Details

sample76.0ms

Algorithm

intervals

Results

23.0ms	280×	body	80	valid
11.0ms	32×	body	640	valid
9.0ms	19×	body	1280	valid
5.0ms	19×	body	320	valid
2.0ms	12×	body	160	valid

simplify497.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	16
1	26	16
2	66	16
3	227	16
4	1011	16
done	5000	16

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 26.8b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
3.4b	(* (* x (pow s 2.0)) x)
9.5b	(* x (pow s 2.0))
16.5b	(* (pow c 2.0) (* (* x (pow s 2.0)) x))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-exp-log`
82×	`prod-exp`
34×	`add-cbrt-cube`
18×	`pow-to-exp` `pow-exp`
17×	`add-sqr-sqrt`
16×	`div-exp` `cbrt-unprod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`associate-r` `associate-l`
7×	`unpow-prod-down`
6×	`pow1`
4×	`cbrt-undiv` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l` `unswap-sqr` `sqr-pow`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 115

Calls

4 calls:

12.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
6.0ms	(* (* x (pow s 2.0)) x)
6.0ms	(* x (pow s 2.0))
10.0ms	(* (pow c 2.0) (* (* x (pow s 2.0)) x))

series248.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
35.0ms	(* (* x (pow s 2.0)) x)
37.0ms	(* x (pow s 2.0))
88.0ms	(* (pow c 2.0) (* (* x (pow s 2.0)) x))

simplify729.0ms

Counts

127 → 127

Iterations

Useful iterations: 2 (384.0ms)

Iter	Nodes	Cost
0	221	2130
1	573	1957
2	2094	1631
done	5001	1631

prune269.0ms

Filtered

71 candidates to 127 candidates (-78.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	117	10	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	10	128

Merged error: 14.5b

Counts

128 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.4b	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
3.4b	(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
16.5b	(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

390×	`add-exp-log`
322×	`prod-exp`
77×	`pow-to-exp` `pow-exp`
47×	`add-cbrt-cube`
43×	`div-exp`
26×	`cbrt-unprod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`associate-l`
6×	`pow1`
5×	`cbrt-undiv`
4×	`associate-r` `add-log-exp`
3×	`unpow-prod-down` `times-frac` `associate-/l*`
2×	`*-commutative`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv` `sqr-pow`

Counts

4 → 163

Calls

4 calls:

2.0ms	(cos (* 2.0 x))
16.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
11.0ms	(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
14.0ms	(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

series218.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(cos (* 2.0 x))
84.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
40.0ms	(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
92.0ms	(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

simplify680.0ms

Counts

175 → 175

Iterations

Useful iterations: done (674.0ms)

Iter	Nodes	Cost
0	235	4671
1	683	3546
2	2557	2879
done	5001	2688

prune271.0ms

Filtered

62 candidates to 175 candidates (-182.3%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	166	9	175
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	169	16	185

Merged error: 10.9b

Counts

185 → 16

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow s (/ 2.0 2))) (* x (pow s (/ 2.0 2))))
0.2b	(cos (* 2.0 x))
0.4b	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s (/ 2.0 2))) (* x (pow s (/ 2.0 2))))))
16.5b	(* (pow c 2.0) (* (* x (pow s (/ 2.0 2))) (* x (pow s (/ 2.0 2)))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

467×	`add-exp-log`
382×	`prod-exp`
90×	`pow-to-exp` `pow-exp`
59×	`add-cbrt-cube`
52×	`div-exp`
34×	`cbrt-unprod`
11×	`pow1`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
6×	`cbrt-undiv`
4×	`unpow-prod-down` `add-log-exp`
3×	`times-frac` `associate-/l*` `unswap-sqr`
2×	`associate-r` `*-commutative` `sqr-pow`
1×	`pow2` `frac-2neg` `pow-plus` `swap-sqr` `pow-prod-down` `clear-num` `associate-/r*` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 193

Calls

4 calls:

10.0ms	(* (* x (pow s (/ 2.0 2))) (* x (pow s (/ 2.0 2))))
2.0ms	(cos (* 2.0 x))
17.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s (/ 2.0 2))) (* x (pow s (/ 2.0 2))))))
14.0ms	(* (pow c 2.0) (* (* x (pow s (/ 2.0 2))) (* x (pow s (/ 2.0 2)))))

series215.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (* x (pow s (/ 2.0 2))) (* x (pow s (/ 2.0 2))))
2.0ms	(cos (* 2.0 x))
86.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s (/ 2.0 2))) (* x (pow s (/ 2.0 2))))))
92.0ms	(* (pow c 2.0) (* (* x (pow s (/ 2.0 2))) (* x (pow s (/ 2.0 2)))))

simplify582.0ms

Counts

205 → 205

Iterations

Useful iterations: done (575.0ms)

Iter	Nodes	Cost
0	235	5429
1	645	4037
2	2287	3336
done	5000	3125

prune259.0ms

Filtered

62 candidates to 205 candidates (-230.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	200	5	205
Fresh	7	7	14
Picked	1	0	1
Done	1	0	1
Total	209	12	221

Merged error: 2.9b

Counts

221 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.4b	(/ (cos (* 2.0 x)) (* (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2)))) (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
6.5b	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
6.5b	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

929×	`add-exp-log`
757×	`prod-exp`
196×	`pow-to-exp` `pow-exp`
170×	`div-exp`
61×	`add-cbrt-cube`
33×	`cbrt-unprod`
14×	`associate-l`
10×	`cbrt-undiv` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down`
4×	`pow1` `add-log-exp`
3×	`times-frac` `associate-/l*`
2×	`associate-r` `*-commutative` `sqr-pow`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 264

Calls

4 calls:

2.0ms	(cos (* 2.0 x))
26.0ms	(/ (cos (* 2.0 x)) (* (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2)))) (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
8.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
8.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

series243.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(cos (* 2.0 x))
88.0ms	(/ (cos (* 2.0 x)) (* (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2)))) (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
74.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
80.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify638.0ms

Counts

276 → 276

Iterations

Useful iterations: 2 (240.0ms)

Iter	Nodes	Cost
0	290	9496
1	891	6318
2	2698	5558
done	5001	5558

prune243.0ms

Filtered

63 candidates to 276 candidates (-338.1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	269	7	276
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	272	16	288

Merged error: 2.7b

Counts

288 → 16

regimes565.0ms

Accuracy

0% (0.3b remaining)

Error of 2.9b against oracle of 2.6b and baseline of 2.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	32
1	17	32
done	17	32

end0.0ms

sample2.2s

Algorithm

intervals

Results

770.0ms	8933×	body	80	valid
368.0ms	793×	body	1280	valid
327.0ms	926×	body	640	valid
149.0ms	612×	body	320	valid
50.0ms	299×	body	160	valid

Details

sample76.0ms

simplify497.0ms

prune4.0ms

localize12.0ms

rewrite44.0ms

series248.0ms

simplify729.0ms

prune269.0ms

localize15.0ms

rewrite55.0ms

series218.0ms

simplify680.0ms

prune271.0ms

localize17.0ms

rewrite59.0ms

series215.0ms

simplify582.0ms

prune259.0ms

localize14.0ms

rewrite77.0ms

series243.0ms

simplify638.0ms

prune243.0ms

regimes565.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.2s

Profiling