Details

Time bar (total: 4.7m)

sample207.0ms

Algorithm
intervals
Results
106.0ms559×body80nan
67.0ms362×body80valid

simplify319.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
319.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize23.0ms

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))

rewrite51.0ms

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
18.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
17.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
13.0ms
(* n (* 2 PI))

series547.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
290.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
196.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
61.0ms
(* n (* 2 PI))

simplify49.5s

Counts
166 → 133
Calls
166 calls:
Slowest
1.0s
(/ (* (* (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)))
816.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k))))
690.0ms
(pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
685.0ms
(pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
674.0ms
(pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

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)))

rewrite101.0ms

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
30.0ms
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))
30.0ms
(* 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
335.0ms
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))
210.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
54.0ms
(* n (* 2 PI))
48.0ms
(/ 1 (sqrt k))

simplify44.7s

Counts
226 → 197
Calls
226 calls:
Slowest
822.0ms
(* (* (* (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))))
713.0ms
(pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
685.0ms
(pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
647.0ms
(pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
646.0ms
(pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))

prune2.7s

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))

rewrite81.0ms

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×expm1-log1p-u pow-pow insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp
2×div-sub *-commutative pow-sub
1×associate-*l/ div-inv
Counts
3 → 109
Calls
3 calls:
Slowest
36.0ms
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow k -1/2))
28.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
13.0ms
(* n (* 2 PI))

series589.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
339.0ms
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow k -1/2))
197.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
53.0ms
(* n (* 2 PI))

simplify29.2s

Counts
125 → 118
Calls
125 calls:
Slowest
734.0ms
(pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
728.0ms
(pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
726.0ms
(pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
656.0ms
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow k (/ -1/2 2)))
624.0ms
(* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

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))))

rewrite112.0ms

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×expm1-log1p-u cbrt-undiv insert-posit16 log1p-expm1-u 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 → 303
Calls
4 calls:
Slowest
31.0ms
(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
28.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
25.0ms
(* n (* 2 PI))
19.0ms
(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))

series913.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
359.0ms
(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
344.0ms
(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
157.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
53.0ms
(* n (* 2 PI))

simplify2.3m

Counts
453 → 315
Calls
453 calls:
Slowest
1.0s
(/ 1 (/ (sqrt 1) (pow n (/ (- 1 k) 2))))
818.0ms
(/ (* (* 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)))))
807.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
797.0ms
(cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
764.0ms
(pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))

prune3.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes132.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample8.0s

Algorithm
intervals
Results
4.7s20456×body80nan
2.4s11762×body80valid