Details

sample254.0ms

Algorithm

intervals

Results

96.0ms	67×	body	1280	valid
59.0ms	51×	body	640	valid
44.0ms	221×	body	80	valid
16.0ms	23×	body	320	valid
4.0ms	11×	body	160	valid

simplify1.0s

Counts

1 → 1

Iterations

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.7b

localize46.0ms

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)))

rewrite220.0ms

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:

12.0ms	(/ 2.0 (* (/ (tan k) l) (/ (pow t 3.0) l)))
9.0ms	(/ (pow t 3.0) l)
54.0ms	(* (/ (tan k) l) (/ (pow t 3.0) l))
136.0ms	(/ (/ 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:

468.0ms	(/ 2.0 (* (/ (tan k) l) (/ (pow t 3.0) l)))
238.0ms	(/ (pow t 3.0) l)
304.0ms	(* (/ (tan k) l) (/ (pow t 3.0) l))
727.0ms	(/ (/ 2.0 (* (/ (tan k) l) (/ (pow t 3.0) l))) (* (sin k) (+ (+ (pow (/ k t) 2.0) 1.0) 1.0)))

simplify575.0ms

Counts

227 → 227

Iterations

Iter	Nodes
done	5001
1	1172
0	374

prune1.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.0b

localize93.0ms

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)))

rewrite479.0ms

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)
21.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))
64.0ms	(* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l))))
320.0ms	(/ (/ 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:

433.0ms	(pow (cbrt t) 3.0)
411.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l)))
468.0ms	(* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (* (cbrt l) (cbrt l))))
814.0ms	(/ (/ 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)))

simplify1.1s

Counts

360 → 360

Iterations

Iter	Nodes
done	5000
1	2437
0	634

prune2.3s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 10.9b

localize69.0ms

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)))

rewrite696.0ms

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:

97.0ms	(* (* (/ (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)
57.0ms	(* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))
386.0ms	(/ (/ 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)))

series2.1s

Counts

4 → 12

Calls

4 calls:

419.0ms	(* (* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))
456.0ms	(pow (cbrt t) 3.0)
413.0ms	(* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))
773.0ms	(/ (/ 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)))

simplify1.5s

Counts

795 → 795

Iterations

Iter	Nodes
done	5000
1	4654
0	1091

prune4.2s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 7.7b

localize147.0ms

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)))))

rewrite30.5s

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:

707.0ms	(/ (sin k) (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (+ (pow (/ k t) 2.0) (+ 1.0 1.0))))
30.0ms	(* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))
274.0ms	(/ (/ (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)))))

series3.0s

Counts

4 → 12

Calls

4 calls:

845.0ms	(/ (sin k) (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (+ (pow (/ k t) 2.0) (+ 1.0 1.0))))
449.0ms	(* (/ (tan k) l) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)))
880.0ms	(/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (+ (pow (/ k t) 2.0) (+ 1.0 1.0)))
865.0ms	(/ (/ (* (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)))))

simplify47.3s

Counts

87371 → 87371

Iterations

Iter	Nodes
done	66676
0	66676

Details

sample254.0ms

simplify1.0s

prune22.0ms

localize46.0ms

rewrite220.0ms

series1.7s

simplify575.0ms

prune1.8s

localize93.0ms

rewrite479.0ms

series2.1s

simplify1.1s

prune2.3s

localize69.0ms

rewrite696.0ms

series2.1s

simplify1.5s

prune4.2s

localize147.0ms

rewrite30.5s

series3.0s

simplify47.3s

prune8.3m