Details

sample97.0ms

Algorithm

intervals

Results

31.0ms	284×	body	80	valid
15.0ms	37×	body	640	valid
14.0ms	22×	body	1280	valid
7.0ms	22×	body	320	valid
2.0ms	9×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	16
1	26	16
2	67	16
3	241	16
4	1097	16
done	5000	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize20.0ms

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))

rewrite209.0ms

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:

99.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
24.0ms	(* (* x (pow sin 2.0)) x)
12.0ms	(* x (pow sin 2.0))
66.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

405.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
252.0ms	(* (* x (pow sin 2.0)) x)
198.0ms	(* x (pow sin 2.0))
371.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.1s

Counts

127 → 127

Iterations

Useful iterations: 2 (324.0ms)

Iter	Nodes	Cost
0	171	1959
1	407	1811
2	1424	1531
done	5001	1531

prune352.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.1b

localize26.0ms

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))

rewrite338.0ms

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:

33.0ms	(* (* x (pow sin 2.0)) x)
199.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
11.0ms	(* x (pow sin 2.0))
83.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

208.0ms	(* (* x (pow sin 2.0)) x)
347.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
221.0ms	(* x (pow sin 2.0))
392.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

simplify1.4s

Counts

158 → 158

Iterations

Useful iterations: 2 (295.0ms)

Iter	Nodes	Cost
0	163	2848
1	395	2022
2	1379	1770
done	5000	1770

prune526.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.0b

localize30.0ms

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))

rewrite1.8s

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:

610.0ms	(/ (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))))
115.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
725.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
287.0ms	(* (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:

463.0ms	(/ (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))))
239.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
416.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
390.0ms	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.4s

Counts

406 → 406

Iterations

Useful iterations: 2 (484.0ms)

Iter	Nodes	Cost
0	259	13801
1	676	6413
2	2465	5761
done	5000	5761

prune501.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.3b

localize39.0ms

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)))

rewrite988.0ms

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`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-undiv`
6×	`pow1` `unpow-prod-down`
4×	`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 → 462

Calls

4 calls:

303.0ms	(/ (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)))))
46.0ms	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
427.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
160.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

series1.8s

Counts

4 → 12

Calls

4 calls:

479.0ms	(/ (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)))))
572.0ms	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
372.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
412.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

simplify1.9s

Counts

474 → 474

Iterations

Useful iterations: 2 (688.0ms)

Iter	Nodes	Cost
0	275	16226
1	676	7516
2	2467	6720
done	5000	6720

prune421.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.7b

regimes616.0ms

Accuracy

0% (1.2b 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

sample4.0s

Algorithm

intervals

Results

1.4s	8983×	body	80	valid
717.0ms	586×	body	320	valid
660.0ms	816×	body	1280	valid
546.0ms	980×	body	640	valid
81.0ms	331×	body	160	valid