Details

Time bar (total: 4.5m)

sample210.0ms

Algorithm
intervals
Results
111.0ms559×body80nan
62.0ms362×body80valid

simplify698.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
698.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize35.0ms

Local error

Found 3 expressions with local error:

2.1b
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.3b
(* n (* 2 PI))
0.2b
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

rewrite55.0ms

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
22.0ms
(* n (* 2 PI))
18.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
14.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

series538.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
326.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
177.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
35.0ms
(* n (* 2 PI))

simplify46.8s

Counts
160 → 127
Calls
160 calls:
Slowest
828.0ms
(/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
766.0ms
(- (+ (* 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)))))
694.0ms
(pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
659.0ms
(pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
628.0ms
(pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

2.1b
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.3b
(/ 1 (sqrt k))
0.3b
(* n (* 2 PI))
0.2b
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))

rewrite122.0ms

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
53.0ms
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))
28.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
26.0ms
(* n (* 2 PI))
10.0ms
(/ 1 (sqrt k))

series585.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
310.0ms
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))
185.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
53.0ms
(/ 1 (sqrt k))
37.0ms
(* n (* 2 PI))

simplify42.4s

Counts
218 → 189
Calls
218 calls:
Slowest
818.0ms
(* (* (* (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))))
802.0ms
(* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ 1 (sqrt (sqrt k))))
750.0ms
(- (+ (* 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)))))
699.0ms
(pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
653.0ms
(* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 3 expressions with local error:

2.1b
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.3b
(* n (* 2 PI))
0.2b
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow k -1/2))

rewrite92.0ms

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
33.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
32.0ms
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow k -1/2))
26.0ms
(* n (* 2 PI))

series627.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
366.0ms
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow k -1/2))
201.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
59.0ms
(* n (* 2 PI))

simplify27.5s

Counts
119 → 112
Calls
119 calls:
Slowest
760.0ms
(- (+ (* 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)))))
730.0ms
(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (sqrt 2)))
705.0ms
(pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
644.0ms
(pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
593.0ms
(* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

2.1b
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.3b
(* 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))))

rewrite92.0ms

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
33.0ms
(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
20.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
17.0ms
(* n (* 2 PI))
13.0ms
(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))

series939.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
371.0ms
(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
336.0ms
(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
187.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
44.0ms
(* n (* 2 PI))

simplify2.2m

Counts
445 → 307
Calls
445 calls:
Slowest
981.0ms
(pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
800.0ms
(/ (sqrt 1) (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
765.0ms
(/ (* (* 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)))))
756.0ms
(- (+ (* 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)))))
732.0ms
(/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))

prune3.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes143.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch2.0ms

end0.0ms

sample7.6s

Algorithm
intervals
Results
4.0s20456×body80nan
2.3s11762×body80valid