Details

sample96.0ms

Algorithm

intervals

Results

42.0ms	284×	body	80	valid
12.0ms	37×	body	640	valid
11.0ms	22×	body	1280	valid
5.0ms	22×	body	320	valid
1.0ms	9×	body	160	valid

simplify2.1s

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.7b	(* (* x (pow sin 2.0)) x)
6.5b	(* x (pow sin 2.0))
20.3b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite241.0ms

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:

96.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
34.0ms	(* (* x (pow sin 2.0)) x)
12.0ms	(* x (pow sin 2.0))
95.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

394.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
217.0ms	(* (* x (pow sin 2.0)) x)
202.0ms	(* x (pow sin 2.0))
375.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.2s

Counts

135 → 135

Iterations

Useful iterations: 2 (420.0ms)

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

prune392.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.1b

localize24.0ms

Local error

Found 4 expressions with local error:

4.7b	(* (* x (pow sin 2.0)) x)
5.9b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
6.5b	(* x (pow sin 2.0))
7.8b	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

rewrite376.0ms

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×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`unswap-sqr`
1×	`pow-prod-down`

Counts

4 → 154

Calls

4 calls:

36.0ms	(* (* x (pow sin 2.0)) x)
214.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
17.0ms	(* x (pow sin 2.0))
92.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

220.0ms	(* (* x (pow sin 2.0)) x)
397.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
196.0ms	(* x (pow sin 2.0))
359.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

simplify1.5s

Counts

166 → 166

Iterations

Useful iterations: 2 (372.0ms)

Iter	Nodes	Cost
0	171	2944
1	418	2102
2	1383	1850
done	5000	1850

prune454.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (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))))
4.7b	(* (* (* 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)))
7.8b	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite2.0s

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 402

Calls

4 calls:

758.0ms	(/ (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))))
104.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
793.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
270.0ms	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.5s

Counts

4 → 12

Calls

4 calls:

446.0ms	(/ (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))))
262.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
418.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
365.0ms	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.7s

Counts

414 → 414

Iterations

Useful iterations: 2 (649.0ms)

Iter	Nodes	Cost
0	267	13999
1	709	6515
2	2512	5853
done	5001	5853

prune538.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (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)))))
0.2b	(* (* 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))))
7.8b	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

rewrite1.0s

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

Counts

4 → 470

Calls

4 calls:

342.0ms	(/ (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)))))
40.0ms	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
381.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
170.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

series1.5s

Counts

4 → 12

Calls

4 calls:

443.0ms	(/ (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)))))
224.0ms	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
419.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
397.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

simplify1.6s

Counts

482 → 482

Iterations

Useful iterations: 2 (606.0ms)

Iter	Nodes	Cost
0	283	16424
1	719	7618
2	2472	6822
done	5000	6822

prune501.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.7b

regimes639.0ms

Accuracy

0% (1.3b remaining)

Error of 6.4b against oracle of 5.1b and baseline of 6.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.8s	8983×	body	80	valid
1.0s	980×	body	640	valid
645.0ms	816×	body	1280	valid
196.0ms	586×	body	320	valid
117.0ms	331×	body	160	valid