Details

sample126.0ms

Algorithm

intervals

Results

49.0ms	285×	body	80	valid
21.0ms	28×	body	1280	valid
14.0ms	25×	body	640	valid
7.0ms	17×	body	320	valid
3.0ms	10×	body	160	valid

simplify1.0s

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (cos (* 2.0 x)) (pow sin 2.0))
5.6b	(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
9.4b	(* (pow cos 2.0) x)
17.6b	(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

rewrite137.0ms

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:

17.0ms	(/ (cos (* 2.0 x)) (pow sin 2.0))
50.0ms	(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
12.0ms	(* (pow cos 2.0) x)
43.0ms	(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

series1.3s

Counts

4 → 12

Calls

4 calls:

281.0ms	(/ (cos (* 2.0 x)) (pow sin 2.0))
449.0ms	(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
266.0ms	(* (pow cos 2.0) x)
335.0ms	(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

simplify666.0ms

Counts

316 → 316

Iterations

Iter	Nodes
done	5000
1	1213
0	460

prune2.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.9b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
10.7b	(* (/ (/ (/ (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))
11.3b	(/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))) (* (cbrt x) (cbrt x))) (pow cos 2.0))

rewrite26.2s

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)
24.6s	(* (/ (/ (/ (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))
263.0ms	(/ (/ (/ (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:

311.0ms	(cbrt x)
271.0ms	(cbrt x)
486.0ms	(* (/ (/ (/ (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))
605.0ms	(/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))) (* (cbrt x) (cbrt x))) (pow cos 2.0))

simplify3.4s

Counts

6247 → 6247

Iterations

Iter	Nodes
done	7418
0	7418

prune1.3m

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 2.2b

localize62.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))
0.6b	(cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))
1.4b	(* (/ (/ (/ (cbrt 1) (* (cbrt (/ (pow sin (/ 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))) (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)))
4.7b	(* (/ (/ (/ (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))

rewrite1.8m

Algorithm

rewrite-expression-head

Rules

62302×	`times-frac`
35544×	`cbrt-prod`
32958×	`add-sqr-sqrt`
20588×	`*-un-lft-identity` `add-cube-cbrt`
13168×	`associate-l`
11904×	`unpow-prod-down`
6876×	`add-exp-log`
4880×	`sqr-pow`
4839×	`div-exp`
1816×	`prod-exp`
1696×	`unswap-sqr`
845×	`associate-r`
636×	`pow-to-exp` `pow-exp`
457×	`add-cbrt-cube`
441×	`cbrt-undiv`
376×	`div-inv`
212×	`cbrt-div`
198×	`cbrt-unprod`
168×	`associate-/r/`
48×	`frac-times` `associate-*r/`
46×	`associate-*l/`
11×	`pow1`
4×	`pow-prod-down` `add-log-exp`
2×	`pow1/3` `*-commutative`

Counts

4 → 16802

Calls

4 calls:

6.0ms	(cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))
6.0ms	(cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))
2.7s	(* (/ (/ (/ (cbrt 1) (* (cbrt (/ (pow sin (/ 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))) (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)))
1.7m	(* (/ (/ (/ (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))

series1.7s

Counts

4 → 12

Calls

4 calls:

280.0ms	(cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))
282.0ms	(cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))
414.0ms	(* (/ (/ (/ (cbrt 1) (* (cbrt (/ (pow sin (/ 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))) (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)))
681.0ms	(* (/ (/ (/ (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))

simplify4.3s

Counts

16814 → 16814

Iterations

Iter	Nodes
done	11270
0	11270

prune3.1m

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 0.1b

localize77.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))))
0.6b	(cbrt (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))))
0.6b	(cbrt (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))))
1.4b	(* (/ (/ (/ (cbrt 1) (* (cbrt (/ (pow sin (/ 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))) (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 (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))))) (cbrt 1)) (* (cbrt x) (cbrt x)))) (/ (/ (cbrt (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2)))) (cbrt x)) (cbrt x))))

rewrite11.1s

Algorithm

rewrite-expression-head

Rules

29345×	`add-exp-log`
17361×	`div-exp`
10873×	`prod-exp`
2457×	`cbrt-undiv`
2128×	`add-cbrt-cube`
1683×	`cbrt-unprod`
1675×	`pow-to-exp` `pow-exp`
1498×	`times-frac`
600×	`cbrt-prod`
578×	`associate-l`
565×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
300×	`unpow-prod-down`
171×	`cbrt-div`
126×	`associate-/r/`
100×	`sqr-pow`
59×	`frac-times`
55×	`associate-*r/`
53×	`associate-*l/` `div-inv`
13×	`pow1`
6×	`pow-prod-down`
4×	`add-log-exp`
3×	`pow1/3`
1×	`associate-r` `*-commutative`

Counts

4 → 3992

Calls

4 calls:

5.0ms	(cbrt (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))))
5.0ms	(cbrt (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))))
5.0ms	(cbrt (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))))
10.1s	(* (/ (/ (/ (cbrt 1) (* (cbrt (/ (pow sin (/ 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))) (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 (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))))) (cbrt 1)) (* (cbrt x) (cbrt x)))) (/ (/ (cbrt (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2)))) (cbrt x)) (cbrt x))))

series1.0s

Counts

4 → 12

Calls

4 calls:

230.0ms	(cbrt (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))))
230.0ms	(cbrt (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))))
229.0ms	(cbrt (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))))
332.0ms	(* (/ (/ (/ (cbrt 1) (* (cbrt (/ (pow sin (/ 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))) (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 (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))))) (cbrt 1)) (* (cbrt x) (cbrt x)))) (/ (/ (cbrt (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2)))) (cbrt x)) (cbrt x))))

simplify1.4s

Counts

4004 → 4004

Iterations

Iter	Nodes
done	5001
0	3071

prune13.5s

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 0.1b

regimes1.3s

Accuracy

0% (1.7b remaining)

Error of 2.0b against oracle of 0.3b and baseline of 2.0b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	40
1	40
0	34

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.4s	9053×	body	80	valid
384.0ms	825×	body	1280	valid
287.0ms	900×	body	640	valid
150.0ms	578×	body	320	valid
78.0ms	323×	body	160	valid