Details

sample116.0ms

Algorithm

intervals

Results

32.0ms	41×	body	1280	valid
29.0ms	17×	body	2560	valid
17.0ms	32×	body	640	valid
15.0ms	135×	body	80	valid
6.0ms	18×	body	320	valid
4.0ms	13×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize20.0ms

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)))

rewrite45.0ms

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` `associate-/r` `associate-/l` `add-log-exp`
2×	`tan-quot`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `associate-/l/`

Counts

3 → 43

Calls

3 calls:

35.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
5.0ms	(sin (/ x (* y 2.0)))
4.0ms	(tan (/ x (* y 2.0)))

series116.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
10.0ms	(sin (/ x (* y 2.0)))
45.0ms	(tan (/ x (* y 2.0)))

simplify2.2s

Counts

52 → 52

Iterations

Useful iterations: 3 (208.0ms)

Iter	Nodes	Cost
0	77	822
1	139	813
2	323	737
3	803	733
4	2504	733
done	5000	733

prune245.0ms

Pruning

14 alts after pruning (14 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

prune61.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 24.9b

localize22.0ms

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)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-exp-log` `add-cbrt-cube`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `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 → 43

Calls

4 calls:

47.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
8.0ms	(sin (/ x (* y 2.0)))
8.0ms	(sin (/ x (* y 2.0)))
8.0ms	(cos (/ x (* y 2.0)))

series80.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
14.0ms	(sin (/ x (* y 2.0)))
15.0ms	(sin (/ x (* y 2.0)))
19.0ms	(cos (/ x (* y 2.0)))

simplify7.9s

Counts

55 → 55

Iterations

Useful iterations: 3 (470.0ms)

Iter	Nodes	Cost
0	71	905
1	145	719
2	409	546
3	1223	542
4	4877	542
done	5000	542

prune192.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 24.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (/ 1 (cos (/ x (* y 2.0))))) (cbrt (/ 1 (cos (/ x (* y 2.0))))))
27.5b	(cos (/ x (* y 2.0)))
27.5b	(cos (/ x (* y 2.0)))
27.5b	(cos (/ x (* y 2.0)))

rewrite48.0ms

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×	`cbrt-div` `add-cbrt-cube` `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 → 108

Calls

4 calls:

28.0ms	(* (cbrt (/ 1 (cos (/ x (* y 2.0))))) (cbrt (/ 1 (cos (/ x (* y 2.0))))))
5.0ms	(cos (/ x (* y 2.0)))
5.0ms	(cos (/ x (* y 2.0)))
5.0ms	(cos (/ x (* y 2.0)))

series180.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (cbrt (/ 1 (cos (/ x (* y 2.0))))) (cbrt (/ 1 (cos (/ x (* y 2.0))))))
13.0ms	(cos (/ x (* y 2.0)))
13.0ms	(cos (/ x (* y 2.0)))
19.0ms	(cos (/ x (* y 2.0)))

simplify4.9s

Counts

120 → 120

Iterations

Useful iterations: 5 (2.8s)

Iter	Nodes	Cost
0	138	2734
1	211	2485
2	395	2371
3	711	2175
4	1356	2153
5	4893	2135
done	5000	2135

prune456.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 24.6b

regimes698.0ms

Accuracy

32.4% (1.8b remaining)

Error of 28.0b against oracle of 26.2b and baseline of 28.8b

bsearch5.0ms

Steps

Iters	Range		Point
2	1.937947126429837	2.1262852432004284	2.094986369407834

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	61
1	17	61
done	17	61

end0.0ms

sample6.8s

Algorithm

intervals

Results

1.8s	1416×	body	1280	valid
1.5s	602×	body	2560	valid
1.4s	1024×	body	640	valid
1.2s	4045×	body	80	valid
405.0ms	600×	body	320	valid
156.0ms	313×	body	160	valid