Details

sample57.0ms

Algorithm

intervals

Results

19.0ms	300×	body	80	valid
10.0ms	28×	body	1280	valid
6.0ms	23×	body	640	valid
3.0ms	15×	body	320	valid
1.0ms	9×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	26	16
2	67	16
3	241	16
4	1097	16
done	5000	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.5b	(* (* x (pow sin 2.0)) x)
8.9b	(* x (pow sin 2.0))
19.6b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite193.0ms

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:

67.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
31.0ms	(* (* x (pow sin 2.0)) x)
12.0ms	(* x (pow sin 2.0))
76.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

397.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
200.0ms	(* (* x (pow sin 2.0)) x)
181.0ms	(* x (pow sin 2.0))
359.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.4s

Counts

127 → 127

Iterations

Useful iterations: 2 (283.0ms)

Iter	Nodes	Cost
0	171	1959
1	407	1811
2	1424	1531
done	5001	1531

prune353.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.5b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
4.5b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
19.6b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite616.0ms

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:

11.0ms	(cos (* 2.0 x))
238.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
89.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
261.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series963.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cos (* 2.0 x))
404.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
182.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
359.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.1s

Counts

175 → 175

Iterations

Useful iterations: 2 (324.0ms)

Iter	Nodes	Cost
0	187	4524
1	491	2705
2	1925	2299
done	5000	2299

prune281.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.2b	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
0.5b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
19.6b	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

rewrite309.0ms

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`
8×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-l*`
6×	`pow1` `cbrt-undiv`
4×	`add-log-exp`
3×	`unpow-prod-down` `times-frac` `associate-/l*`
2×	`associate-r` `*-commutative`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv` `sqr-pow`

Counts

4 → 185

Calls

4 calls:

11.0ms	(cos (* 2.0 x))
61.0ms	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
99.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
117.0ms	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

series931.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cos (* 2.0 x))
202.0ms	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
352.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
353.0ms	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

simplify1.1s

Counts

197 → 197

Iterations

Useful iterations: 2 (382.0ms)

Iter	Nodes	Cost
0	190	5189
1	478	3099
2	1918	2615
done	5000	2615

prune301.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.5b	(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
7.3b	(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
11.0b	(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

rewrite397.0ms

Algorithm

rewrite-expression-head

Rules

456×	`add-exp-log`
371×	`prod-exp`
89×	`pow-to-exp` `pow-exp`
59×	`add-cbrt-cube`
53×	`div-exp`
33×	`cbrt-unprod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-l*`
7×	`cbrt-undiv`
6×	`pow1`
4×	`add-log-exp`
3×	`unpow-prod-down` `times-frac` `associate-/l*`
2×	`associate-r` `*-commutative`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv` `sqr-pow`

Counts

4 → 183

Calls

4 calls:

15.0ms	(cos (* 2.0 x))
154.0ms	(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
149.0ms	(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
51.0ms	(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

series1.2s

Counts

4 → 12

Calls

4 calls:

25.0ms	(cos (* 2.0 x))
424.0ms	(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
438.0ms	(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
292.0ms	(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify1.6s

Counts

195 → 195

Iterations

Useful iterations: 2 (576.0ms)

Iter	Nodes	Cost
0	193	5039
1	516	3277
2	2019	2735
done	5001	2735

prune371.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.3b

regimes434.0ms

Accuracy

0% (1.8b remaining)

Error of 6.8b against oracle of 5.0b and baseline of 6.8b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	20	32
done	20	32

end0.0ms

sample2.4s

Algorithm

intervals

Results

812.0ms	9054×	body	80	valid
405.0ms	802×	body	1280	valid
353.0ms	979×	body	640	valid
146.0ms	548×	body	320	valid
53.0ms	305×	body	160	valid