Details

sample108.0ms

Algorithm

intervals

Results

33.0ms	284×	body	80	valid
17.0ms	26×	body	1280	valid
15.0ms	32×	body	640	valid
7.0ms	21×	body	320	valid
4.0ms	13×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1263
3	241
2	67
1	26
0	12

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (cos (* 2.0 x)) (pow sin 2.0))
5.8b	(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
9.0b	(* (pow cos 2.0) x)
18.8b	(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

359×	`times-frac`
146×	`add-sqr-sqrt`
141×	`*-un-lft-identity` `add-cube-cbrt`
128×	`add-exp-log`
76×	`div-exp`
70×	`unpow-prod-down`
57×	`associate-/l*`
38×	`add-cbrt-cube`
27×	`prod-exp`
24×	`sqr-pow`
18×	`pow-to-exp` `cbrt-undiv` `pow-exp`
13×	`div-inv`
11×	`associate-/r*`
7×	`associate-l`
5×	`cbrt-unprod`
4×	`pow1` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `unswap-sqr`
2×	`associate-/l/`
1×	`*-commutative`

Counts

4 → 304

Calls

4 calls:

20.0ms	(/ (cos (* 2.0 x)) (pow sin 2.0))
39.0ms	(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
21.0ms	(* (pow cos 2.0) x)
33.0ms	(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

series1.4s

Counts

4 → 12

Calls

4 calls:

298.0ms	(/ (cos (* 2.0 x)) (pow sin 2.0))
526.0ms	(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
264.0ms	(* (pow cos 2.0) x)
339.0ms	(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

simplify718.0ms

Counts

316 → 316

Iterations

Iter	Nodes
done	5000
1	1213
0	460

prune2.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.3b

localize51.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
9.8b	(* (/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))) (* (cbrt x) (cbrt x))) (pow cos 2.0)) (/ (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)) x))
13.4b	(/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))) (* (cbrt x) (cbrt x))) (pow cos 2.0))

rewrite25.1s

Algorithm

rewrite-expression-head

Rules

23294×	`times-frac`
10984×	`add-sqr-sqrt`
6035×	`*-un-lft-identity` `add-cube-cbrt`
6019×	`cbrt-prod`
4301×	`unpow-prod-down`
1999×	`associate-l`
1863×	`sqr-pow`
1540×	`add-exp-log`
1143×	`div-exp`
844×	`associate-r`
784×	`unswap-sqr`
309×	`prod-exp`
285×	`associate-/l*`
153×	`pow-to-exp` `pow-exp`
149×	`add-cbrt-cube`
144×	`div-inv`
143×	`cbrt-undiv`
47×	`cbrt-unprod`
15×	`associate-/r/`
7×	`associate-/r*`
6×	`pow1`
4×	`add-log-exp`
2×	`pow1/3`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

4 → 6235

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
23.4s	(* (/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))) (* (cbrt x) (cbrt x))) (pow cos 2.0)) (/ (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)) x))
242.0ms	(/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))) (* (cbrt x) (cbrt x))) (pow cos 2.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

288.0ms	(cbrt x)
251.0ms	(cbrt x)
533.0ms	(* (/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))) (* (cbrt x) (cbrt x))) (pow cos 2.0)) (/ (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)) x))
625.0ms	(/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))) (* (cbrt x) (cbrt x))) (pow cos 2.0))

simplify3.3s

Counts

6247 → 6247

Iterations

Iter	Nodes
done	7418
0	7418

prune1.3m

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 3.5b

localize63.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (pow sin (/ 2.0 2)))
0.6b	(cbrt (pow sin (/ 2.0 2)))
1.1b	(* (/ (/ (/ 1 (/ (* (cbrt (pow sin (/ 2.0 2))) (cbrt (pow sin (/ 2.0 2)))) 1)) (cbrt x)) (pow cos (/ 2.0 2))) (* (/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (cbrt (pow sin (/ 2.0 2))) (cbrt (cos (* 2.0 x))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)) x)))
4.2b	(* (/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (cbrt (pow sin (/ 2.0 2))) (cbrt (cos (* 2.0 x))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)) x))

rewrite2.0m

Algorithm

rewrite-expression-head

Rules

81646×	`times-frac`
41804×	`add-sqr-sqrt`
40959×	`cbrt-prod`
38786×	`add-exp-log`
30843×	`div-exp`
27710×	`*-un-lft-identity` `add-cube-cbrt`
17494×	`associate-l`
13840×	`unpow-prod-down`
9664×	`prod-exp`
5600×	`sqr-pow`
3304×	`pow-to-exp` `pow-exp`
2607×	`1-exp`
1888×	`unswap-sqr`
1185×	`rec-exp`
845×	`associate-r`
794×	`add-cbrt-cube`
784×	`cbrt-undiv`
500×	`div-inv`
287×	`cbrt-unprod`
84×	`associate-/r/`
11×	`pow1`
6×	`frac-times` `associate-*r/`
4×	`pow-prod-down` `associate-*l/` `add-log-exp`
2×	`pow1/3` `*-commutative`

Counts

4 → 24618

Calls

4 calls:

2.0ms	(cbrt (pow sin (/ 2.0 2)))
2.0ms	(cbrt (pow sin (/ 2.0 2)))
3.2s	(* (/ (/ (/ 1 (/ (* (cbrt (pow sin (/ 2.0 2))) (cbrt (pow sin (/ 2.0 2)))) 1)) (cbrt x)) (pow cos (/ 2.0 2))) (* (/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (cbrt (pow sin (/ 2.0 2))) (cbrt (cos (* 2.0 x))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)) x)))
1.9m	(* (/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (cbrt (pow sin (/ 2.0 2))) (cbrt (cos (* 2.0 x))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)) x))

series1.6s

Counts

4 → 12

Calls

4 calls:

342.0ms	(cbrt (pow sin (/ 2.0 2)))
335.0ms	(cbrt (pow sin (/ 2.0 2)))
403.0ms	(* (/ (/ (/ 1 (/ (* (cbrt (pow sin (/ 2.0 2))) (cbrt (pow sin (/ 2.0 2)))) 1)) (cbrt x)) (pow cos (/ 2.0 2))) (* (/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (cbrt (pow sin (/ 2.0 2))) (cbrt (cos (* 2.0 x))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)) x)))
541.0ms	(* (/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (cbrt (pow sin (/ 2.0 2))) (cbrt (cos (* 2.0 x))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)) x))

simplify5.7s

Counts

24630 → 24630

Iterations

Iter	Nodes
done	14182
0	14182

prune4.0m

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 0.4b

localize76.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (/ (/ (/ 1 (/ (* (cbrt (pow sin (/ 2.0 2))) (cbrt (pow sin (/ 2.0 2)))) 1)) (cbrt x)) (pow cos (/ 2.0 2))) (* (* (/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (cbrt (pow sin (/ 2.0 2))) (cbrt (cos (* 2.0 x))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (* (cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x))) (cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))) (* (cbrt x) (cbrt x)))) (/ (cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x))) (cbrt x))))
4.7b	(cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))
4.7b	(cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))
4.7b	(cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))

rewrite15.6s

Algorithm

rewrite-expression-head

Rules

72917×	`add-exp-log`
46385×	`div-exp`
28342×	`prod-exp`
5056×	`times-frac`
4389×	`1-exp`
4341×	`pow-to-exp` `pow-exp`
2178×	`cbrt-prod`
2049×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
1995×	`rec-exp`
1753×	`add-cbrt-cube`
1738×	`cbrt-undiv`
1223×	`cbrt-unprod`
1124×	`associate-l`
804×	`unpow-prod-down`
268×	`sqr-pow`
197×	`div-inv`
42×	`associate-/r/`
17×	`frac-times`
13×	`pow1` `associate-*r/`
11×	`associate-*l/`
6×	`pow-prod-down`
4×	`add-log-exp`
3×	`cbrt-div` `pow1/3`
1×	`associate-r` `*-commutative`

Counts

4 → 9252

Calls

4 calls:

13.5s	(* (/ (/ (/ 1 (/ (* (cbrt (pow sin (/ 2.0 2))) (cbrt (pow sin (/ 2.0 2)))) 1)) (cbrt x)) (pow cos (/ 2.0 2))) (* (* (/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (cbrt (pow sin (/ 2.0 2))) (cbrt (cos (* 2.0 x))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (* (cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x))) (cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))) (* (cbrt x) (cbrt x)))) (/ (cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x))) (cbrt x))))
18.0ms	(cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))
18.0ms	(cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))
20.0ms	(cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))

series1.3s

Counts

4 → 12

Calls

4 calls:

322.0ms	(* (/ (/ (/ 1 (/ (* (cbrt (pow sin (/ 2.0 2))) (cbrt (pow sin (/ 2.0 2)))) 1)) (cbrt x)) (pow cos (/ 2.0 2))) (* (* (/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (cbrt (pow sin (/ 2.0 2))) (cbrt (cos (* 2.0 x))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (* (cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x))) (cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))) (* (cbrt x) (cbrt x)))) (/ (cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x))) (cbrt x))))
308.0ms	(cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))
309.0ms	(cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))
313.0ms	(cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))

simplify2.9s

Counts

9264 → 9264

Iterations

Iter	Nodes
done	6232
0	6232

prune1.1m

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 0.4b

regimes1.5s

Accuracy

0% (2.5b remaining)

Error of 2.8b against oracle of 0.2b and baseline of 2.8b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	39
1	39
0	33

end0.0ms

sample2.4s

Algorithm

intervals

Results

717.0ms	9119×	body	80	valid
647.0ms	784×	body	1280	valid
415.0ms	965×	body	640	valid
146.0ms	598×	body	320	valid
43.0ms	311×	body	160	valid