Details

sample124.0ms

Algorithm

intervals

Results

35.0ms	284×	body	80	valid
27.0ms	21×	body	320	valid
18.0ms	26×	body	1280	valid
15.0ms	32×	body	640	valid
3.0ms	13×	body	160	valid

simplify995.0ms

Counts

1 → 1

Iterations

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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.5b

localize34.0ms

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))

rewrite110.0ms

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:

16.0ms	(/ (cos (* 2.0 x)) (pow sin 2.0))
44.0ms	(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
10.0ms	(* (pow cos 2.0) x)
23.0ms	(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

series1.4s

Counts

4 → 12

Calls

4 calls:

295.0ms	(/ (cos (* 2.0 x)) (pow sin 2.0))
450.0ms	(/ (/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x)) x)
271.0ms	(* (pow cos 2.0) x)
358.0ms	(/ (/ (cos (* 2.0 x)) (pow sin 2.0)) (* (pow cos 2.0) x))

simplify587.0ms

Counts

316 → 316

Iterations

Iter	Nodes
done	5000
1	1213
0	460

prune2.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.3b

localize71.0ms

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))

rewrite27.9s

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)
26.1s	(* (/ (/ (/ (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))
238.0ms	(/ (/ (/ (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:

269.0ms	(cbrt x)
310.0ms	(cbrt x)
480.0ms	(* (/ (/ (/ (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))
632.0ms	(/ (/ (/ (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

prune1.2m

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 3.5b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.3m

Algorithm

rewrite-expression-head

Rules

96766×	`times-frac`
47538×	`add-sqr-sqrt`
39158×	`add-exp-log`
38482×	`cbrt-prod`
33444×	`*-un-lft-identity` `add-cube-cbrt`
32430×	`div-exp`
21400×	`associate-l`
21184×	`unpow-prod-down`
8590×	`prod-exp`
6912×	`sqr-pow`
5200×	`pow-exp`
4510×	`pow-to-exp`
1888×	`unswap-sqr`
1380×	`1-exp`
845×	`associate-r`
645×	`add-cbrt-cube`
630×	`cbrt-undiv`
626×	`div-inv`
225×	`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 → 28333

Calls

4 calls:

1.0ms	(cbrt sin)
1.0ms	(cbrt sin)
4.7s	(* (/ (/ (/ (cbrt 1) (/ (pow (* (cbrt sin) (cbrt sin)) (/ 2.0 2)) 1)) (cbrt x)) (pow cos (/ 2.0 2))) (* (/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow (cbrt 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)))
2.2m	(* (/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow (cbrt 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:

180.0ms	(cbrt sin)
179.0ms	(cbrt sin)
445.0ms	(* (/ (/ (/ (cbrt 1) (/ (pow (* (cbrt sin) (cbrt sin)) (/ 2.0 2)) 1)) (cbrt x)) (pow cos (/ 2.0 2))) (* (/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow (cbrt 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)))
554.0ms	(* (/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow (cbrt 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))

simplify6.6s

Counts

28345 → 28345

Iterations

Iter	Nodes
done	16384
0	16384

prune5.2m

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 0.4b

localize81.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.5s

Algorithm

rewrite-expression-head

Rules

72579×	`add-exp-log`
48794×	`div-exp`
25876×	`prod-exp`
20176×	`times-frac`
7785×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
7499×	`pow-exp`
6525×	`cbrt-prod`
6341×	`pow-to-exp`
5030×	`associate-l`
3234×	`unpow-prod-down`
2316×	`1-exp`
1582×	`sqr-pow`
1379×	`add-cbrt-cube`
1360×	`cbrt-undiv`
975×	`cbrt-unprod`
323×	`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 → 12751

Calls

4 calls:

15.8s	(* (/ (/ (/ (cbrt 1) (/ (pow (* (cbrt sin) (cbrt sin)) (/ 2.0 2)) 1)) (cbrt x)) (pow cos (/ 2.0 2))) (* (* (/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow (cbrt 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))))
20.0ms	(cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))
22.0ms	(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)))

series1.4s

Counts

4 → 12

Calls

4 calls:

431.0ms	(* (/ (/ (/ (cbrt 1) (/ (pow (* (cbrt sin) (cbrt sin)) (/ 2.0 2)) 1)) (cbrt x)) (pow cos (/ 2.0 2))) (* (* (/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow (cbrt 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))))
320.0ms	(cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))
321.0ms	(cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))
328.0ms	(cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))

simplify3.9s

Counts

12763 → 12763

Iterations

Iter	Nodes
done	7860
0	7860

Details

sample124.0ms

simplify995.0ms

prune25.0ms

localize34.0ms

rewrite110.0ms

series1.4s

simplify587.0ms

prune2.6s

localize71.0ms

rewrite27.9s

series1.7s

simplify3.3s

prune1.2m

localize61.0ms

rewrite2.3m

series1.4s

simplify6.6s

prune5.2m

localize81.0ms

rewrite18.5s

series1.4s

simplify3.9s

prune2.0s