Details

sample288.0ms

Algorithm

intervals

Results

134.0ms	673×	body	80	nan
109.0ms	378×	body	80	valid

simplify330.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

329.0ms

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 3 expressions with local error:

0.7b	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.2b	(* n (* 2 PI))
0.1b	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

rewrite50.0ms

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

24.0ms	(* n (* 2 PI))
14.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
11.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

series567.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

354.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
164.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
49.0ms	(* n (* 2 PI))

simplify26.7s

Counts

124 → 133

Calls

124 calls:

Slowest

694.0ms	(/ (* (* (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)))
660.0ms	(/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (cbrt (sqrt k)))
562.0ms	(/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
550.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
532.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k)))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

3.2b	(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
0.3b	(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
0.2b	(* n (* 2 PI))
0.1b	(/ (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (sqrt k))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
86×	`add-sqr-sqrt` `*-un-lft-identity`
62×	`add-cube-cbrt`
50×	`pow-unpow`
49×	`unpow-prod-down`
42×	`sqrt-prod`
37×	`add-exp-log`
19×	`pow-exp`
17×	`sqr-pow`
15×	`pow1`
12×	`prod-exp` `difference-of-squares`
11×	`add-cbrt-cube`
9×	`associate-/l*`
7×	`div-exp`
6×	`associate-/r*` `pow-prod-down` `distribute-lft-out` `distribute-lft-out--`
5×	`pow-to-exp`
4×	`expm1-log1p-u` `pow-pow` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `cbrt-unprod` `div-inv`
2×	`div-sub` `pow-sub`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate-r` `*-commutative` `associate-/l/`

Counts

4 → 205

Calls

4 calls:

Slowest

24.0ms	(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
18.0ms	(* n (* 2 PI))
15.0ms	(/ (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (sqrt k))
11.0ms	(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))

series2.2s

Counts

4 → 12

Calls

4 calls:

Slowest

1.1s	(/ (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (sqrt k))
736.0ms	(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
322.0ms	(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
70.0ms	(* n (* 2 PI))

simplify41.3s

Counts

220 → 217

Calls

220 calls:

Slowest

758.0ms	(/ (pow (cbrt (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))) (/ (- 1 (sqrt k)) 2)) (sqrt (sqrt k)))
643.0ms	(* (+ (log n) (+ (log 2) (log PI))) (/ (+ 1 (sqrt k)) 1))
583.0ms	(* (* (+ (log n) (log (* 2 PI))) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
562.0ms	(- (* (* (log (* n (* 2 PI))) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (log (sqrt k)))
536.0ms	(* (log (* n (* 2 PI))) (/ (+ 1 (sqrt k)) 1))

prune3.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize67.0ms

Local error

Found 4 expressions with local error:

3.2b	(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
0.3b	(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
0.2b	(* n (* 2 PI))
0.2b	(/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
86×	`add-sqr-sqrt` `*-un-lft-identity`
62×	`add-cube-cbrt`
50×	`pow-unpow`
49×	`unpow-prod-down`
42×	`sqrt-prod`
37×	`add-exp-log`
19×	`pow-exp`
17×	`sqr-pow`
15×	`pow1`
12×	`prod-exp` `difference-of-squares`
11×	`add-cbrt-cube`
9×	`associate-/r*`
7×	`div-exp`
6×	`pow-prod-down` `distribute-lft-out` `associate-/l*` `distribute-lft-out--`
5×	`pow-to-exp`
4×	`expm1-log1p-u` `pow-pow` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `cbrt-unprod` `div-inv`
2×	`div-sub` `pow-sub`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate-r` `associate-/r/` `*-commutative`

Counts

4 → 205

Calls

4 calls:

Slowest

33.0ms	(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
26.0ms	(/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)))
20.0ms	(* n (* 2 PI))
12.0ms	(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))

series2.4s

Counts

4 → 12

Calls

4 calls:

Slowest

1.1s	(/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)))
694.0ms	(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
531.0ms	(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
66.0ms	(* n (* 2 PI))

simplify39.3s

Counts

220 → 217

Calls

220 calls:

Slowest

665.0ms	(/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))) (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))))
652.0ms	(* (* (+ (log n) (log (* 2 PI))) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
566.0ms	(/ (sqrt 1) (pow (pow n (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)))
554.0ms	(- (log (sqrt k)) (* (log (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))) (/ (- 1 (sqrt k)) 2)))
552.0ms	(* (+ (log n) (+ (log 2) (log PI))) (/ (+ 1 (sqrt k)) 1))

prune3.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize60.0ms

Local error

Found 4 expressions with local error:

3.2b	(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
0.3b	(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
0.2b	(* n (* 2 PI))
0.2b	(/ 1 (sqrt k))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt` `*-un-lft-identity`
60×	`times-frac`
50×	`pow-unpow`
43×	`add-cube-cbrt`
26×	`add-exp-log`
24×	`sqrt-prod`
17×	`pow1`
12×	`difference-of-squares`
11×	`add-cbrt-cube` `pow-exp`
9×	`prod-exp`
7×	`unpow-prod-down`
6×	`associate-/r*` `pow-prod-down` `distribute-lft-out` `distribute-lft-out--`
4×	`expm1-log1p-u` `pow-pow` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `associate-l` `cbrt-unprod` `div-inv` `pow-flip` `associate-/l*` `sqr-pow`
2×	`div-exp`
1×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `div-sub` `associate-r` `*-commutative` `inv-pow` `pow-sub`

Counts

4 → 162

Calls

4 calls:

Slowest

20.0ms	(* n (* 2 PI))
19.0ms	(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
11.0ms	(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
10.0ms	(/ 1 (sqrt k))

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

680.0ms	(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
311.0ms	(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
45.0ms	(/ 1 (sqrt k))
41.0ms	(* n (* 2 PI))

simplify8.1s

Counts

139 → 174

Calls

139 calls:

Slowest

603.0ms	(* (+ (log n) (+ (log 2) (log PI))) (/ (+ 1 (sqrt k)) 1))
588.0ms	(* (* (+ (log n) (log (* 2 PI))) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
523.0ms	(* (log (* n (* 2 PI))) (/ (+ 1 (sqrt k)) 1))
516.0ms	(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
470.0ms	(* (+ (log n) (log (* 2 PI))) (/ (+ 1 (sqrt k)) 1))

prune2.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes165.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch3.0ms

end0.0ms

sample7.3s

Algorithm

intervals

Results

3.8s	21207×	body	80	nan
2.6s	11907×	body	80	valid
1.0ms	2×	body	160	nan