Details

sample63.0ms

Algorithm

intervals

Results

21.0ms	292×	body	80	valid
10.0ms	33×	body	640	valid
8.0ms	20×	body	1280	valid
4.0ms	17×	body	320	valid
2.0ms	15×	body	160	valid

simplify862.0ms

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (cos (* 2.0 x)) (pow sin 2.0))
5.6b	(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
6.3b	(* (pow cos 2.0) x)
19.5b	(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

rewrite130.0ms

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:

18.0ms	(/ (cos (* 2.0 x)) (pow sin 2.0))
46.0ms	(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
13.0ms	(* (pow cos 2.0) x)
34.0ms	(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

221.0ms	(/ (cos (* 2.0 x)) (pow sin 2.0))
359.0ms	(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
204.0ms	(* (pow cos 2.0) x)
278.0ms	(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

simplify568.0ms

Counts

316 → 316

Iterations

Iter	Nodes
done	5000
1	1213
0	460

prune1.8s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.6b	(* (cbrt x) (cbrt x))
8.6b	(* (/ (/ (/ (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))
12.0b	(/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))) (* (cbrt x) (cbrt x))) (pow cos 2.0))

rewrite25.0s

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))
23.3s	(* (/ (/ (/ (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))
541.0ms	(/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))) (* (cbrt x) (cbrt x))) (pow cos 2.0))

series1.8s

Counts

4 → 12

Calls

4 calls:

292.0ms	(cbrt x)
347.0ms	(* (cbrt x) (cbrt x))
524.0ms	(* (/ (/ (/ (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))
649.0ms	(/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))) (* (cbrt x) (cbrt x))) (pow cos 2.0))

simplify3.2s

Counts

6276 → 6276

Iterations

Iter	Nodes
done	7447
0	7447

prune1.4m

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 2.0b

localize204.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))
0.5b	(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)))))) (cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))))
3.4b	(* (/ (/ (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))

rewrite2.0m

Algorithm

rewrite-expression-head

Rules

62200×	`times-frac`
38568×	`cbrt-prod`
33556×	`add-sqr-sqrt`
20736×	`*-un-lft-identity` `add-cube-cbrt`
12244×	`associate-l`
12072×	`unpow-prod-down`
4984×	`sqr-pow`
1856×	`unswap-sqr`
1128×	`associate-r`
366×	`div-inv`
284×	`swap-sqr`
209×	`add-exp-log`
138×	`div-exp`
48×	`associate-/r/`
43×	`prod-exp`
41×	`add-cbrt-cube`
30×	`cbrt-undiv`
19×	`pow-to-exp` `pow-exp`
13×	`pow1` `cbrt-unprod`
8×	`pow1/3`
6×	`cbrt-div`
4×	`add-log-exp`
3×	`pow-prod-down`
2×	`frac-times` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow2` `pow-plus`

Counts

4 → 16179

Calls

4 calls:

22.0ms	(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))))))
875.0ms	(* (cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))) (cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))))
1.9m	(* (/ (/ (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:

247.0ms	(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))))))
261.0ms	(* (cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))) (cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))))
677.0ms	(* (/ (/ (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))

simplify3.7s

Counts

16191 → 16191

Iterations

Iter	Nodes
done	11578
0	11578

prune3.0m

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 0.3b

localize175.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (pow sin (/ 2.0 2)))
0.6b	(cbrt (pow sin (/ 2.0 2)))
0.6b	(cbrt (* (cbrt x) (cbrt x)))
1.3b	(* (* (/ (/ (cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (/ (* (cbrt (cbrt (cos (* 2.0 x)))) (cbrt (cbrt (cos (* 2.0 x))))) (* (cbrt (pow sin (/ 2.0 2))) (cbrt (pow sin (/ 2.0 2))))) (cbrt (* (cbrt x) (cbrt x)))) 1)) (/ (/ (/ (cbrt (cbrt (cos (* 2.0 x)))) (cbrt (pow sin (/ 2.0 2)))) (cbrt (cbrt x))) x))

rewrite3.8s

Algorithm

rewrite-expression-head

Rules

7518×	`times-frac`
6684×	`cbrt-prod`
3274×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
2916×	`add-exp-log`
2554×	`associate-r`
1860×	`div-exp`
956×	`prod-exp`
735×	`unpow-prod-down`
408×	`add-cbrt-cube`
396×	`cbrt-undiv`
245×	`sqr-pow`
220×	`cbrt-unprod`
168×	`1-exp`
104×	`pow-to-exp` `pow-exp`
31×	`div-inv`
9×	`pow1`
5×	`frac-times` `associate-*l/`
4×	`add-log-exp`
3×	`pow1/3` `pow-prod-down` `associate-*r/`
1×	`associate-l` `*-commutative`

Counts

4 → 3067

Calls

4 calls:

2.0ms	(cbrt (pow sin (/ 2.0 2)))
2.0ms	(cbrt (pow sin (/ 2.0 2)))
4.0ms	(cbrt (* (cbrt x) (cbrt x)))
3.5s	(* (* (/ (/ (cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (/ (* (cbrt (cbrt (cos (* 2.0 x)))) (cbrt (cbrt (cos (* 2.0 x))))) (* (cbrt (pow sin (/ 2.0 2))) (cbrt (pow sin (/ 2.0 2))))) (cbrt (* (cbrt x) (cbrt x)))) 1)) (/ (/ (/ (cbrt (cbrt (cos (* 2.0 x)))) (cbrt (pow sin (/ 2.0 2)))) (cbrt (cbrt x))) x))

series1.7s

Counts

4 → 12

Calls

4 calls:

351.0ms	(cbrt (pow sin (/ 2.0 2)))
350.0ms	(cbrt (pow sin (/ 2.0 2)))
272.0ms	(cbrt (* (cbrt x) (cbrt x)))
688.0ms	(* (* (/ (/ (cbrt (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (/ (* (cbrt (cbrt (cos (* 2.0 x)))) (cbrt (cbrt (cos (* 2.0 x))))) (* (cbrt (pow sin (/ 2.0 2))) (cbrt (pow sin (/ 2.0 2))))) (cbrt (* (cbrt x) (cbrt x)))) 1)) (/ (/ (/ (cbrt (cbrt (cos (* 2.0 x)))) (cbrt (pow sin (/ 2.0 2)))) (cbrt (cbrt x))) x))

simplify1.5s

Counts

3079 → 3079

Iterations

Iter	Nodes
done	6756
0	6756

prune39.0s

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 0.3b

regimes1.4s

Accuracy

0% (1.8b remaining)

Error of 2.2b against oracle of 0.5b and baseline of 2.2b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	43
1	43
0	37

end0.0ms

sample2.3s

Algorithm

intervals

Results

855.0ms	9056×	body	80	valid
608.0ms	1005×	body	640	valid
404.0ms	780×	body	1280	valid
111.0ms	537×	body	320	valid
47.0ms	330×	body	160	valid