Details

sample475.0ms

Algorithm

intervals

Results

143.0ms	72×	body	2560	valid
134.0ms	30×	body	5120	valid
102.0ms	125×	body	1280	valid
47.0ms	80×	body	640	valid
11.0ms	31×	body	320	valid
10.0ms	83×	body	80	valid
6.0ms	25×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 4 (283.0ms)

Iter	Nodes	Cost
0	19	25
1	44	25
2	145	25
3	723	23
4	4042	21
done	5000	21

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin k) (tan k))
0.6b	(* (* (sin k) (tan k)) (pow (/ k t) 2.0))
13.6b	(/ (pow t 3.0) (* l l))
27.8b	(/ (/ 2.0 (/ (pow t 3.0) (* l l))) (* (* (sin k) (tan k)) (pow (/ k t) 2.0)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

405×	`add-exp-log`
213×	`div-exp`
162×	`times-frac`
139×	`prod-exp`
70×	`add-cbrt-cube`
62×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
56×	`pow-exp`
45×	`associate-/l*`
38×	`pow-to-exp`
37×	`unpow-prod-down`
29×	`cbrt-undiv`
20×	`associate-r` `cbrt-unprod`
11×	`div-inv`
9×	`sqr-pow`
6×	`pow1`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`tan-quot` `associate-*r/` `associate-/r/`
2×	`frac-2neg` `associate-l/` `clear-num` `associate-/r` `*-commutative`
1×	`pow-prod-down` `associate-/l/` `unswap-sqr`

Counts

4 → 270

Calls

4 calls:

4.0ms	(* (sin k) (tan k))
21.0ms	(* (* (sin k) (tan k)) (pow (/ k t) 2.0))
5.0ms	(/ (pow t 3.0) (* l l))
27.0ms	(/ (/ 2.0 (/ (pow t 3.0) (* l l))) (* (* (sin k) (tan k)) (pow (/ k t) 2.0)))

series1.0s

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin k) (tan k))
244.0ms	(* (* (sin k) (tan k)) (pow (/ k t) 2.0))
185.0ms	(/ (pow t 3.0) (* l l))
575.0ms	(/ (/ 2.0 (/ (pow t 3.0) (* l l))) (* (* (sin k) (tan k)) (pow (/ k t) 2.0)))

simplify485.0ms

Counts

282 → 282

Iterations

Useful iterations: done (476.0ms)

Iter	Nodes	Cost
0	483	6338
1	1445	5836
done	5000	5815

prune854.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 15.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin k) 2)
5.0b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.1b	(* (pow k 2.0) (pow t 1.0))
15.2b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

1597×	`add-exp-log`
1095×	`prod-exp`
882×	`pow-exp`
668×	`div-exp`
492×	`pow-to-exp`
130×	`rec-exp` `1-exp`
37×	`add-sqr-sqrt`
32×	`unpow-prod-down`
20×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
19×	`times-frac` `associate-r`
18×	`associate-l`
14×	`sqr-pow`
12×	`unswap-sqr`
8×	`associate-/r*`
6×	`cbrt-unprod`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp`
3×	`pow-unpow` `div-inv`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `associate-r/` `clear-num` `associate-/l`

Counts

4 → 575

Calls

4 calls:

2.0ms	(pow (sin k) 2)
6.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.0ms	(* (pow k 2.0) (pow t 1.0))
37.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (sin k) 2)
89.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
341.0ms	(* (pow k 2.0) (pow t 1.0))
658.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify855.0ms

Iterations

Useful iterations: 1 (248.0ms)

Iter	Nodes	Cost
0	446	14510
1	1280	12421