Details

sample251.0ms

Algorithm

intervals

Results

141.0ms	690×	body	80	nan
78.0ms	390×	body	80	valid

simplify368.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

367.0ms

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

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

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))

rewrite65.0ms

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

26.0ms	(* n (* 2 PI))
19.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
18.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))

series567.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

334.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
184.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
49.0ms	(* n (* 2 PI))

simplify26.1s

Counts

124 → 133

Calls

124 calls:

Slowest

763.0ms	(/ (* (* (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)))
613.0ms	(- (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))
529.0ms	(/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k))))
522.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
500.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

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

40.0ms	(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))
14.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
13.0ms	(* n (* 2 PI))
5.0ms	(/ 1 (sqrt k))

series617.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

336.0ms	(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))
186.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
49.0ms	(/ 1 (sqrt k))
45.0ms	(* n (* 2 PI))

simplify18.9s

Counts

173 → 197

Calls

173 calls:

Slowest

776.0ms	(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
705.0ms	(* (* (* (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))))
573.0ms	(* (pow (* n (* 2 PI)) (/ k 2)) (sqrt k))
465.0ms	(* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ 1 (sqrt (sqrt k))))
451.0ms	(exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

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)) (pow k -1/2))

rewrite105.0ms

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

45.0ms	(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow k -1/2))
33.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
25.0ms	(* n (* 2 PI))

series603.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

341.0ms	(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow k -1/2))
207.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
55.0ms	(* n (* 2 PI))

simplify11.2s

Counts

87 → 118

Calls

87 calls:

Slowest

798.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
551.0ms	(exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
400.0ms	(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
366.0ms	(exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
356.0ms	(sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
0.6b	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
0.3b	(* n (* 2 PI))
0.3b	(* n (* 2 PI))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
166×	`add-sqr-sqrt` `*-un-lft-identity`
140×	`pow-unpow`
112×	`add-cube-cbrt`
36×	`difference-of-squares`
26×	`pow1` `add-exp-log`
18×	`distribute-lft-out--`
14×	`add-cbrt-cube`
12×	`pow-prod-down` `prod-exp`
8×	`div-inv`
6×	`pow-pow` `associate-l` `pow-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `div-sub` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `associate-r` `*-commutative` `pow-sub` `sqr-pow`

Counts

4 → 222

Calls

4 calls:

Slowest

36.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
30.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
23.0ms	(* n (* 2 PI))
13.0ms	(* n (* 2 PI))

series434.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

179.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
163.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
50.0ms	(* n (* 2 PI))
41.0ms	(* n (* 2 PI))

simplify13.2s

Counts

184 → 234

Calls

184 calls:

Slowest

471.0ms	(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
429.0ms	(exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
428.0ms	(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
415.0ms	(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
367.0ms	(pow n (/ (/ (- 1 k) 2) 2))

prune3.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes155.0ms

Accuracy

0% (0.3b remaining)

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

bsearch4.0ms

end0.0ms

sample7.6s

Algorithm

intervals

Results

4.1s	20679×	body	80	nan
2.3s	11951×	body	80	valid
1.0ms	2×	body	160	nan