Details

sample140.0ms

Algorithm

intervals

Results

39.0ms	24×	body	2560	valid
28.0ms	36×	body	1280	valid
19.0ms	11×	body	160	valid
16.0ms	139×	body	80	valid
14.0ms	26×	body	640	valid
6.0ms	20×	body	320	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: 34.2b

localize12.0ms

Local error

Found 3 expressions with local error:

7.7b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
26.3b	(sin (/ x (* y 2.0)))
27.0b	(tan (/ x (* y 2.0)))

rewrite23.0ms

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:

12.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
5.0ms	(sin (/ x (* y 2.0)))
4.0ms	(tan (/ x (* y 2.0)))

series151.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
12.0ms	(sin (/ x (* y 2.0)))
88.0ms	(tan (/ x (* y 2.0)))

simplify2.1s

Counts

58 → 58

Iterations

Useful iterations: 3 (161.0ms)

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

prune324.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 24.3b

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune60.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 24.3b

localize13.0ms

Local error

Found 4 expressions with local error:

7.7b	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
26.3b	(sin (/ x (* y 2.0)))
26.3b	(sin (/ x (* y 2.0)))
26.6b	(cos (/ x (* y 2.0)))

rewrite97.0ms

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:

58.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
19.0ms	(sin (/ x (* y 2.0)))
10.0ms	(sin (/ x (* y 2.0)))
9.0ms	(cos (/ x (* y 2.0)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
14.0ms	(sin (/ x (* y 2.0)))
12.0ms	(sin (/ x (* y 2.0)))
20.0ms	(cos (/ x (* y 2.0)))

simplify6.5s

Counts

63 → 63

Iterations

Useful iterations: 3 (488.0ms)

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

prune381.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 24.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (cos (/ x (* y 2.0))))
0.1b	(* (sqrt (/ 1 (cos (/ x (* y 2.0))))) (sqrt (/ 1 (cos (/ x (* y 2.0))))))
26.6b	(cos (/ x (* y 2.0)))
26.6b	(cos (/ x (* y 2.0)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-sqr-sqrt`
82×	`sqrt-prod`
61×	`times-frac`
54×	`*-un-lft-identity`
44×	`add-cube-cbrt`
28×	`pow1`
24×	`sqrt-pow1`
20×	`swap-sqr`
16×	`associate-r` `associate-l` `unswap-sqr`
10×	`add-exp-log`
9×	`pow-flip` `pow-prod-up` `inv-pow`
8×	`pow1/2` `add-cbrt-cube`
7×	`div-inv`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`div-exp`
1×	`cbrt-undiv` `pow2` `frac-times` `rec-exp` `frac-2neg` `pow-plus` `sqrt-unprod` `1-exp` `associate-r/` `associate-l/` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 157

Calls

4 calls:

13.0ms	(/ 1 (cos (/ x (* y 2.0))))
69.0ms	(* (sqrt (/ 1 (cos (/ x (* y 2.0))))) (sqrt (/ 1 (cos (/ x (* y 2.0))))))
5.0ms	(cos (/ x (* y 2.0)))
6.0ms	(cos (/ x (* y 2.0)))

series110.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1 (cos (/ x (* y 2.0))))
39.0ms	(* (sqrt (/ 1 (cos (/ x (* y 2.0))))) (sqrt (/ 1 (cos (/ x (* y 2.0))))))
19.0ms	(cos (/ x (* y 2.0)))
25.0ms	(cos (/ x (* y 2.0)))

simplify4.6s

Counts

169 → 169

Iterations

Useful iterations: done (4.6s)

Iter	Nodes	Cost
0	171	3412
1	261	2287
2	483	2121
3	1057	2094
4	3095	2007
done	5000	1998

prune544.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 24.3b

regimes660.0ms

Accuracy

38.7% (1.5b remaining)

Error of 27.6b against oracle of 26.1b and baseline of 28.5b

bsearch2.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	39
1	19	39
done	19	39

end0.0ms

sample6.9s

Algorithm

intervals

Results

1.9s	4103×	body	80	valid
1.6s	1363×	body	1280	valid
1.6s	648×	body	2560	valid
835.0ms	972×	body	640	valid
357.0ms	595×	body	320	valid
157.0ms	319×	body	160	valid