Details

sample859.0ms

Algorithm

intervals

Results

253.0ms	79×	body	2560	valid
220.0ms	125×	body	1280	valid
193.0ms	29×	body	5120	valid
119.0ms	87×	body	640	valid
25.0ms	36×	body	320	valid
16.0ms	74×	body	80	valid
7.0ms	15×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	1013
2	173
1	51
0	19

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.7b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ l t) (/ l t))
1.3b	(/ t (* (/ l t) (/ l t)))
3.0b	(/ (/ 2 (/ t (* (/ l t) (/ l t)))) (* (tan k) (sin k)))
27.4b	(/ (/ (/ 2 (/ t (* (/ l t) (/ l t)))) (* (tan k) (sin k))) (* (/ k t) (/ k t)))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

672×	`add-cbrt-cube` `add-exp-log`
412×	`cbrt-undiv` `div-exp`
344×	`times-frac`
158×	`prod-exp` `cbrt-unprod`
116×	`add-sqr-sqrt`
104×	`*-un-lft-identity` `add-cube-cbrt`
78×	`associate-/l*`
49×	`associate-/r/`
25×	`div-inv`
18×	`associate-*l/`
15×	`frac-times` `associate-*r/`
13×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
4×	`insert-posit16` `add-log-exp` `unswap-sqr`
3×	`clear-num` `associate-/r*` `frac-2neg` `tan-quot`
2×	`associate-/l/`
1×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 457

Calls

4 calls:

17.0ms	(* (/ l t) (/ l t))
13.0ms	(/ t (* (/ l t) (/ l t)))
35.0ms	(/ (/ 2 (/ t (* (/ l t) (/ l t)))) (* (tan k) (sin k)))
78.0ms	(/ (/ (/ 2 (/ t (* (/ l t) (/ l t)))) (* (tan k) (sin k))) (* (/ k t) (/ k t)))

series799.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (/ l t) (/ l t))
41.0ms	(/ t (* (/ l t) (/ l t)))
329.0ms	(/ (/ 2 (/ t (* (/ l t) (/ l t)))) (* (tan k) (sin k)))
391.0ms	(/ (/ (/ 2 (/ t (* (/ l t) (/ l t)))) (* (tan k) (sin k))) (* (/ k t) (/ k t)))

simplify1.8s

Counts

469 → 469

Iterations

Iter	Nodes
done	5000
1	2153
0	708

prune2.5s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.3b

localize110.0ms

Local error

Found 4 expressions with local error:

1.7b	(/ (/ (sqrt 2) (/ (* (cbrt t) (cbrt t)) (/ l t))) (tan k))
2.1b	(/ (/ (sqrt 2) (/ (cbrt t) (/ l t))) (sin k))
14.9b	(/ (/ (/ (sqrt 2) (/ (cbrt t) (/ l t))) (sin k)) (/ k t))
18.1b	(/ (/ (/ (sqrt 2) (/ (* (cbrt t) (cbrt t)) (/ l t))) (tan k)) (/ k t))

rewrite3.7s

Algorithm

rewrite-expression-head

Rules

138972×	`times-frac`
52923×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
13938×	`sqrt-prod`
10764×	`cbrt-prod`
4467×	`div-inv`
2473×	`associate-/l*`
661×	`associate-/r/`
161×	`add-exp-log`
143×	`add-cbrt-cube`
117×	`cbrt-undiv` `div-exp`
32×	`associate-/r*`
15×	`tan-quot`
6×	`prod-exp` `cbrt-unprod`
4×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp` `associate-/l/`

Counts

4 → 28613

Calls

4 calls:

52.0ms	(/ (/ (sqrt 2) (/ (* (cbrt t) (cbrt t)) (/ l t))) (tan k))
39.0ms	(/ (/ (sqrt 2) (/ (cbrt t) (/ l t))) (sin k))
129.0ms	(/ (/ (/ (sqrt 2) (/ (cbrt t) (/ l t))) (sin k)) (/ k t))
61.0ms	(/ (/ (/ (sqrt 2) (/ (* (cbrt t) (cbrt t)) (/ l t))) (tan k)) (/ k t))

series1.8s

Counts

4 → 12

Calls

4 calls:

446.0ms	(/ (/ (sqrt 2) (/ (* (cbrt t) (cbrt t)) (/ l t))) (tan k))
337.0ms	(/ (/ (sqrt 2) (/ (cbrt t) (/ l t))) (sin k))
408.0ms	(/ (/ (/ (sqrt 2) (/ (cbrt t) (/ l t))) (sin k)) (/ k t))
568.0ms	(/ (/ (/ (sqrt 2) (/ (* (cbrt t) (cbrt t)) (/ l t))) (tan k)) (/ k t))

simplify47.9s

Counts

28625 → 28625

Iterations

Iter	Nodes
done	35045
0	35045

prune4.0m

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.2b

localize64.0ms

Local error

Found 4 expressions with local error:

2.1b	(/ (/ (sqrt 2) (/ (cbrt t) (/ l t))) (sin k))
2.5b	(/ (/ l t) (tan k))
4.5b	(/ (/ (/ l t) (tan k)) (/ k (cbrt t)))
14.9b	(/ (/ (/ (sqrt 2) (/ (cbrt t) (/ l t))) (sin k)) (/ k t))

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

118641×	`times-frac`
46320×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
11454×	`sqrt-prod`
11169×	`cbrt-prod`
3651×	`div-inv`
2073×	`associate-/l*`
348×	`associate-/r/`
89×	`add-exp-log`
80×	`add-cbrt-cube`
63×	`cbrt-undiv` `div-exp`
41×	`associate-/r*`
24×	`tan-quot`
4×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp` `associate-/l/`

Counts

4 → 24394

Calls

4 calls:

36.0ms	(/ (/ (sqrt 2) (/ (cbrt t) (/ l t))) (sin k))
8.0ms	(/ (/ l t) (tan k))
16.0ms	(/ (/ (/ l t) (tan k)) (/ k (cbrt t)))
76.0ms	(/ (/ (/ (sqrt 2) (/ (cbrt t) (/ l t))) (sin k)) (/ k t))

series880.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(/ (/ (sqrt 2) (/ (cbrt t) (/ l t))) (sin k))
150.0ms	(/ (/ l t) (tan k))
256.0ms	(/ (/ (/ l t) (tan k)) (/ k (cbrt t)))
257.0ms	(/ (/ (/ (sqrt 2) (/ (cbrt t) (/ l t))) (sin k)) (/ k t))

simplify24.1s

Counts

24406 → 24406

Iterations

Iter	Nodes
done	29572
0	29572

prune3.0m

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.7b

localize92.0ms

Local error

Found 4 expressions with local error:

2.4b	(/ (/ (cbrt (sqrt 2)) (/ (cbrt t) (/ l (cbrt t)))) (sin k))
2.5b	(/ (/ l t) (tan k))
3.2b	(/ (/ (/ (cbrt (sqrt 2)) (/ (cbrt t) (/ l (cbrt t)))) (sin k)) (/ k (cbrt t)))
4.5b	(/ (/ (/ l t) (tan k)) (/ k (cbrt t)))

rewrite9.6s

Algorithm

rewrite-expression-head

Rules

488934×	`times-frac`
190406×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
172722×	`cbrt-prod`
30003×	`sqrt-prod`
8559×	`div-inv`
5013×	`associate-/l*`
756×	`associate-/r/`
89×	`add-exp-log`
63×	`cbrt-undiv` `add-cbrt-cube` `div-exp`
50×	`associate-/r*`
24×	`tan-quot`
4×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp` `associate-/l/`

Counts

4 → 91675

Calls

4 calls:

53.0ms	(/ (/ (cbrt (sqrt 2)) (/ (cbrt t) (/ l (cbrt t)))) (sin k))
8.0ms	(/ (/ l t) (tan k))
266.0ms	(/ (/ (/ (cbrt (sqrt 2)) (/ (cbrt t) (/ l (cbrt t)))) (sin k)) (/ k (cbrt t)))
16.0ms	(/ (/ (/ l t) (tan k)) (/ k (cbrt t)))

series1.1s

Counts

4 → 12

Calls

4 calls:

343.0ms	(/ (/ (cbrt (sqrt 2)) (/ (cbrt t) (/ l (cbrt t)))) (sin k))
146.0ms	(/ (/ l t) (tan k))
366.0ms	(/ (/ (/ (cbrt (sqrt 2)) (/ (cbrt t) (/ l (cbrt t)))) (sin k)) (/ k (cbrt t)))
267.0ms	(/ (/ (/ l t) (tan k)) (/ k (cbrt t)))

simplify1.4m

Iterations

Iter	Nodes
done	96447
0	96447