Details

sample234.0ms

Algorithm

intervals

Results

108.0ms	710×	body	80	nan
89.0ms	371×	body	80	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
6	2053
5	821
4	322
3	123
2	60
1	29
0	13

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize49.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
0.3b	(* PI (* n 2))
0.7b	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

493×	`times-frac`
383×	`add-sqr-sqrt`
380×	`*-un-lft-identity`
378×	`add-cube-cbrt`
328×	`unpow-prod-up`
312×	`prod-diff`
141×	`sqrt-prod`
46×	`associate-/l*`
26×	`add-exp-log`
25×	`div-inv`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`prod-exp`
8×	`sub-neg` `unpow-prod-down` `sqr-pow`
6×	`pow-unpow` `associate-/r*` `pow-prod-down` `pow-exp`
5×	`div-exp`
3×	`expm1-log1p-u` `pow-pow` `associate-l` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-sub` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate-r` `*-commutative` `distribute-lft-out--` `associate-/l/`

Counts

3 → 436

Calls

3 calls:

24.0ms	(/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
13.0ms	(* PI (* n 2))
18.0ms	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

series617.0ms

Counts

3 → 9

Calls

3 calls:

360.0ms	(/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
44.0ms	(* PI (* n 2))
212.0ms	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

simplify3.2s

Counts

445 → 445

Iterations

Iter	Nodes
2	4287
1	1515
0	698

prune5.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))
0.2b	(/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
0.3b	(* PI (* n 2))
0.7b	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

3088×	`times-frac`
1878×	`add-sqr-sqrt`
1875×	`*-un-lft-identity`
1873×	`add-cube-cbrt`
1312×	`unpow-prod-up`
1248×	`prod-diff`
693×	`sqrt-prod`
327×	`associate-/r*`
102×	`div-inv`
72×	`add-exp-log`
32×	`sub-neg` `unpow-prod-down` `div-exp` `sqr-pow`
18×	`prod-exp`
16×	`pow1` `add-cbrt-cube`
15×	`pow-exp`
9×	`associate-/l*`
6×	`rec-exp` `pow-unpow` `1-exp` `pow-prod-down` `associate-/r/` `pow-sub`
5×	`pow-to-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `associate-l` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `difference-of-squares`
1×	`associate-r` `*-commutative` `pow-flip` `distribute-lft-out--` `inv-pow`

Counts

4 → 1599

Calls

4 calls:

30.0ms	(/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))
13.0ms	(/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
14.0ms	(* PI (* n 2))
17.0ms	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

series1.0s

Counts

4 → 12

Calls

4 calls:

354.0ms	(/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))
388.0ms	(/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
62.0ms	(* PI (* n 2))
211.0ms	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

simplify3.0m

Counts

1611 → 1611

Iterations

Iter	Nodes
1	4705
0	1731

prune15.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (/ 1 (pow (* PI (* n 2)) (fma 1 1/2 (- (* (/ k 2) 1)))))) (/ (sqrt k) (pow (* PI (* n 2)) (fma (- (/ k 2)) 1 (* (/ k 2) 1)))))
0.3b	(* PI (* n 2))
0.3b	(* PI (* n 2))
0.7b	(pow (* PI (* n 2)) (fma 1 1/2 (- (* (/ k 2) 1))))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

10352×	`times-frac`
3548×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
1296×	`sqrt-prod`
1245×	`add-exp-log`
911×	`div-exp`
802×	`unpow-prod-up` `unpow-prod-down` `fma-udef` `sqr-pow`
318×	`prod-exp`
312×	`pow-exp`
237×	`div-inv`
186×	`rec-exp` `1-exp`
104×	`pow-to-exp`
71×	`associate-/l*`
42×	`associate-/r/`
40×	`associate-/r*`
35×	`add-cbrt-cube`
20×	`pow1`
15×	`cbrt-undiv`
9×	`pow-prod-down`
6×	`associate-l` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-pow`
2×	`associate-r` `*-commutative`
1×	`clear-num` `frac-2neg` `associate-/l/`

Counts

4 → 3331

Calls

4 calls:

35.0ms	(/ (/ 1 (/ 1 (pow (* PI (* n 2)) (fma 1 1/2 (- (* (/ k 2) 1)))))) (/ (sqrt k) (pow (* PI (* n 2)) (fma (- (/ k 2)) 1 (* (/ k 2) 1)))))
15.0ms	(* PI (* n 2))
12.0ms	(* PI (* n 2))
11.0ms	(pow (* PI (* n 2)) (fma 1 1/2 (- (* (/ k 2) 1))))

series5.3m

Counts

4 → 12

Calls

4 calls:

5.3m	(/ (/ 1 (/ 1 (pow (* PI (* n 2)) (fma 1 1/2 (- (* (/ k 2) 1)))))) (/ (sqrt k) (pow (* PI (* n 2)) (fma (- (/ k 2)) 1 (* (/ k 2) 1)))))
32.0ms	(* PI (* n 2))
38.0ms	(* PI (* n 2))
139.0ms	(pow (* PI (* n 2)) (fma 1 1/2 (- (* (/ k 2) 1))))

simplify1.3m

Iterations

Iter	Nodes
0	4706