Details

sample116.0ms

Algorithm

intervals

Results

36.0ms	289×	body	80	valid
22.0ms	28×	body	1280	valid
17.0ms	31×	body	640	valid
7.0ms	18×	body	320	valid
3.0ms	10×	body	160	valid

simplify2.5s

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.5b	(* (* x (pow sin 2.0)) x)
9.6b	(* x (pow sin 2.0))
19.2b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite228.0ms

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:

94.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
38.0ms	(* (* x (pow sin 2.0)) x)
18.0ms	(* x (pow sin 2.0))
73.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

396.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
169.0ms	(* (* x (pow sin 2.0)) x)
171.0ms	(* x (pow sin 2.0))
337.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.2s

Counts

127 → 127

Iterations

Useful iterations: 2 (359.0ms)

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

prune381.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.8b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.5b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
19.2b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite757.0ms

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:

8.0ms	(cos (* 2.0 x))
296.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
122.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
318.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.0s

Counts

4 → 12

Calls

4 calls:

15.0ms	(cos (* 2.0 x))
463.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
186.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
360.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.3s

Counts

175 → 175

Iterations

Useful iterations: 2 (405.0ms)

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

prune424.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.3b	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
0.8b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
19.2b	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

rewrite367.0ms

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:

12.0ms	(cos (* 2.0 x))
63.0ms	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
107.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
161.0ms	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

14.0ms	(cos (* 2.0 x))
235.0ms	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
467.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
402.0ms	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

simplify1.4s

Counts

197 → 197

Iterations

Useful iterations: 2 (510.0ms)

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

prune423.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.8b	(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
6.4b	(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
12.8b	(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

rewrite386.0ms

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:

9.0ms	(cos (* 2.0 x))
150.0ms	(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
148.0ms	(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
62.0ms	(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

series1.2s

Counts

4 → 12

Calls

4 calls:

33.0ms	(cos (* 2.0 x))
496.0ms	(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
380.0ms	(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
312.0ms	(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify1.4s

Counts

195 → 195

Iterations

Useful iterations: 2 (531.0ms)

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

prune317.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.7b

regimes1.1s

Accuracy

0% (1.6b remaining)

Error of 6.9b against oracle of 5.2b and baseline of 6.9b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.9s	8961×	body	80	valid
608.0ms	838×	body	1280	valid
589.0ms	925×	body	640	valid
311.0ms	602×	body	320	valid
76.0ms	319×	body	160	valid