan (/ x (* y 2.0)))

series132.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
14.0ms	(sin (/ x (* y 2.0)))
58.0ms	(tan (/ x (* y 2.0)))

simplify2.0s

Counts

58 → 58

Iterations

Useful iterations: 3 (234.0ms)

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

prune304.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 24.9b

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

prune39.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 24.9b

localize19.0ms

Local error

Found 4 expressions with local error:

5.7b	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
27.2b	(sin (/ x (* y 2.0)))
27.2b	(sin (/ x (* y 2.0)))
27.5b	(cos (/ x (* y 2.0)))

rewrite47.0ms

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:

30.0ms	(/ (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)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
16.0ms	(sin (/ x (* y 2.0)))
12.0ms	(sin (/ x (* y 2.0)))
17.0ms	(cos (/ x (* y 2.0)))

simplify6.2s

Counts

63 → 63

Iterations

Useful iterations: 3 (449.0ms)

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

prune301.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 24.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (cos (/ x (* y 2.0))))
0.8b	(expm1 (/ 1 (cos (/ x (* y 2.0)))))
0.9b	(log1p (expm1 (/ 1 (cos (/ x (* y 2.0))))))
27.5b	(cos (/ x (* y 2.0)))

rewrite24.0ms

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:

11.0ms	(/ 1 (cos (/ x (* y 2.0))))
1.0ms	(expm1 (/ 1 (cos (/ x (* y 2.0)))))
1.0ms	(log1p (expm1 (/ 1 (cos (/ x (* y 2.0))))))
10.0ms	(cos (/ x (* y 2.0)))

series268.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ 1 (cos (/ x (* y 2.0))))
89.0ms	(expm1 (/ 1 (cos (/ x (* y 2.0)))))
110.0ms	(log1p (expm1 (/ 1 (cos (/ x (* y 2.0))))))
25.0ms	(cos (/ x (* y 2.0)))

simplify7.6s

Counts

76 → 76

Iterations

Useful iterations: 5 (1.1s)

Iter	Nodes	Cost
0	91	887
1	150	807
2	250	731
3	462	731
4	978	731
5	1562	729
6	2008	729
7	3260	729
done	5000	729

prune275.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 24.8b

regimes464.0ms

Accuracy

0% (2.5b remaining)

Error of 28.9b against oracle of 26.3b and baseline of 28.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	12
1	15	12
done	15	12

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.7s	1416×	body	1280	valid
1.4s	602×	body	2560	valid
857.0ms	1024×	body	640	valid
831.0ms	4045×	body	80	valid
342.0ms	600×	body	320	valid
107.0ms	313×	body	160	valid