Details

sample113.0ms

Algorithm

intervals

Results

46.0ms	292×	body	80	valid
16.0ms	26×	body	1280	valid
14.0ms	33×	body	640	valid
8.0ms	25×	body	320	valid
3.0ms	7×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1263
3	241
2	67
1	26
0	12

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.9b	(* (* x (pow sin 2.0)) x)
8.5b	(* x (pow sin 2.0))
19.2b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite203.0ms

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×	`cbrt-undiv` `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 → 115

Calls

4 calls:

80.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
28.0ms	(* (* x (pow sin 2.0)) x)
15.0ms	(* x (pow sin 2.0))
72.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series959.0ms

Counts

4 → 12

Calls

4 calls:

323.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
180.0ms	(* (* x (pow sin 2.0)) x)
142.0ms	(* x (pow sin 2.0))
312.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify2.2s

Counts

127 → 127

Iterations

Iter	Nodes
done	5002
2	2350
1	430
0	166

prune747.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 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)))
3.9b	(* (* (* 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))

rewrite611.0ms

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×	`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 → 186

Calls

4 calls:

32.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
212.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
95.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
251.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

191.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
388.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
203.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
342.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify2.4s

Counts

198 → 198

Iterations

Iter	Nodes
done	5002
2	3307
1	575
0	198

prune759.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.4b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x))
0.4b	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x))))
4.1b	(* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))
6.5b	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x)))

rewrite761.0ms

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

Counts

4 → 466

Calls

4 calls:

112.0ms	(* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x))
293.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x))))
36.0ms	(* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))
247.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x)))

series2.2s

Counts

4 → 12

Calls

4 calls:

646.0ms	(* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x))
412.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x))))
473.0ms	(* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))
631.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x)))

simplify3.0s

Counts

478 → 478

Iterations

Iter	Nodes
done	5000
2	3700
1	860
0	267

prune907.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 1.9b

localize51.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (cos (* 2.0 x)) (* (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))) (* (pow sin (/ 2.0 2)) x)))
1.8b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)))
4.1b	(* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))
5.3b	(* (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))) (* (pow sin (/ 2.0 2)) x))

rewrite633.0ms

Algorithm

rewrite-expression-head

Rules

1643×	`add-exp-log`
1499×	`prod-exp`
393×	`pow-to-exp` `pow-exp`
161×	`div-exp`
92×	`add-cbrt-cube`
57×	`cbrt-unprod`
15×	`associate-l`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`cbrt-undiv`
6×	`pow1` `unpow-prod-down`
4×	`add-log-exp`
3×	`times-frac` `associate-r` `-commutative` `associate-/l`
2×	`sqr-pow`
1×	`clear-num` `associate-/r*` `frac-2neg` `pow-prod-down` `div-inv`

Counts

4 → 454

Calls

4 calls:

214.0ms	(/ (cos (* 2.0 x)) (* (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))) (* (pow sin (/ 2.0 2)) x)))
71.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)))
44.0ms	(* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))
229.0ms	(* (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))) (* (pow sin (/ 2.0 2)) x))

series2.3s

Counts

4 → 12

Calls

4 calls:

459.0ms	(/ (cos (* 2.0 x)) (* (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))) (* (pow sin (/ 2.0 2)) x)))
519.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)))
528.0ms	(* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))
754.0ms	(* (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))) (* (pow sin (/ 2.0 2)) x))

simplify3.1s

Counts

466 → 466

Iterations

Iter	Nodes
done	5002
2	4154
1	905
0	264

prune718.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 1.8b

regimes971.0ms

Accuracy

0% (5.0b remaining)

Error of 7.2b against oracle of 2.2b and baseline of 7.2b

bsearch0.0ms

simplify14.0ms

Iterations

Iter	Nodes
done	24
1	24
0	18

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.4s	8991×	body	80	valid
1.0s	834×	body	1280	valid
644.0ms	985×	body	640	valid
195.0ms	581×	body	320	valid
76.0ms	321×	body	160	valid