Details

sample1.0s

Algorithm

intervals

Results

279.0ms	82×	body	2560	valid
276.0ms	33×	body	5120	valid
241.0ms	128×	body	1280	valid
167.0ms	85×	body	640	valid
21.0ms	24×	body	320	valid
18.0ms	61×	body	80	valid
8.0ms	15×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
4	7847
3	994
2	173
1	51
0	19

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.9b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 2 (tan k))
2.8b	(/ (/ 2 (tan k)) (* (/ t l) t))
2.8b	(* (/ t l) (sin k))
29.9b	(/ (/ (/ (/ 2 (tan k)) (* (/ t l) t)) (* (/ t l) (sin k))) (* (/ k t) (/ k t)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

863×	`add-cbrt-cube` `add-exp-log`
516×	`cbrt-undiv` `div-exp`
224×	`prod-exp` `cbrt-unprod`
159×	`times-frac`
57×	`add-sqr-sqrt`
52×	`*-un-lft-identity` `add-cube-cbrt`
41×	`associate-/l*`
13×	`associate-l` `associate-/r/`
12×	`div-inv`
7×	`associate-*l/`
6×	`pow1`
5×	`associate-/r*` `tan-quot`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r`
2×	`unswap-sqr` `associate-/l/`
1×	`frac-times` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 400

Calls

4 calls:

6.0ms	(/ 2 (tan k))
18.0ms	(/ (/ 2 (tan k)) (* (/ t l) t))
15.0ms	(* (/ t l) (sin k))
67.0ms	(/ (/ (/ (/ 2 (tan k)) (* (/ t l) t)) (* (/ t l) (sin k))) (* (/ k t) (/ k t)))

series543.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 2 (tan k))
144.0ms	(/ (/ 2 (tan k)) (* (/ t l) t))
84.0ms	(* (/ t l) (sin k))
277.0ms	(/ (/ (/ (/ 2 (tan k)) (* (/ t l) t)) (* (/ t l) (sin k))) (* (/ k t) (/ k t)))

simplify2.8s

Counts

412 → 412

Iterations

Iter	Nodes
2	7652
1	1848
0	657

prune5.5s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.9b

localize80.0ms

Local error

Found 4 expressions with local error:

2.6b	(/ (/ (sqrt 2) (/ t l)) (* (/ t l) (/ k t)))
10.2b	(* (/ (/ (sqrt 2) (/ t l)) (* (/ t l) (/ k t))) (/ (/ (/ (/ (sqrt 2) (tan k)) t) (sin k)) (/ k t)))
11.3b	(/ (/ (/ (/ (sqrt 2) (tan k)) t) (sin k)) (/ k t))
13.9b	(* (/ t l) (/ k t))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

26314×	`times-frac`
10524×	`add-sqr-sqrt`
10457×	`*-un-lft-identity` `add-cube-cbrt`
2917×	`associate-r`
2306×	`sqrt-prod`
1275×	`add-cbrt-cube` `add-exp-log`
832×	`cbrt-undiv` `div-exp`
825×	`div-inv`
306×	`associate-/l*`
268×	`prod-exp` `cbrt-unprod`
254×	`associate-/r/`
243×	`tan-quot`
103×	`associate-l`
15×	`unswap-sqr`
14×	`associate-/r*`
8×	`pow1`
4×	`frac-times` `associate-l/` `associate-r/` `insert-posit16` `add-log-exp`
2×	`clear-num` `frac-2neg` `pow-prod-down` `*-commutative` `associate-/l/`

Counts

4 → 6733

Calls

4 calls:

33.0ms	(/ (/ (sqrt 2) (/ t l)) (* (/ t l) (/ k t)))
365.0ms	(* (/ (/ (sqrt 2) (/ t l)) (* (/ t l) (/ k t))) (/ (/ (/ (/ (sqrt 2) (tan k)) t) (sin k)) (/ k t)))
48.0ms	(/ (/ (/ (/ (sqrt 2) (tan k)) t) (sin k)) (/ k t))
34.0ms	(* (/ t l) (/ k t))

series1.5s

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (/ (sqrt 2) (/ t l)) (* (/ t l) (/ k t)))
612.0ms	(* (/ (/ (sqrt 2) (/ t l)) (* (/ t l) (/ k t))) (/ (/ (/ (/ (sqrt 2) (tan k)) t) (sin k)) (/ k t)))
715.0ms	(/ (/ (/ (/ (sqrt 2) (tan k)) t) (sin k)) (/ k t))
38.0ms	(* (/ t l) (/ k t))

simplify51.5s

Counts

6745 → 6745

Iterations

Iter	Nodes
1	32958
0	8544

prune2.2m

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.9b

localize77.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (/ (* (/ (sqrt 2) (/ t l)) (/ (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sin k))) (cbrt (sin k))) k)) (* (/ k t) (/ t l))) (/ (/ (/ (/ (cbrt (sqrt 2)) (tan k)) t) (cbrt (sin k))) (/ 1 t)))
1.7b	(/ (/ (/ (/ (cbrt (sqrt 2)) (tan k)) t) (cbrt (sin k))) (/ 1 t))
7.1b	(* (/ (sqrt 2) (/ t l)) (/ (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sin k))) (cbrt (sin k))) k))
13.9b	(* (/ k t) (/ t l))

rewrite3.0s

Algorithm

rewrite-expression-head

Rules

72354×	`times-frac`
29130×	`add-sqr-sqrt`
28752×	`*-un-lft-identity`
28741×	`add-cube-cbrt`
17044×	`cbrt-prod`
15105×	`add-exp-log`
10000×	`div-exp`
8066×	`associate-r`
6475×	`add-cbrt-cube`
5200×	`cbrt-undiv`
4435×	`sqrt-prod`
4017×	`prod-exp`
2137×	`cbrt-unprod`
1918×	`div-inv`
604×	`associate-/l*`
492×	`associate-/r/`
486×	`tan-quot`
328×	`rec-exp` `1-exp`
104×	`associate-l`
78×	`unswap-sqr`
13×	`associate-/r*`
10×	`pow1`
4×	`frac-times` `associate-l/` `associate-r/` `insert-posit16` `add-log-exp`
3×	`pow-prod-down` `*-commutative`
1×	`clear-num` `frac-2neg` `associate-/l/`

Counts

4 → 18937

Calls

4 calls:

488.0ms	(* (/ (* (/ (sqrt 2) (/ t l)) (/ (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sin k))) (cbrt (sin k))) k)) (* (/ k t) (/ t l))) (/ (/ (/ (/ (cbrt (sqrt 2)) (tan k)) t) (cbrt (sin k))) (/ 1 t)))
58.0ms	(/ (/ (/ (/ (cbrt (sqrt 2)) (tan k)) t) (cbrt (sin k))) (/ 1 t))
97.0ms	(* (/ (sqrt 2) (/ t l)) (/ (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sin k))) (cbrt (sin k))) k))
18.0ms	(* (/ k t) (/ t l))

series1.6s

Counts

4 → 12

Calls

4 calls:

568.0ms	(* (/ (* (/ (sqrt 2) (/ t l)) (/ (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sin k))) (cbrt (sin k))) k)) (* (/ k t) (/ t l))) (/ (/ (/ (/ (cbrt (sqrt 2)) (tan k)) t) (cbrt (sin k))) (/ 1 t)))
301.0ms	(/ (/ (/ (/ (cbrt (sqrt 2)) (tan k)) t) (cbrt (sin k))) (/ 1 t))
722.0ms	(* (/ (sqrt 2) (/ t l)) (/ (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sin k))) (cbrt (sin k))) k))
17.0ms	(* (/ k t) (/ t l))

simplify6.6m

Iterations

Iter	Nodes
0	20326