Details

sample145.0ms

Algorithm

intervals

Results

69.0ms	652×	body	80	nan
52.0ms	406×	body	80	valid

simplify310.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

310.0ms

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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize44.0ms

Local error

Found 3 expressions with local error:

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

rewrite69.0ms

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×	`expm1-log1p-u` `pow-pow` `associate-l` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `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 → 124

Calls

3 calls:

Slowest

29.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
23.0ms	(* n (* 2 PI))
15.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

series547.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

304.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
202.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
40.0ms	(* n (* 2 PI))

simplify26.3s

Counts

124 → 133

Calls

124 calls:

Slowest

711.0ms	(/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
681.0ms	(/ (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
535.0ms	(/ (pow n (/ (- 1 k) 2)) 1)
511.0ms	(/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1))
508.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt` `add-exp-log`
62×	`times-frac`
57×	`*-un-lft-identity`
44×	`add-cube-cbrt`
38×	`prod-exp`
25×	`sqrt-prod`
23×	`associate-r`
22×	`pow-unpow`
17×	`pow1`
16×	`add-cbrt-cube`
15×	`pow-exp`
12×	`div-exp`
10×	`unswap-sqr`
8×	`associate-l`
7×	`sqr-pow`
6×	`rec-exp` `associate-/r*` `1-exp` `pow-prod-down` `difference-of-squares`
5×	`pow-to-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `div-sub` `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/` `un-div-inv` `inv-pow`

Counts

4 → 185

Calls

4 calls:

Slowest

32.0ms	(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))
28.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
26.0ms	(* n (* 2 PI))
10.0ms	(/ 1 (sqrt k))

series638.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

374.0ms	(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))
184.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
41.0ms	(/ 1 (sqrt k))
40.0ms	(* n (* 2 PI))

simplify19.3s

Counts

173 → 197

Calls

173 calls:

Slowest

760.0ms	(* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt 1) (sqrt (sqrt k))))
681.0ms	(* (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))))
564.0ms	(* (pow (* n (* 2 PI)) (/ k 2)) (sqrt k))
468.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
436.0ms	(exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))

prune2.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 3 expressions with local error:

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

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
33×	`add-sqr-sqrt`
30×	`prod-exp`
26×	`*-un-lft-identity`
22×	`pow-unpow`
18×	`times-frac`
17×	`pow-exp` `add-cube-cbrt`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`pow-to-exp`
8×	`associate-r` `associate-l` `sqr-pow`
7×	`unpow-prod-down`
6×	`pow-prod-down` `difference-of-squares` `unswap-sqr`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `pow-pow` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
2×	`div-sub` `*-commutative` `pow-sub`
1×	`associate-*l/` `div-inv`

Counts

3 → 109

Calls

3 calls:

Slowest

32.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
23.0ms	(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow k -1/2))
13.0ms	(* n (* 2 PI))

series594.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

367.0ms	(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow k -1/2))
192.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
34.0ms	(* n (* 2 PI))

simplify11.5s

Counts

87 → 118

Calls

87 calls:

Slowest

434.0ms	(exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
416.0ms	(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
415.0ms	(sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
398.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
380.0ms	(* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

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×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `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 → 303

Calls

4 calls:

Slowest

19.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
17.0ms	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
13.0ms	(* n (* 2 PI))
10.0ms	(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))

series954.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

358.0ms	(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
346.0ms	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
202.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
47.0ms	(* n (* 2 PI))

simplify1.7m

Counts

390 → 315

Calls

390 calls:

Slowest

1.0s	(/ (* (* 1 1) 1) (* (* (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
770.0ms	(/ 1 (/ 1 (pow n (/ (- 1 k) 2))))
701.0ms	(/ (cbrt 1) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
686.0ms	(/ (sqrt 1) (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
667.0ms	(/ 1 (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2))))

prune3.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes120.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch4.0ms

end0.0ms

sample7.4s

Algorithm

intervals

Results

3.7s	20730×	body	80	nan
2.5s	11909×	body	80	valid