Details

sample258.0ms

Algorithm

intervals

Results

140.0ms	680×	body	80	nan
79.0ms	397×	body	80	valid

simplify363.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

363.0ms

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

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize26.0ms

Local error

Found 3 expressions with local error:

1.4b	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.3b	(* n (* 2 PI))
0.2b	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

rewrite41.0ms

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

15.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
13.0ms	(* n (* 2 PI))
12.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

series510.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

299.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
153.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
58.0ms	(* n (* 2 PI))

simplify27.1s

Counts

124 → 133

Calls

124 calls:

Slowest

709.0ms	(/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))
662.0ms	(/ (* (* (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)))
553.0ms	(/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1))
525.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
517.0ms	(/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt k)))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow n (/ (- 1 k) 2))
0.5b	(pow (* 2 PI) (/ (- 1 k) 2))
0.2b	(* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2)))
0.2b	(/ (* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-exp-log`
57×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
44×	`pow-unpow`
42×	`times-frac`
32×	`add-cube-cbrt`
31×	`prod-exp`
23×	`pow-exp`
16×	`pow-to-exp`
13×	`div-exp`
12×	`difference-of-squares`
11×	`add-cbrt-cube`
10×	`unpow-prod-down` `div-sub` `pow-sub`
9×	`sqr-pow`
8×	`pow1`
7×	`associate-l`
6×	`associate-/r*` `sqrt-prod` `distribute-lft-out--` `unswap-sqr`
5×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `div-inv` `associate-/l/`
2×	`frac-times` `cbrt-undiv` `pow-prod-down` `associate-l/` `associate-r/` `cbrt-unprod`
1×	`clear-num` `frac-2neg` `-commutative` `associate-/l`

Counts

4 → 170

Calls

4 calls:

Slowest

37.0ms	(/ (* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k))
23.0ms	(* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2)))
8.0ms	(pow (* 2 PI) (/ (- 1 k) 2))
5.0ms	(pow n (/ (- 1 k) 2))

series964.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

478.0ms	(/ (* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k))
302.0ms	(* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2)))
101.0ms	(pow (* 2 PI) (/ (- 1 k) 2))
82.0ms	(pow n (/ (- 1 k) 2))

simplify24.1s

Counts

146 → 182

Calls

146 calls:

Slowest

804.0ms	(/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))
773.0ms	(/ (* (* (* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2)))) (* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
648.0ms	(* (pow n (/ 1 2)) (pow (* 2 PI) (/ 1 2)))
640.0ms	(* (pow n (/ 1 2)) (pow (* 2 PI) (/ 1 2)))
504.0ms	(/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt k)))

prune2.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow n (/ (- 1 k) 2))
0.5b	(pow PI (/ (- 1 k) 2))
0.2b	(* (pow n (/ (- 1 k) 2)) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))))
0.2b	(/ (* (pow n (/ (- 1 k) 2)) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2)))) (sqrt k))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

156×	`add-exp-log`
114×	`prod-exp`
58×	`pow-to-exp` `pow-exp`
50×	`add-sqr-sqrt` `*-un-lft-identity`
44×	`pow-unpow`
42×	`times-frac`
32×	`add-cube-cbrt`
31×	`div-exp`
26×	`div-sub` `pow-sub`
18×	`add-cbrt-cube`
12×	`difference-of-squares`
10×	`frac-times` `associate-*r/`
9×	`unpow-prod-down`
7×	`associate-l` `associate-/l/`
6×	`pow1` `associate-/r` `associate-l/` `sqrt-prod` `cbrt-unprod` `distribute-lft-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-inv` `sqr-pow`
2×	`pow-pow` `pow-prod-down`
1×	`clear-num` `frac-2neg` `associate-r` `-commutative` `associate-/l`

Counts

4 → 206

Calls

4 calls:

Slowest

54.0ms	(* (pow n (/ (- 1 k) 2)) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))))
52.0ms	(/ (* (pow n (/ (- 1 k) 2)) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2)))) (sqrt k))
10.0ms	(pow PI (/ (- 1 k) 2))
5.0ms	(pow n (/ (- 1 k) 2))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

595.0ms	(/ (* (pow n (/ (- 1 k) 2)) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2)))) (sqrt k))
405.0ms	(* (pow n (/ (- 1 k) 2)) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))))
93.0ms	(pow n (/ (- 1 k) 2))
74.0ms	(pow PI (/ (- 1 k) 2))

simplify39.5s

Counts

177 → 218

Calls

177 calls:

Slowest

1.0s	(/ (* (* (* (pow n (/ (- 1 k) 2)) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2)))) (* (pow n (/ (- 1 k) 2)) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))))) (* (pow n (/ (- 1 k) 2)) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
940.0ms	(/ (* (* (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (* (* (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2)))) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
886.0ms	(- (log (* (pow n (/ (- 1 k) 2)) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))))) (log (sqrt k)))
726.0ms	(* (pow n (/ (- 1 k) 2)) (* (pow 2 (/ 1 2)) (pow PI (/ (- 1 k) 2))))
688.0ms	(* (pow n (/ k 2)) (* (pow 2 (/ k 2)) (pow PI (/ k 2))))

prune3.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow n (/ (- 1 k) 2))
0.5b	(pow PI (/ (- 1 k) 2))
0.2b	(/ (sqrt k) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))))
0.2b	(/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2)))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

181×	`times-frac`
123×	`add-exp-log`
100×	`add-sqr-sqrt` `*-un-lft-identity`
82×	`add-cube-cbrt`
73×	`div-exp`
48×	`unpow-prod-down`
44×	`pow-unpow`
39×	`div-sub` `pow-sub`
37×	`pow-to-exp` `pow-exp`
36×	`prod-exp`
30×	`sqrt-prod`
28×	`associate-/r/`
18×	`add-cbrt-cube`
16×	`sqr-pow`
14×	`associate-/r*`
13×	`associate-/l*`
12×	`div-inv` `difference-of-squares`
9×	`frac-times` `associate-l/` `associate-r/`
7×	`cbrt-undiv`
6×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `pow-pow` `frac-2neg` `cbrt-unprod`
1×	`associate-/l/`

Counts

4 → 283

Calls

4 calls:

Slowest

37.0ms	(/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2)))))
13.0ms	(/ (sqrt k) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))))
5.0ms	(pow n (/ (- 1 k) 2))
5.0ms	(pow PI (/ (- 1 k) 2))

series1.6s

Counts

4 → 12

Calls

4 calls:

Slowest

946.0ms	(/ (sqrt k) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))))
512.0ms	(/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2)))))
87.0ms	(pow n (/ (- 1 k) 2))
53.0ms	(pow PI (/ (- 1 k) 2))

simplify1.6m

Counts

338 → 295

Calls

338 calls:

Slowest

1.2s	(/ (pow (* (cbrt n) (cbrt n)) (/ (- 1 k) 2)) (/ (sqrt 1) (pow 2 (/ (- 1 k) 2))))
1.1s	(/ (* (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2)))) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))))))
1.0s	(/ (pow n (/ (/ (- 1 k) 2) 2)) (/ (sqrt k) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2)))))
937.0ms	(/ (pow n (/ (- 1 k) 2)) (pow 2 (/ k 2)))
906.0ms	(/ (pow (sqrt n) (/ (- 1 k) 2)) (pow 2 (/ k 2)))

prune4.1s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes196.0ms

Accuracy

0% (0.4b remaining)

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

bsearch5.0ms

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.5s	20621×	body	80	nan
2.5s	11881×	body	80	valid
1.0ms	3×	body	160	nan