Details

Time bar (total: 3.3m)

sample217.0ms

Algorithm
intervals
Results
121.0ms696×body80nan
64.0ms375×body80valid

simplify304.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
304.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize47.0ms

Local error

Found 3 expressions with local error:

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

rewrite49.0ms

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×pow-pow associate-*l* cbrt-unprod insert-posit16 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 → 118
Calls
3 calls:
Slowest
23.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
13.0ms
(* n (* 2 PI))
11.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

series556.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
299.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
204.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
53.0ms
(* n (* 2 PI))

simplify28.7s

Counts
124 → 127
Calls
124 calls:
Slowest
1.0s
(- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
742.0ms
(/ (* (* (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)))
706.0ms
(* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
684.0ms
(/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
658.0ms
(/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite106.0ms

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×insert-posit16 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 → 177
Calls
4 calls:
Slowest
33.0ms
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))
32.0ms
(* n (* 2 PI))
27.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
10.0ms
(/ 1 (sqrt k))

series648.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
350.0ms
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))
217.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
45.0ms
(* n (* 2 PI))
35.0ms
(/ 1 (sqrt k))

simplify21.1s

Counts
173 → 189
Calls
173 calls:
Slowest
855.0ms
(* (* (* (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))))
799.0ms
(- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
726.0ms
(* (pow (* n (* 2 PI)) (/ k 2)) (sqrt k))
511.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
473.0ms
(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize54.0ms

Local error

Found 3 expressions with local error:

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

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log
33×add-sqr-sqrt
30×prod-exp
26×*-un-lft-identity
22×pow-unpow
18×times-frac
17×pow-exp add-cube-cbrt
14×pow1
10×add-cbrt-cube
9×pow-to-exp
8×associate-*r* associate-*l* sqr-pow
7×unpow-prod-down
6×pow-prod-down difference-of-squares unswap-sqr
4×cbrt-unprod
3×pow-pow insert-posit16 distribute-lft-out-- add-log-exp
2×div-sub *-commutative pow-sub
1×associate-*l/ div-inv
Counts
3 → 103
Calls
3 calls:
Slowest
40.0ms
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow k -1/2))
32.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
14.0ms
(* n (* 2 PI))

series544.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
327.0ms
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow k -1/2))
175.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
41.0ms
(* n (* 2 PI))

simplify12.8s

Counts
87 → 112
Calls
87 calls:
Slowest
837.0ms
(- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
549.0ms
(* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))
457.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
446.0ms
(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
417.0ms
(sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.2b
(* n (* 2 PI))
0.2b
(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
0.1b
(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
273×times-frac
147×add-sqr-sqrt *-un-lft-identity
138×add-cube-cbrt
78×sqrt-prod
72×add-exp-log
40×associate-/r*
32×unpow-prod-down div-exp sqr-pow
22×pow-unpow
18×prod-exp
16×pow1 add-cbrt-cube
15×pow-exp
9×associate-/l*
7×div-inv
6×rec-exp 1-exp div-sub pow-prod-down associate-/r/ pow-sub difference-of-squares
5×pow-to-exp
4×cbrt-undiv insert-posit16 add-log-exp
3×pow-pow associate-*l* cbrt-unprod distribute-lft-out--
2×clear-num frac-2neg
1×associate-*r* *-commutative pow-flip inv-pow
Counts
4 → 295
Calls
4 calls:
Slowest
31.0ms
(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
23.0ms
(* n (* 2 PI))
19.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
18.0ms
(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))

series901.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
330.0ms
(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
294.0ms
(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
234.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
43.0ms
(* n (* 2 PI))

simplify1.9m

Counts
390 → 307
Calls
390 calls:
Slowest
1.0s
(/ (* (* 1 1) 1) (* (* (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
784.0ms
(/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
772.0ms
(- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
769.0ms
(/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2))))
755.0ms
(/ (sqrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))

prune3.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes127.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample7.8s

Algorithm
intervals
Results
4.6s20798×body80nan
2.3s11849×body80valid
1.0ms3×body160nan