Details

sample105.0ms

Algorithm

intervals

Results

34.0ms	24×	body	2560	valid
25.0ms	36×	body	1280	valid
14.0ms	139×	body	80	valid
11.0ms	26×	body	640	valid
6.0ms	20×	body	320	valid
3.0ms	11×	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

prune38.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize13.0ms

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)))

rewrite32.0ms

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:

22.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
5.0ms	(sin (/ x (* y 2.0)))
4.0ms	(tan (/ x (* y 2.0)))

series170.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
32.0ms	(sin (/ x (* y 2.0)))
58.0ms	(tan (/ x (* y 2.0)))

simplify1.8s

Counts

52 → 52

Iterations

Useful iterations: 3 (214.0ms)

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

prune210.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 24.3b

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

prune34.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 24.3b

localize22.0ms

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)))

rewrite81.0ms

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:

41.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
11.0ms	(sin (/ x (* y 2.0)))
17.0ms	(sin (/ x (* y 2.0)))
10.0ms	(cos (/ x (* y 2.0)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (cos (/ x (* y 2.0)))))
11.0ms	(sin (/ x (* y 2.0)))
13.0ms	(sin (/ x (* y 2.0)))
24.0ms	(cos (/ x (* y 2.0)))

simplify9.0s

Counts

55 → 55

Iterations

Useful iterations: 3 (507.0ms)

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

prune244.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 24.3b

localize11.0ms

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)))

rewrite76.0ms

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×	`sqrt-div` `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 → 149

Calls

4 calls:

10.0ms	(/ 1 (cos (/ x (* y 2.0))))
45.0ms	(* (sqrt (/ 1 (cos (/ x (* y 2.0))))) (sqrt (/ 1 (cos (/ x (* y 2.0))))))
5.0ms	(cos (/ x (* y 2.0)))
5.0ms	(cos (/ x (* y 2.0)))

series96.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1 (cos (/ x (* y 2.0))))
34.0ms	(* (sqrt (/ 1 (cos (/ x (* y 2.0))))) (sqrt (/ 1 (cos (/ x (* y 2.0))))))
14.0ms	(cos (/ x (* y 2.0)))
20.0ms	(cos (/ x (* y 2.0)))

simplify3.8s

Counts

161 → 161

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	165	3326
1	255	2227
2	484	2061
3	1066	2022
4	3191	1947
done	5000	1938

prune394.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 24.3b

regimes600.0ms

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

sample6.0s

Algorithm

intervals

Results

1.6s	1363×	body	1280	valid
1.4s	648×	body	2560	valid
1.2s	4103×	body	80	valid
1.0s	972×	body	640	valid
331.0ms	595×	body	320	valid
103.0ms	319×	body	160	valid