Details

sample77.0ms

Algorithm

intervals

Results

25.0ms	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

simplify515.0ms

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	5001	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

localize13.0ms

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))

rewrite38.0ms

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:

11.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
7.0ms	(* (* 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))

series243.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
38.0ms	(* (* x (pow s 2.0)) x)
33.0ms	(* x (pow s 2.0))
90.0ms	(* (pow c 2.0) (* (* x (pow s 2.0)) x))

simplify685.0ms

Counts

127 → 127

Iterations

Useful iterations: done (682.0ms)

Iter	Nodes	Cost
0	221	2130
1	573	2052
2	2217	1755
done	5000	1721

prune290.0ms

Filtered

82 candidates to 127 candidates (-54.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	116	11	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	11	128

Merged error: 12.9b

Counts

128 → 11

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))

rewrite54.0ms

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)))
10.0ms	(* (* (* 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))

series212.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(cos (* 2.0 x))
81.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
38.0ms	(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
91.0ms	(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

simplify977.0ms

Counts

175 → 175

Iterations

Useful iterations: done (971.0ms)

Iter	Nodes	Cost
0	235	4671
1	683	4144
2	2706	2960
done	5001	2727

prune276.0ms

Filtered

64 candidates to 175 candidates (-173.4%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	165	10	175
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	168	18	186

Merged error: 9.3b

Counts

186 → 18

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)))))

rewrite56.0ms

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:

9.0ms	(* (* 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:

34.0ms	(* (* x (pow s (/ 2.0 2))) (* x (pow s (/ 2.0 2))))
2.0ms	(cos (* 2.0 x))
87.0ms	(/ (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)))))

simplify739.0ms

Counts

205 → 205

Iterations

Useful iterations: done (731.0ms)

Iter	Nodes	Cost
0	235	5429
1	645	4576
2	2358	3438
done	5001	3125

prune255.0ms

Filtered

63 candidates to 205 candidates (-225.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	202	3	205
Fresh	7	9	16
Picked	1	0	1
Done	1	0	1
Total	211	12	223

Merged error: 2.3b

Counts

223 → 12

localize13.0ms

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))))

rewrite75.0ms

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))
25.0ms	(/ (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))))

series235.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(cos (* 2.0 x))
85.0ms	(/ (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))))))
76.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
71.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify951.0ms

Counts

276 → 276

Iterations

Useful iterations: done (941.0ms)

Iter	Nodes	Cost
0	290	9496
1	891	8401
2	2858	5660
done	5000	5562

prune246.0ms

Filtered

65 candidates to 276 candidates (-324.6%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	269	7	276
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	271	17	288

Merged error: 2.0b

Counts

288 → 17

regimes695.0ms

Accuracy

0% (0.6b remaining)

Error of 2.9b against oracle of 2.3b and baseline of 2.9b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.1s

Algorithm

intervals

Results

729.0ms	8933×	body	80	valid
369.0ms	793×	body	1280	valid
309.0ms	926×	body	640	valid
154.0ms	612×	body	320	valid
48.0ms	299×	body	160	valid

Details

sample77.0ms

simplify515.0ms

prune4.0ms

localize13.0ms

rewrite38.0ms

series243.0ms

simplify685.0ms

prune290.0ms

localize15.0ms

rewrite54.0ms

series212.0ms

simplify977.0ms

prune276.0ms

localize17.0ms

rewrite56.0ms

series215.0ms

simplify739.0ms

prune255.0ms

localize13.0ms

rewrite75.0ms

series235.0ms

simplify951.0ms

prune246.0ms

regimes695.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.1s

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