Details

sample57.0ms

Algorithm

intervals

Results

21.0ms	289×	body	80	valid
8.0ms	23×	body	1280	valid
7.0ms	29×	body	640	valid
4.0ms	21×	body	320	valid
1.0ms	12×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	16
1	26	16
2	66	16
3	223	16
4	931	16
done	5000	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
2.7b	(* (* x (pow sin 2.0)) x)
7.6b	(* x (pow sin 2.0))
18.5b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite72.0ms

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:

25.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
11.0ms	(* (* x (pow sin 2.0)) x)
6.0ms	(* x (pow sin 2.0))
26.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series842.0ms

Counts

4 → 12

Calls

4 calls:

296.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
147.0ms	(* (* x (pow sin 2.0)) x)
136.0ms	(* x (pow sin 2.0))
263.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify893.0ms

Counts

127 → 127

Iterations

Useful iterations: 2 (190.0ms)

Iter	Nodes	Cost
0	171	1959
1	425	1811
2	1532	1541
done	5001	1541

prune267.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.0b

localize19.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (* x (pow sin 2.0)) x)
5.8b	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
5.9b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
7.6b	(* x (pow sin 2.0))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

226×	`add-exp-log`
202×	`prod-exp`
50×	`pow-to-exp` `pow-exp`
34×	`add-cbrt-cube`
20×	`cbrt-unprod`
18×	`associate-l`
17×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
10×	`unpow-prod-down`
6×	`pow1`
4×	`*-commutative` `add-log-exp` `sqr-pow`
3×	`unswap-sqr`
1×	`pow-prod-down`

Counts

4 → 146

Calls

4 calls:

8.0ms	(* (* x (pow sin 2.0)) x)
25.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
69.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
5.0ms	(* x (pow sin 2.0))

series802.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (* x (pow sin 2.0)) x)
260.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
253.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
137.0ms	(* x (pow sin 2.0))

simplify914.0ms

Counts

158 → 158

Iterations

Useful iterations: 2 (181.0ms)

Iter	Nodes	Cost
0	163	2848
1	418	2022
2	1378	1770
done	5000	1770

prune300.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))))
2.7b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
5.8b	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))
5.9b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))

rewrite680.0ms

Algorithm

rewrite-expression-head

Rules

1410×	`add-exp-log`
1300×	`prod-exp`
338×	`pow-to-exp` `pow-exp`
130×	`div-exp`
74×	`add-cbrt-cube`
46×	`cbrt-unprod`
15×	`associate-l`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-undiv` `unpow-prod-down`
5×	`associate-r`
4×	`add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`sqr-pow`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 394

Calls

4 calls:

247.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))))
32.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
90.0ms	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))
264.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))

series995.0ms

Counts

4 → 12

Calls

4 calls:

302.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))))
156.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
267.0ms	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))
269.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))

simplify1.1s

Counts

406 → 406

Iterations

Useful iterations: 2 (318.0ms)

Iter	Nodes	Cost
0	259	13801
1	785	6413
2	2665	5751
done	5001	5751

prune313.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
0.7b	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))))
5.8b	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))
5.9b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))

rewrite340.0ms

Algorithm

rewrite-expression-head

Rules

1691×	`add-exp-log`
1549×	`prod-exp`
399×	`pow-to-exp` `pow-exp`
157×	`div-exp`
92×	`add-cbrt-cube`
59×	`cbrt-unprod`
15×	`associate-l`
12×	`add-sqr-sqrt`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-undiv` `unpow-prod-down`
4×	`add-log-exp`
3×	`times-frac` `associate-r` `-commutative` `associate-/l` `unswap-sqr` `sqr-pow`
1×	`pow2` `frac-2neg` `pow-plus` `swap-sqr` `pow-prod-down` `clear-num` `associate-/r*` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 470

Calls

4 calls:

14.0ms	(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
115.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))))
41.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))
115.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

158.0ms	(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
308.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))))
277.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))
280.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))

simplify864.0ms

Counts

482 → 482

Iterations

Useful iterations: 2 (261.0ms)

Iter	Nodes	Cost
0	272	16331
1	745	7619
2	2240	6815
done	5001	6815

prune285.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.7b

regimes376.0ms

Accuracy

0% (1.1b remaining)

Error of 5.6b against oracle of 4.5b and baseline of 5.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	20	32
done	20	32

end0.0ms

sample1.5s

Algorithm

intervals

Results

549.0ms	9026×	body	80	valid
285.0ms	789×	body	1280	valid
237.0ms	943×	body	640	valid
117.0ms	576×	body	320	valid
42.0ms	317×	body	160	valid