Details

sample91.0ms

Algorithm

intervals

Results

30.0ms	307×	body	80	valid
21.0ms	36×	body	1280	valid
10.0ms	24×	body	640	valid
7.0ms	24×	body	320	valid
1.0ms	6×	body	160	valid

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	4217
4	728
3	160
2	57
1	26
0	12

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
2.6b	(* (* x (pow sin 2.0)) x)
10.5b	(* x (pow sin 2.0))
18.3b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite144.0ms

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:

62.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
17.0ms	(* (* x (pow sin 2.0)) x)
11.0ms	(* x (pow sin 2.0))
47.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

415.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
188.0ms	(* (* x (pow sin 2.0)) x)
177.0ms	(* x (pow sin 2.0))
427.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.5s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
2	1502
1	414
0	166

prune645.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
0.1b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
2.6b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
18.3b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite566.0ms

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:

212.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
34.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
82.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
228.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

448.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
188.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
205.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
339.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.7s

Counts

198 → 198

Iterations

Iter	Nodes
done	5001
2	1842
1	561
0	198

prune524.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.7b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (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))))))
0.2b	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
4.6b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.7b	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2)))))

rewrite574.0ms

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:

182.0ms	(/ (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))))))
77.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
34.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
210.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

357.0ms	(/ (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))))))
353.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
281.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
340.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2)))))

simplify2.0s

Counts

478 → 478

Iterations

Iter	Nodes
done	5016
2	2437
1	771
0	266

prune771.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 1.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
0.3b	(/ (cos (* 2.0 x)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2)))))
4.6b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.8b	(* (/ 1 (pow cos (/ 2.0 2))) (/ (cos (* 2.0 x)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))))

rewrite556.0ms

Algorithm

rewrite-expression-head

Rules

3406×	`add-exp-log`
2661×	`prod-exp`
907×	`div-exp`
661×	`pow-to-exp` `pow-exp`
162×	`rec-exp` `1-exp`
143×	`add-cbrt-cube`
79×	`cbrt-unprod`
39×	`add-sqr-sqrt`
33×	`times-frac` `associate-l`
29×	`cbrt-undiv`
27×	`*-un-lft-identity`
24×	`add-cube-cbrt`
14×	`unpow-prod-down`
9×	`associate-r`
8×	`pow1`
7×	`unswap-sqr`
6×	`sqr-pow`
4×	`add-log-exp`
3×	`-commutative` `div-inv` `associate-/l`
2×	`pow-prod-down`
1×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `associate-l/` `associate-*r/`

Counts

4 → 783

Calls

4 calls:

83.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
83.0ms	(/ (cos (* 2.0 x)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2)))))
21.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
236.0ms	(* (/ 1 (pow cos (/ 2.0 2))) (/ (cos (* 2.0 x)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

375.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))
390.0ms	(/ (cos (* 2.0 x)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2)))))
324.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
446.0ms	(* (/ 1 (pow cos (/ 2.0 2))) (/ (cos (* 2.0 x)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* x (pow sin (/ 2.0 2))))))

simplify2.2s

Counts

795 → 795

Iterations

Iter	Nodes
done	5001
1	1387
0	437

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 1.3b

regimes1.0s

Accuracy

46.7% (2.4b remaining)

Error of 4.4b against oracle of 2.0b and baseline of 6.6b

bsearch443.0ms

Steps

Iters	Range		Point
5	9.005684471541738e+198	2.285195398158317e+199	2.0890880390963893e+199
6	6.158800139311755e-217	6.137239153578748e-216	5.984974754441588e-216
9	-1.0481349004974627e-138	-2.880736350102469e-147	-2.950166798107947e-147
5	-1.3461928284248461e+209	-4.020065562148192e+208	-5.981995449898381e+208

simplify16.0ms

Iterations

Iter	Nodes
done	52
1	52
0	37

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.7s	9028×	body	80	valid
916.0ms	949×	body	640	valid
527.0ms	816×	body	1280	valid
222.0ms	560×	body	320	valid
102.0ms	309×	body	160	valid