Details

Time bar (total: 9.8m)

sample196.0ms

Algorithm
intervals
Results
95.0ms700×body80nan
68.0ms373×body80valid

simplify328.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
328.0ms
(* (/ 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

localize37.0ms

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))

rewrite83.0ms

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
31.0ms
(* n (* 2 PI))
27.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
21.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

series650.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
368.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
215.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
67.0ms
(* n (* 2 PI))

simplify50.6s

Counts
166 → 133
Calls
166 calls:
Slowest
920.0ms
(pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
812.0ms
(pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
788.0ms
(/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
748.0ms
(log (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
718.0ms
(* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite110.0ms

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-*l*
22×pow-unpow
17×pow1
16×add-cbrt-cube
15×pow-exp
12×div-exp
10×unswap-sqr
8×associate-*r*
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/ inv-pow
Counts
4 → 184
Calls
4 calls:
Slowest
40.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
37.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
17.0ms
(* (* 2 PI) n)
10.0ms
(/ 1 (sqrt k))

series583.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
317.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
173.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
54.0ms
(* (* 2 PI) n)
38.0ms
(/ 1 (sqrt k))

simplify45.3s

Counts
226 → 196
Calls
226 calls:
Slowest
881.0ms
(* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
795.0ms
(pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
771.0ms
(* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
752.0ms
(pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
740.0ms
(pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))

prune2.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
954×times-frac sqrt-prod
452×add-sqr-sqrt *-un-lft-identity
443×add-cube-cbrt
101×unpow-prod-down sqr-pow
54×associate-/l*
46×add-exp-log
22×pow-unpow
18×associate-/r*
16×add-cbrt-cube div-exp
15×pow1
13×div-inv
12×prod-exp
9×pow-exp
6×pow-prod-down difference-of-squares
4×expm1-log1p-u cbrt-undiv insert-posit16 log1p-expm1-u add-log-exp
3×pow-to-exp pow-pow associate-*l* cbrt-unprod distribute-lft-out--
2×clear-num frac-2neg div-sub pow-sub associate-/l/
1×associate-*r* *-commutative
Counts
4 → 663
Calls
4 calls:
Slowest
22.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
22.0ms
(* n (* 2 PI))
21.0ms
(/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k)))
13.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))

series926.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
332.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
328.0ms
(/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k)))
229.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
38.0ms
(* n (* 2 PI))

simplify6.6m

Counts
1165 → 675
Calls
1165 calls:
Slowest
877.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
845.0ms
(/ (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k)))
838.0ms
(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (sqrt 2)))
824.0ms
(/ (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
818.0ms
(/ (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))

prune9.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite123.0ms

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
32.0ms
(* n (* 2 PI))
29.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
29.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
24.0ms
(* n (* 2 PI))

series489.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
208.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
184.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
55.0ms
(* n (* 2 PI))
42.0ms
(* n (* 2 PI))

simplify1.1m

Counts
238 → 234
Calls
238 calls:
Slowest
786.0ms
(pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) 1) (sqrt 2)))
751.0ms
(pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) 1) (sqrt 2)))
731.0ms
(pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (sqrt 2)))
730.0ms
(pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) 1))
714.0ms
(pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) 1) (sqrt 2)))

prune3.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes132.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch4.0ms

end0.0ms

sample7.6s

Algorithm
intervals
Results
4.1s20746×body80nan
2.3s11932×body80valid
1.0ms2×body160nan