Details

Time bar (total: 2.5m)

sample204.0ms

Algorithm
intervals
Results
95.0ms643×body80nan
74.0ms388×body80valid

simplify351.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
351.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize47.0ms

Local error

Found 3 expressions with local error:

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

rewrite56.0ms

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
28.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
16.0ms
(* n (* 2 PI))
11.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

series554.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
335.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
160.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
59.0ms
(* n (* 2 PI))

simplify27.2s

Counts
124 → 133
Calls
124 calls:
Slowest
857.0ms
(/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k))))
664.0ms
(/ (* (* (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))
528.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
526.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

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
25.0ms
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))
19.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
14.0ms
(* n (* 2 PI))
5.0ms
(/ 1 (sqrt k))

series618.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
307.0ms
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))
237.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
38.0ms
(* n (* 2 PI))
36.0ms
(/ 1 (sqrt k))

simplify19.3s

Counts
173 → 197
Calls
173 calls:
Slowest
1.1s
(* (* (* (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))))
550.0ms
(* (pow (* n (* 2 PI)) (/ k 2)) (sqrt k))
485.0ms
(exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
427.0ms
(* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ 1 (sqrt (sqrt k))))
422.0ms
(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))

prune2.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

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

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
173×add-sqr-sqrt
169×*-un-lft-identity
140×pow-unpow
115×add-cube-cbrt
91×add-exp-log
64×prod-exp
36×pow-exp difference-of-squares
21×pow1
18×distribute-lft-out--
12×pow-to-exp div-sub
11×add-cbrt-cube
10×pow-prod-down sqr-pow
8×associate-*l* div-inv
6×unpow-prod-down pow-pow associate-*r* pow-sub
5×swap-sqr
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×*-commutative
1×pow2 frac-times associate-*l/ associate-*r/ pow-sqr pow-prod-up
Counts
4 → 264
Calls
4 calls:
Slowest
41.0ms
(* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
29.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
25.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
22.0ms
(* n (* 2 PI))

series687.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
259.0ms
(* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
217.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
172.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
39.0ms
(* n (* 2 PI))

simplify37.0s

Counts
239 → 276
Calls
239 calls:
Slowest
826.0ms
(+ (* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2)) (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)))
716.0ms
(+ (* (+ (log n) (+ (log 2) (log PI))) (/ (/ (- 1 k) 2) 2)) (* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2)))
628.0ms
(+ (* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2)) (* (+ (log n) (+ (log 2) (log PI))) (/ (/ (- 1 k) 2) 2)))
561.0ms
(pow (exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 2)
554.0ms
(+ (* (+ (log n) (+ (log 2) (log PI))) (/ (/ (- 1 k) 2) 2)) (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)))

prune3.8s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
0.6b
(pow n (/ (/ (- 1 k) 2) 2))
0.2b
(* n (* 2 PI))
0.2b
(* (pow n (/ (/ (- 1 k) 2) 2)) (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
205×add-exp-log
180×prod-exp
168×add-sqr-sqrt *-un-lft-identity
140×pow-unpow
114×add-cube-cbrt
91×pow-exp
50×pow-to-exp
36×difference-of-squares
28×div-sub
18×distribute-lft-out--
16×pow1
14×add-cbrt-cube pow-sub
10×associate-*l*
8×pow-prod-down div-inv
7×unpow-prod-down
6×cbrt-unprod
5×frac-times associate-*r/
4×expm1-log1p-u pow-pow insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l/ sqr-pow
2×associate-*r* *-commutative
Counts
4 → 291
Calls
4 calls:
Slowest
154.0ms
(* (pow n (/ (/ (- 1 k) 2) 2)) (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
32.0ms
(* n (* 2 PI))
30.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
12.0ms
(pow n (/ (/ (- 1 k) 2) 2))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
539.0ms
(* (pow n (/ (/ (- 1 k) 2) 2)) (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
470.0ms
(* n (* 2 PI))
184.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
72.0ms
(pow n (/ (/ (- 1 k) 2) 2))

simplify44.0s

Counts
257 → 303
Calls
257 calls:
Slowest
727.0ms
(* (pow n (/ (/ 1 2) 2)) (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
684.0ms
(* (pow n (/ (/ k 2) 2)) (* (pow (* 2 PI) (/ (/ k 2) 2)) (pow (* n (* 2 PI)) (/ (/ k 2) 2))))
647.0ms
(* (pow n (/ (/ 1 2) 2)) (* (pow (* 2 PI) (/ (/ 1 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
554.0ms
(+ (log (pow n (/ (/ (- 1 k) 2) 2))) (+ (log (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (log (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))))
535.0ms
(+ (log (pow n (/ (/ (- 1 k) 2) 2))) (+ (* (log (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2))))

prune4.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes165.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
4.0s20932×body80nan
2.2s11922×body80valid
1.0ms3×body160nan