Details

sample62.0ms

Algorithm

intervals

Results

20.0ms	300×	body	80	valid
11.0ms	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

localize18.0ms

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))

rewrite171.0ms

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:

63.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
22.0ms	(* (* x (pow sin 2.0)) x)
12.0ms	(* x (pow sin 2.0))
67.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

377.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
184.0ms	(* (* x (pow sin 2.0)) x)
171.0ms	(* x (pow sin 2.0))
336.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.1s

Counts

135 → 135

Iterations

Useful iterations: 2 (320.0ms)

Iter	Nodes	Cost
0	179	2045
1	421	1897
2	1445	1617
done	5000	1617

prune393.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.8b

localize34.0ms

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))

rewrite632.0ms

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:

7.0ms	(cos (* 2.0 x))
268.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
88.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
254.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

20.0ms	(cos (* 2.0 x))
490.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
219.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
356.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.2s

Counts

183 → 183

Iterations

Useful iterations: 2 (413.0ms)

Iter	Nodes	Cost
0	195	4656
1	509	2788
2	1976	2382
done	5000	2382

prune382.0ms

Pruning

9 alts after pruning (9 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)))

rewrite365.0ms

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:

14.0ms	(cos (* 2.0 x))
75.0ms	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
131.0ms	(/ (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)))

series1.1s

Counts

4 → 12

Calls

4 calls:

25.0ms	(cos (* 2.0 x))
222.0ms	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
475.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
426.0ms	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

simplify1.2s

Counts

205 → 205

Iterations

Useful iterations: 2 (367.0ms)

Iter	Nodes	Cost
0	198	5321
1	501	3182
2	1910	2698
done	5000	2698

prune410.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.5b

localize32.0ms

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))))

rewrite334.0ms

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:

7.0ms	(cos (* 2.0 x))
118.0ms	(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
141.0ms	(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
52.0ms	(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

series1.2s

Counts

4 → 12

Calls

4 calls:

14.0ms	(cos (* 2.0 x))
483.0ms	(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
371.0ms	(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
345.0ms	(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify1.3s

Counts

203 → 203

Iterations

Useful iterations: 2 (489.0ms)

Iter	Nodes	Cost
0	201	5163
1	531	3368
2	1987	2826
done	5000	2826

prune407.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.4b

regimes474.0ms

Accuracy

0% (1.8b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample2.4s

Algorithm

intervals

Results

797.0ms	9054×	body	80	valid
415.0ms	802×	body	1280	valid
344.0ms	979×	body	640	valid
151.0ms	548×	body	320	valid
52.0ms	305×	body	160	valid