Details

sample186.0ms

Algorithm

intervals

Results

102.0ms	616×	body	80	nan
56.0ms	359×	body	80	valid
0.0ms	1×	body	160	nan

simplify269.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

269.0ms

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize40.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.3b	(* n (* 2 PI))
0.2b	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

rewrite78.0ms

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

27.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
26.0ms	(* n (* 2 PI))
21.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

series545.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

284.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
201.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
59.0ms	(* n (* 2 PI))

simplify26.2s

Counts

124 → 133

Calls

124 calls:

Slowest

893.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
669.0ms	(/ (* (* (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)))
539.0ms	(/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1))
511.0ms	(/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
491.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(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)))

rewrite84.0ms

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

38.0ms	(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))
26.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
12.0ms	(* n (* 2 PI))
5.0ms	(/ 1 (sqrt k))

series628.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

363.0ms	(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))
168.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
56.0ms	(* n (* 2 PI))
41.0ms	(/ 1 (sqrt k))

simplify19.2s

Counts

173 → 197

Calls

173 calls:

Slowest

718.0ms	(* (* (* (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))))
556.0ms	(* (pow (* n (* 2 PI)) (/ k 2)) (sqrt k))
470.0ms	(* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ 1 (sqrt (sqrt k))))
469.0ms	(exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
444.0ms	(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))

prune2.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
0.4b	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
0.3b	(* n (* 2 PI))
0.3b	(* n (* 2 PI))

rewrite107.0ms

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

30.0ms	(* n (* 2 PI))
28.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
26.0ms	(* n (* 2 PI))
15.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))

series449.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

187.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
158.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
62.0ms	(* n (* 2 PI))
42.0ms	(* n (* 2 PI))

simplify14.2s

Counts

184 → 234

Calls

184 calls:

Slowest

507.0ms	(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
462.0ms	(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
456.0ms	(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
415.0ms	(exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
393.0ms	(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))

prune3.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow (* 2 PI) (/ (- 1 k) 2))
0.4b	(pow n (/ (- 1 k) 2))
0.3b	(/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2)))
0.2b	(/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

551×	`times-frac`
270×	`add-sqr-sqrt` `*-un-lft-identity`
252×	`add-cube-cbrt`
167×	`unpow-prod-down`
138×	`sqrt-prod`
93×	`sqr-pow`
53×	`add-exp-log`
44×	`pow-unpow`
40×	`associate-/r*`
31×	`div-exp`
16×	`pow-exp`
13×	`associate-/l*`
12×	`div-sub` `div-inv` `pow-sub` `difference-of-squares`
11×	`pow-to-exp` `add-cbrt-cube`
10×	`associate-/r/`
8×	`pow1`
6×	`distribute-lft-out--`
5×	`prod-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow`
2×	`clear-num` `frac-2neg`
1×	`pow-prod-down` `associate-/l/`

Counts

4 → 459

Calls

4 calls:

Slowest

16.0ms	(/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))
10.0ms	(pow (* 2 PI) (/ (- 1 k) 2))
7.0ms	(/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2)))
5.0ms	(pow n (/ (- 1 k) 2))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

572.0ms	(/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2)))
448.0ms	(/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))
110.0ms	(pow n (/ (- 1 k) 2))
73.0ms	(pow (* 2 PI) (/ (- 1 k) 2))

simplify3.4m

Counts

693 → 471

Calls

693 calls:

Slowest

1.2s	(/ (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ k 2)))
849.0ms	(/ (sqrt (pow n (/ (- 1 k) 2))) (cbrt (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2)))))
837.0ms	(/ (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ k 2)))
831.0ms	(/ (pow (sqrt n) (/ (- 1 k) 2)) (/ (sqrt (sqrt k)) (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2))))))
828.0ms	(/ (pow n (/ (- 1 k) 2)) (/ (sqrt (cbrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))

prune6.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes121.0ms

Accuracy

0% (0.4b remaining)

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

bsearch3.0ms

end0.0ms

sample7.5s

Algorithm

intervals

Results

4.4s	20430×	body	80	nan
2.2s	11919×	body	80	valid
1.0ms	3×	body	160	nan