Details

sample90.0ms

Algorithm

intervals

Results

29.0ms	300×	body	80	valid
14.0ms	35×	body	640	valid
14.0ms	24×	body	1280	valid
6.0ms	20×	body	320	valid
1.0ms	6×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	26	16
2	67	16
3	242	16
4	1255	16
done	5001	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
5.1b	(* (* x (pow sin 2.0)) x)
6.1b	(* x (pow sin 2.0))
21.2b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite249.0ms

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:

97.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
36.0ms	(* (* x (pow sin 2.0)) x)
20.0ms	(* x (pow sin 2.0))
88.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

390.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
216.0ms	(* (* x (pow sin 2.0)) x)
194.0ms	(* x (pow sin 2.0))
373.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.7s

Counts

135 → 135

Iterations

Useful iterations: 2 (396.0ms)

Iter	Nodes	Cost
0	179	2045
1	457	1907
2	2414	1649
done	5001	1649

prune398.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.8b

localize21.0ms

Local error

Found 4 expressions with local error:

5.1b	(* (* x (pow sin 2.0)) x)
6.1b	(* x (pow sin 2.0))
6.7b	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
8.0b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))

rewrite430.0ms

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:

31.0ms	(* (* x (pow sin 2.0)) x)
20.0ms	(* x (pow sin 2.0))
100.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
269.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

172.0ms	(* (* x (pow sin 2.0)) x)
181.0ms	(* x (pow sin 2.0))
363.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
361.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))

simplify1.8s

Counts

166 → 166

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	171	2944
1	454	2114
2	2259	1890
done	5000	1872

prune847.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (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))))
5.1b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
6.7b	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))
8.0b	(* (pow cos (/ 2.0 2)) (* (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:

720.0ms	(/ (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))))
121.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
327.0ms	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))
814.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))

series1.4s

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))))
198.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
355.0ms	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))
368.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))

simplify2.7s

Counts

414 → 414

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	267	13999
1	792	6515
2	3599	6019
done	5001	5919

prune547.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
0.5b	(/ (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)))))
6.7b	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))
8.0b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))

rewrite1.1s

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:

60.0ms	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
387.0ms	(/ (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)))))
144.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))
431.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))

series1.4s

Counts

4 → 12

Calls

4 calls:

239.0ms	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
399.0ms	(/ (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)))))
349.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))
452.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))

simplify2.6s

Counts

482 → 482

Iterations

Useful iterations: 2 (715.0ms)

Iter	Nodes	Cost
0	283	16424
1	852	7618
2	3555	6822
done	5000	6822

prune485.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.1b

regimes495.0ms

Accuracy

0% (1.2b remaining)

Error of 5.9b against oracle of 4.7b and baseline of 5.9b

bsearch0.0ms

simplify12.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	32
1	20	32
2	21	32
done	21	32

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.4s	9191×	body	80	valid
940.0ms	1002×	body	640	valid
727.0ms	818×	body	1280	valid
243.0ms	567×	body	320	valid
157.0ms	333×	body	160	valid