Details

sample70.0ms

Algorithm

intervals

Results

22.0ms	288×	body	80	valid
11.0ms	28×	body	1280	valid
10.0ms	35×	body	640	valid
4.0ms	20×	body	320	valid
2.0ms	10×	body	160	valid

simplify996.0ms

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: 24.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (cos (* 2.0 x)) (pow sin 2.0))
6.0b	(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
8.3b	(* (pow cos 2.0) x)
15.6b	(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

rewrite161.0ms

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:

24.0ms	(/ (cos (* 2.0 x)) (pow sin 2.0))
42.0ms	(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
19.0ms	(* (pow cos 2.0) x)
42.0ms	(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

series1.7s

Counts

4 → 12

Calls

4 calls:

279.0ms	(/ (cos (* 2.0 x)) (pow sin 2.0))
864.0ms	(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
206.0ms	(* (pow cos 2.0) x)
330.0ms	(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

simplify649.0ms

Counts

316 → 316

Iterations

Iter	Nodes
done	5000
1	1213
0	460

prune2.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.7b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(* (cbrt x) (cbrt x))
10.0b	(* (/ (/ (/ (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))

rewrite24.7s

Algorithm

rewrite-expression-head

Rules

23294×	`times-frac`
10999×	`add-sqr-sqrt`
6042×	`*-un-lft-identity` `add-cube-cbrt`
6032×	`cbrt-prod`
4301×	`unpow-prod-down`
2005×	`associate-l`
1863×	`sqr-pow`
1542×	`add-exp-log`
1143×	`div-exp`
850×	`associate-r`
788×	`unswap-sqr`
310×	`prod-exp`
285×	`associate-/l*`
153×	`pow-to-exp` `pow-exp`
149×	`add-cbrt-cube`
144×	`div-inv`
143×	`cbrt-undiv`
48×	`cbrt-unprod`
15×	`associate-/r/`
13×	`pow1`
7×	`associate-/r*` `pow1/3`
6×	`swap-sqr`
4×	`add-log-exp`
3×	`pow-prod-down`
2×	`pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow2` `frac-times` `clear-num` `frac-2neg` `pow-plus` `associate-l/` `associate-r/` `associate-/l/`

Counts

4 → 6264

Calls

4 calls:

1.0ms	(cbrt x)
18.0ms	(* (cbrt x) (cbrt x))
23.2s	(* (/ (/ (/ (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))
208.0ms	(/ (/ (/ (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:

292.0ms	(cbrt x)
323.0ms	(* (cbrt x) (cbrt x))
496.0ms	(* (/ (/ (/ (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))
593.0ms	(/ (/ (/ (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

6276 → 6276

Iterations

Iter	Nodes
done	7447
0	7447

prune1.3m

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 2.7b

localize63.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))
0.6b	(cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))
0.6b	(cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))
4.1b	(* (/ (/ (cbrt (/ (cbrt (cos (* 2.0 x))) (/ (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))

rewrite1.5m

Algorithm

rewrite-expression-head

Rules

59784×	`times-frac`
36037×	`cbrt-prod`
31571×	`add-sqr-sqrt`
19967×	`*-un-lft-identity` `add-cube-cbrt`
11960×	`associate-l`
11620×	`unpow-prod-down`
4748×	`sqr-pow`
1600×	`unswap-sqr`
844×	`associate-r`
345×	`div-inv`
207×	`add-exp-log`
138×	`div-exp`
45×	`associate-/r/`
42×	`prod-exp`
41×	`add-cbrt-cube`
30×	`cbrt-undiv`
19×	`pow-to-exp` `pow-exp`
12×	`cbrt-unprod`
6×	`pow1`
4×	`add-log-exp`
3×	`cbrt-div` `pow1/3`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 15340

Calls

4 calls:

19.0ms	(cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))
32.0ms	(cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))
19.0ms	(cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))
1.5m	(* (/ (/ (cbrt (/ (cbrt (cos (* 2.0 x))) (/ (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))

series1.4s

Counts

4 → 12

Calls

4 calls:

248.0ms	(cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))
247.0ms	(cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))
248.0ms	(cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))
668.0ms	(* (/ (/ (cbrt (/ (cbrt (cos (* 2.0 x))) (/ (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))

simplify3.6s

Counts

15352 → 15352

Iterations

Iter	Nodes
done	10544
0	10544

prune3.0m

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 0.5b

localize88.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.6b	(cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))
0.6b	(cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))
0.6b	(cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

1651×	`cbrt-prod`
1584×	`times-frac`
785×	`add-sqr-sqrt`
777×	`*-un-lft-identity` `add-cube-cbrt`
324×	`unpow-prod-down`
108×	`sqr-pow`
21×	`div-inv`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`cbrt-div` `associate-/r/`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 910

Calls

4 calls:

8.0ms	(* (cbrt x) (cbrt x))
21.0ms	(cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))
19.0ms	(cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))
19.0ms	(cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))

series986.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(* (cbrt x) (cbrt x))
260.0ms	(cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))
259.0ms	(cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))
261.0ms	(cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))

simplify823.0ms

Counts

922 → 922

Iterations

Iter	Nodes
done	5000
1	1821
0	917

prune7.1s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 0.5b

regimes1.3s

Accuracy

0% (1.6b remaining)

Error of 2.2b against oracle of 0.6b and baseline of 2.2b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	41
1	41
0	37

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.1s	9036×	body	80	valid
412.0ms	830×	body	1280	valid
309.0ms	998×	body	640	valid
203.0ms	576×	body	320	valid
46.0ms	326×	body	160	valid