Details

sample66.0ms

Algorithm

intervals

Results

25.0ms	307×	body	80	valid
11.0ms	28×	body	1280	valid
9.0ms	32×	body	640	valid
3.0ms	14×	body	320	valid
1.0ms	7×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	4217
4	728
3	160
2	57
1	26
0	12

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.6b	(* (* x (pow sin 2.0)) x)
8.0b	(* x (pow sin 2.0))
17.3b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite126.0ms

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×	`*-un-lft-identity` `add-cube-cbrt`
11×	`associate-r` `associate-l`
7×	`unpow-prod-down`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l` `unswap-sqr` `sqr-pow`
1×	`clear-num` `associate-/r*` `frac-2neg` `pow-prod-down` `div-inv`

Counts

4 → 123

Calls

4 calls:

48.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
17.0ms	(* (* x (pow sin 2.0)) x)
11.0ms	(* x (pow sin 2.0))
46.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

343.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
433.0ms	(* (* x (pow sin 2.0)) x)
180.0ms	(* x (pow sin 2.0))
279.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.4s

Counts

135 → 135

Iterations

Iter	Nodes
done	5000
2	1436
1	432
0	174

prune759.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.4b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.6b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
17.3b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite547.0ms

Algorithm

rewrite-expression-head

Rules

416×	`add-exp-log`
343×	`prod-exp`
84×	`pow-to-exp` `pow-exp`
52×	`add-cbrt-cube`
43×	`div-exp`
29×	`cbrt-unprod`
11×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*` `add-cube-cbrt`
9×	`associate-l`
6×	`pow1` `unpow-prod-down`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`sqr-pow`
1×	`clear-num` `associate-/r*` `frac-2neg` `pow-prod-down` `div-inv`

Counts

4 → 194

Calls

4 calls:

24.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
185.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
93.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
227.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

197.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
456.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
191.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
366.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.8s

Counts

206 → 206

Iterations

Iter	Nodes
done	5001
2	2086
1	564
0	206

prune756.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))))
3.5b	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0))))
8.0b	(* x (pow sin 2.0))
9.0b	(* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

472×	`add-exp-log`
385×	`prod-exp`
91×	`pow-to-exp` `pow-exp`
61×	`add-cbrt-cube`
52×	`div-exp`
35×	`cbrt-unprod`
16×	`add-sqr-sqrt`
11×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
9×	`associate-r`
7×	`unpow-prod-down`
6×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l` `unswap-sqr` `sqr-pow`
1×	`clear-num` `associate-/r*` `frac-2neg` `pow-prod-down` `div-inv`

Counts

4 → 211

Calls

4 calls:

73.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))))
81.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0))))
9.0ms	(* x (pow sin 2.0))
29.0ms	(* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

430.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))))
369.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0))))
164.0ms	(* x (pow sin 2.0))
334.0ms	(* (* (pow cos (/ 2.0 2)) x) (* x (pow sin 2.0)))

simplify2.3s

Counts

223 → 223

Iterations

Iter	Nodes
done	5022
2	2132
1	588
0	219

prune994.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.4b	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))))
3.5b	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))))
9.0b	(* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

rewrite611.0ms

Algorithm

rewrite-expression-head

Rules

1711×	`add-exp-log`
1564×	`prod-exp`
400×	`pow-to-exp` `pow-exp`
160×	`div-exp`
97×	`add-cbrt-cube`
62×	`cbrt-unprod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`associate-r` `associate-l`
8×	`cbrt-undiv`
6×	`pow1` `unpow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`sqr-pow`
1×	`clear-num` `associate-/r*` `frac-2neg` `pow-prod-down` `div-inv`

Counts

4 → 474

Calls

4 calls:

26.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
196.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))))
214.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))))
99.0ms	(* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

series1.4s

Counts

4 → 12

Calls

4 calls:

172.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
495.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))))
406.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))))
365.0ms	(* (* (pow cos (/ 2.0 2)) x) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

simplify2.5s

Counts

486 → 486

Iterations

Iter	Nodes
done	5012
2	2790
1	843
0	291

prune624.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.7b

regimes945.0ms

Accuracy

0% (4.0b remaining)

Error of 9.5b against oracle of 5.5b and baseline of 9.5b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	22
1	22
0	16

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.3s	8961×	body	80	valid
687.0ms	842×	body	1280	valid
587.0ms	623×	body	320	valid
517.0ms	958×	body	640	valid
65.0ms	301×	body	160	valid