Details

sample233.0ms

Algorithm

intervals

Results

100.0ms	371×	body	80	valid
96.0ms	591×	body	80	nan

simplify1.2s

Counts: 1 → 1

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize42.0ms

Local error

Found 3 expressions with local error:

1.1b	(pow (* PI (* n 2)) (/ (- 1 k) 2))
0.2b	(* PI (* n 2))
0.2b	(/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
42×	`add-sqr-sqrt` `*-un-lft-identity`
33×	`add-cube-cbrt`
26×	`add-exp-log`
22×	`pow-unpow`
18×	`sqrt-prod`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`prod-exp`
8×	`unpow-prod-down` `sqr-pow`
6×	`associate-/r*` `pow-prod-down` `pow-exp` `difference-of-squares`
5×	`div-exp` `associate-/l*`
3×	`pow-pow` `associate-l` `cbrt-unprod` `insert-posit16` `distribute-lft-out--` `add-log-exp`
2×	`pow-to-exp` `div-sub` `div-inv` `pow-sub`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate-r` `*-commutative` `associate-/l/`

Counts

3 → 118

Calls

3 calls:

Slowest

31.0ms	(pow (* PI (* n 2)) (/ (- 1 k) 2))
24.0ms	(* PI (* n 2))
20.0ms	(/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))

series559.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

303.0ms	(/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))
205.0ms	(pow (* PI (* n 2)) (/ (- 1 k) 2))
51.0ms	(* PI (* n 2))

simplify1.5s

Counts: 127 → 127

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

1.1b	(pow (* PI (* n 2)) (/ (- 1 k) 2))
0.2b	(* PI (* n 2))
0.2b	(/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2)))
0.2b	(/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

273×	`times-frac`
147×	`add-sqr-sqrt` `*-un-lft-identity`
138×	`add-cube-cbrt`
78×	`sqrt-prod`
72×	`add-exp-log`
40×	`associate-/r*`
32×	`unpow-prod-down` `div-exp` `sqr-pow`
22×	`pow-unpow`
18×	`prod-exp`
16×	`pow1` `add-cbrt-cube`
15×	`pow-exp`
9×	`associate-/l*`
7×	`div-inv`
6×	`rec-exp` `1-exp` `div-sub` `pow-prod-down` `associate-/r/` `pow-sub` `difference-of-squares`
5×	`pow-to-exp`
4×	`cbrt-undiv` `insert-posit16` `add-log-exp`
3×	`pow-pow` `associate-l` `cbrt-unprod` `distribute-lft-out--`
2×	`clear-num` `frac-2neg`
1×	`associate-r` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 295

Calls

4 calls:

Slowest

24.0ms	(pow (* PI (* n 2)) (/ (- 1 k) 2))
23.0ms	(/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2))))
12.0ms	(* PI (* n 2))
9.0ms	(/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2)))

series885.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

357.0ms	(/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2))))
355.0ms	(/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2)))
140.0ms	(pow (* PI (* n 2)) (/ (- 1 k) 2))
32.0ms	(* PI (* n 2))

simplify1.4s

Counts: 307 → 307

prune3.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

1.1b	(pow (* PI (* n 2)) (/ (- 1 k) 2))
0.2b	(* PI (* n 2))
0.2b	(/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2)))
0.2b	(/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

273×	`times-frac`
147×	`add-sqr-sqrt` `*-un-lft-identity`
138×	`add-cube-cbrt`
78×	`sqrt-prod`
72×	`add-exp-log`
40×	`associate-/r*`
32×	`unpow-prod-down` `div-exp` `sqr-pow`
22×	`pow-unpow`
18×	`prod-exp`
16×	`pow1` `add-cbrt-cube`
15×	`pow-exp`
9×	`associate-/l*`
7×	`div-inv`
6×	`rec-exp` `1-exp` `div-sub` `pow-prod-down` `associate-/r/` `pow-sub` `difference-of-squares`
5×	`pow-to-exp`
4×	`cbrt-undiv` `insert-posit16` `add-log-exp`
3×	`pow-pow` `associate-l` `cbrt-unprod` `distribute-lft-out--`
2×	`clear-num` `frac-2neg`
1×	`associate-r` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 295

Calls

4 calls:

Slowest

32.0ms	(/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2))))
16.0ms	(/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2)))
15.0ms	(* PI (* n 2))
13.0ms	(pow (* PI (* n 2)) (/ (- 1 k) 2))

series951.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

395.0ms	(/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2)))
351.0ms	(/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2))))
171.0ms	(pow (* PI (* n 2)) (/ (- 1 k) 2))
33.0ms	(* PI (* n 2))

simplify1.4s

Counts: 307 → 307

prune3.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

1.1b	(pow (* (* PI n) 2) (/ (- 1 k) 2))
0.3b	(/ 1 (sqrt k))
0.2b	(* PI n)
0.2b	(* (/ 1 (sqrt k)) (pow (* (* PI n) 2) (/ (- 1 k) 2)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
69×	`add-exp-log`
62×	`times-frac`
58×	`*-un-lft-identity`
45×	`add-cube-cbrt`
36×	`prod-exp`
25×	`associate-l` `sqrt-prod`
22×	`pow-unpow`
15×	`pow-exp`
14×	`pow1`
13×	`add-cbrt-cube`
12×	`div-exp`
11×	`unswap-sqr`
8×	`associate-r`
7×	`sqr-pow`
6×	`rec-exp` `associate-/r*` `1-exp` `difference-of-squares`
5×	`pow-to-exp`
4×	`pow-prod-down` `insert-posit16` `add-log-exp`
3×	`pow-pow` `div-sub` `cbrt-unprod` `div-inv` `pow-flip` `associate-/l*` `distribute-lft-out--` `pow-sub`
2×	`cbrt-undiv` `unpow-prod-down` `*-commutative`
1×	`frac-times` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `inv-pow`

Counts

4 → 176

Calls

4 calls:

Slowest

51.0ms	(* (/ 1 (sqrt k)) (pow (* (* PI n) 2) (/ (- 1 k) 2)))
27.0ms	(pow (* (* PI n) 2) (/ (- 1 k) 2))
5.0ms	(* PI n)
5.0ms	(/ 1 (sqrt k))

series562.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

313.0ms	(* (/ 1 (sqrt k)) (pow (* (* PI n) 2) (/ (- 1 k) 2)))
191.0ms	(pow (* (* PI n) 2) (/ (- 1 k) 2))
37.0ms	(/ 1 (sqrt k))
21.0ms	(* PI n)

simplify1.2s

Counts: 188 → 188

prune2.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes114.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample7.2s

Algorithm

intervals

Results

4.0s	20564×	body	80	nan
2.5s	11848×	body	80	valid
1.0ms	3×	body	160	nan