Details

sample84.0ms

Algorithm

intervals

Results

30.0ms	308×	body	80	valid
11.0ms	22×	body	1280	valid
10.0ms	27×	body	640	valid
6.0ms	21×	body	320	valid
1.0ms	7×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	16
1	26	16
2	67	16
3	242	16
4	1255	16
done	5001	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.3b	(* (* x (pow sin 2.0)) x)
6.4b	(* x (pow sin 2.0))
15.1b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite226.0ms

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` `expm1-log1p-u` `log1p-expm1-u` `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 → 123

Calls

4 calls:

78.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
34.0ms	(* (* x (pow sin 2.0)) x)
15.0ms	(* x (pow sin 2.0))
94.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

429.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
233.0ms	(* (* x (pow sin 2.0)) x)
185.0ms	(* x (pow sin 2.0))
344.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.8s

Counts

135 → 135

Iterations

Useful iterations: 2 (431.0ms)

Iter	Nodes	Cost
0	179	2045
1	457	1907
2	2414	1649
done	5001	1649

prune499.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.4b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.3b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
15.1b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite822.0ms

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×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `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 → 171

Calls

4 calls:

17.0ms	(cos (* 2.0 x))
288.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
154.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
351.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

14.0ms	(cos (* 2.0 x))
446.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
243.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
449.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify2.4s

Counts

183 → 183

Iterations

Useful iterations: 2 (521.0ms)

Iter	Nodes	Cost
0	195	4656
1	551	2788
2	3151	2442
done	5001	2442

prune438.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
0.2b	(cos (* 2.0 x))
0.4b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
15.1b	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

rewrite442.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 193

Calls

4 calls:

81.0ms	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
15.0ms	(cos (* 2.0 x))
181.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
134.0ms	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

203.0ms	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
25.0ms	(cos (* 2.0 x))
455.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
411.0ms	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

simplify2.1s

Counts

205 → 205

Iterations

Useful iterations: 2 (538.0ms)

Iter	Nodes	Cost
0	198	5321
1	566	3182
2	2986	2698
done	5001	2698

prune367.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.4b	(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
4.2b	(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
10.2b	(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

rewrite291.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 191

Calls

4 calls:

12.0ms	(cos (* 2.0 x))
114.0ms	(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
104.0ms	(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
43.0ms	(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

series1.2s

Counts

4 → 12

Calls

4 calls:

24.0ms	(cos (* 2.0 x))
430.0ms	(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
435.0ms	(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
323.0ms	(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify2.7s

Counts

203 → 203

Iterations

Useful iterations: 2 (658.0ms)

Iter	Nodes	Cost
0	201	5163
1	607	3368
2	3214	2826
done	5001	2826

prune372.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

regimes404.0ms

Accuracy

0% (1.7b remaining)

Error of 6.8b against oracle of 5.1b and baseline of 6.8b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	20	32
2	21	32
done	21	32

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.4s	9059×	body	80	valid
1.0s	724×	body	1280	valid
633.0ms	1003×	body	640	valid
307.0ms	585×	body	320	valid
70.0ms	302×	body	160	valid