Details

sample317.0ms

Algorithm

intervals

Results

149.0ms	67×	body	1280	valid
53.0ms	221×	body	80	valid
52.0ms	51×	body	640	valid
18.0ms	23×	body	320	valid
6.0ms	11×	body	160	valid

simplify954.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	873
2	158
1	48
0	19

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.7b

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 2.0 (* (/ (tan k) l) (/ (pow t 3.0) l)))
5.0b	(/ (pow t 3.0) l)
9.1b	(* (/ (tan k) l) (/ (pow t 3.0) l))
15.8b	(/ (/ 2.0 (* (/ (tan k) l) (/ (pow t 3.0) l))) (* (sin k) (+ (+ (pow (/ k t) 2.0) 1.0) 1.0)))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

167×	`add-exp-log`
92×	`add-cbrt-cube`
90×	`div-exp`
80×	`times-frac`
71×	`add-sqr-sqrt`
47×	`*-un-lft-identity` `add-cube-cbrt`
44×	`cbrt-undiv`
42×	`prod-exp`
25×	`associate-r`
23×	`unpow-prod-down`
22×	`cbrt-unprod`
20×	`associate-/l*`
13×	`associate-l`
11×	`associate-/r/`
9×	`pow-to-exp` `pow-exp` `sqr-pow`
8×	`unswap-sqr`
7×	`div-inv`
6×	`pow1` `associate-*r/`
5×	`associate-/r*`
4×	`frac-times` `associate-*l/` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+` `associate-/l/`

Counts

4 → 215

Calls

4 calls:

17.0ms	(/ 2.0 (* (/ (tan k) l) (/ (pow t 3.0) l)))
15.0ms	(/ (pow t 3.0) l)
45.0ms	(* (/ (tan k) l) (/ (pow t 3.0) l))
112.0ms	(/ (/ 2.0 (* (/ (tan k) l) (/ (pow t 3.0) l))) (* (sin k) (+ (+ (pow (/ k t) 2.0) 1.0) 1.0)))

series1.7s

Counts

4 → 12

Calls

4 calls:

440.0ms	(/ 2.0 (* (/ (tan k) l) (/ (pow t 3.0) l)))
203.0ms	(/ (pow t 3.0) l)
327.0ms	(* (/ (tan k) l) (/ (pow t 3.0) l))
712.0ms	(/ (/ 2.0 (* (/ (tan k) l) (/ (pow t 3.0) l))) (* (sin k) (+ (+ (pow (/ k t) 2.0) 1.0) 1.0)))

simplify626.0ms

Counts

227 → 227

Iterations

Iter	Nodes
done	5001
1	1172
0	374

prune2.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.0b

localize88.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (cbrt t) 3.0)
5.7b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))
8.1b	(* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l))))
15.8b	(/ (/ 2.0 (* (* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (/ (pow (cbrt t) 3.0) (cbrt l)))) (* (sin k) (+ (+ (pow (/ k t) 2.0) 1.0) 1.0)))

rewrite395.0ms

Algorithm

rewrite-expression-head

Rules

1274×	`add-exp-log`
657×	`div-exp`
506×	`prod-exp`
206×	`add-cbrt-cube`
115×	`pow-exp`
113×	`cbrt-undiv`
85×	`cbrt-unprod`
77×	`pow-to-exp`
49×	`times-frac`
38×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
19×	`associate-/l*`
16×	`associate-/r/`
13×	`associate-l`
11×	`frac-times` `unpow-prod-down` `associate-*l/`
9×	`associate-r` `associate-*r/`
8×	`unswap-sqr`
7×	`pow1`
6×	`div-inv` `sqr-pow`
4×	`add-log-exp`
3×	`cbrt-prod` `pow-unpow`
2×	`clear-num` `associate-/r*` `pow-pow` `frac-2neg`
1×	`flip3-+` `pow1/3` `pow-prod-down` `*-commutative` `flip-+` `associate-/l/`

Counts

4 → 348

Calls

4 calls:

5.0ms	(pow (cbrt t) 3.0)
17.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))
37.0ms	(* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l))))
275.0ms	(/ (/ 2.0 (* (* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (/ (pow (cbrt t) 3.0) (cbrt l)))) (* (sin k) (+ (+ (pow (/ k t) 2.0) 1.0) 1.0)))

series2.1s

Counts

4 → 12

Calls

4 calls:

462.0ms	(pow (cbrt t) 3.0)
361.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))
454.0ms	(* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l))))
809.0ms	(/ (/ 2.0 (* (* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))) (/ (pow (cbrt t) 3.0) (cbrt l)))) (* (sin k) (+ (+ (pow (/ k t) 2.0) 1.0) 1.0)))

simplify1.2s

Counts

360 → 360

Iterations

Iter	Nodes
done	5000
1	2437
0	634

prune2.1s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 10.9b

localize84.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))
0.8b	(pow (cbrt t) 3.0)
2.7b	(* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))
15.8b	(/ (/ 2.0 (* (* (* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l)))) (* (sin k) (+ (+ (pow (/ k t) 2.0) 1.0) 1.0)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

4271×	`add-exp-log`
2232×	`div-exp`
1820×	`prod-exp`
495×	`pow-exp`
344×	`add-cbrt-cube`
304×	`pow-to-exp`
185×	`cbrt-undiv`
162×	`cbrt-unprod`
116×	`times-frac`
91×	`add-sqr-sqrt`
68×	`associate-r`
52×	`*-un-lft-identity` `add-cube-cbrt`
40×	`frac-times` `associate-*l/`
39×	`cbrt-prod`
32×	`associate-/r/`
22×	`unpow-prod-down` `associate-/l*`
20×	`associate-*r/`
17×	`sqr-pow`
14×	`associate-l` `unswap-sqr`
12×	`pow1`
6×	`div-inv`
4×	`pow-prod-down` `add-log-exp`
3×	`pow-unpow`
2×	`pow-pow` `*-commutative`
1×	`clear-num` `associate-/r*` `frac-2neg` `flip3-+` `pow1/3` `flip-+` `associate-/l/`

Counts

4 → 783

Calls

4 calls:

85.0ms	(* (* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))
5.0ms	(pow (cbrt t) 3.0)
58.0ms	(* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))
740.0ms	(/ (/ 2.0 (* (* (* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l)))) (* (sin k) (+ (+ (pow (/ k t) 2.0) 1.0) 1.0)))

series2.2s

Counts

4 → 12

Calls

4 calls:

459.0ms	(* (* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))
485.0ms	(pow (cbrt t) 3.0)
444.0ms	(* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))
781.0ms	(/ (/ 2.0 (* (* (* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l)))) (* (sin k) (+ (+ (pow (/ k t) 2.0) 1.0) 1.0)))

simplify1.6s

Counts

795 → 795

Iterations

Iter	Nodes
done	5000
1	4654
0	1091

prune3.6s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 7.7b

localize87.0ms

Local error

Found 4 expressions with local error:

2.2b	(/ (sin k) (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (+ (pow (/ k t) 2.0) (+ 1.0 1.0))))
2.7b	(* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))
4.8b	(/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (+ (pow (/ k t) 2.0) (+ 1.0 1.0)))
11.0b	(/ (/ (* (cbrt 2.0) (cbrt 2.0)) (* (* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))) (/ (sin k) (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (+ (pow (/ k t) 2.0) (+ 1.0 1.0)))))

rewrite31.9s

Algorithm

rewrite-expression-head

Rules

408159×	`times-frac`
216183×	`*-un-lft-identity`
130637×	`add-sqr-sqrt`
130598×	`add-cube-cbrt`
106101×	`cbrt-prod`
51351×	`distribute-lft-out`
47746×	`unpow-prod-down`
41337×	`associate-/r/`
29296×	`frac-times` `associate-*l/`
17578×	`associate-*r/`
7966×	`sqr-pow`
7814×	`associate-/r*`
7751×	`add-exp-log`
7467×	`div-inv`
5178×	`div-exp`
2168×	`prod-exp`
707×	`pow-exp`
697×	`add-cbrt-cube`
605×	`cbrt-undiv`
411×	`pow-to-exp`
404×	`associate-/l*`
239×	`cbrt-unprod`
44×	`flip3-+` `flip-+`
34×	`associate-r`
14×	`unswap-sqr`
13×	`associate-l`
6×	`pow1`
4×	`add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`associate-/l/`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 87359

Calls

4 calls:

1.4s	(/ (sin k) (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (+ (pow (/ k t) 2.0) (+ 1.0 1.0))))
43.0ms	(* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))
283.0ms	(/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (+ (pow (/ k t) 2.0) (+ 1.0 1.0)))
3.6s	(/ (/ (* (cbrt 2.0) (cbrt 2.0)) (* (* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))) (/ (sin k) (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (+ (pow (/ k t) 2.0) (+ 1.0 1.0)))))

series2.9s

Counts

4 → 12

Calls

4 calls:

754.0ms	(/ (sin k) (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (+ (pow (/ k t) 2.0) (+ 1.0 1.0))))
377.0ms	(* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))
954.0ms	(/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (+ (pow (/ k t) 2.0) (+ 1.0 1.0)))
852.0ms	(/ (/ (* (cbrt 2.0) (cbrt 2.0)) (* (* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))) (/ (sin k) (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (+ (pow (/ k t) 2.0) (+ 1.0 1.0)))))

simplify48.2s

Counts

87371 → 87371

Iterations

Iter	Nodes
done	66676
0	66676

Details

sample317.0ms

simplify954.0ms

prune32.0ms

localize44.0ms

rewrite199.0ms

series1.7s

simplify626.0ms

prune2.0s

localize88.0ms

rewrite395.0ms

series2.1s

simplify1.2s

prune2.1s

localize84.0ms

rewrite1.0s

series2.2s

simplify1.6s

prune3.6s

localize87.0ms

rewrite31.9s

series2.9s

simplify48.2s

prune8.3m