Details

Time bar (total: 37.8s)

sample191.0ms

Algorithm
intervals
Results
102.0ms641×body80nan
58.0ms381×body80valid

simplify9.4s

Counts
1 → 1
Iterations
IterNodes
76334
61992
5827
4330
3124
262
131
013

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
0.3b
(* n (* 2 PI))
1.1b
(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
43×times-frac
33×add-sqr-sqrt
30×*-un-lft-identity
28×add-cube-cbrt
26×add-exp-log
24×sqrt-prod
16×unpow-prod-up
14×pow1
10×add-cbrt-cube
9×prod-exp
8×sub-neg unpow-prod-down sqr-pow
7×associate-/l*
6×pow-unpow associate-/r* pow-prod-down pow-exp
5×div-exp
3×pow-pow associate-*l* cbrt-unprod insert-posit16 add-log-exp
2×pow-to-exp pow-sub difference-of-squares
1×cbrt-undiv clear-num frac-2neg associate-*r* *-commutative div-inv distribute-lft-out-- associate-/l/
Counts
3 → 118
Calls
3 calls:
22.0ms
(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
25.0ms
(* n (* 2 PI))
31.0ms
(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series508.0ms

Counts
3 → 9
Calls
3 calls:
280.0ms
(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
42.0ms
(* n (* 2 PI))
185.0ms
(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify1.1s

Counts
127 → 127
Iterations
IterNodes
22029
1645
0267

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
0.1b
(/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
0.3b
(* n (* 2 PI))
1.1b
(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
352×times-frac
166×add-sqr-sqrt
163×*-un-lft-identity
161×add-cube-cbrt
108×sqrt-prod
72×add-exp-log
64×unpow-prod-up
54×associate-/r*
32×sub-neg unpow-prod-down div-exp sqr-pow
18×prod-exp
16×pow1 add-cbrt-cube
15×pow-exp
9×associate-/l*
6×rec-exp pow-unpow 1-exp pow-prod-down associate-/r/ div-inv pow-sub
5×pow-to-exp
4×cbrt-undiv insert-posit16 add-log-exp
3×pow-pow associate-*l* cbrt-unprod
2×clear-num frac-2neg difference-of-squares
1×associate-*r* *-commutative pow-flip distribute-lft-out-- inv-pow
Counts
4 → 343
Calls
4 calls:
35.0ms
(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
20.0ms
(/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
12.0ms
(* n (* 2 PI))
14.0ms
(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series867.0ms

Counts
4 → 12
Calls
4 calls:
315.0ms
(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
330.0ms
(/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
38.0ms
(* n (* 2 PI))
185.0ms
(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify2.1s

Counts
355 → 355
Iterations
IterNodes
24327
11425
0532

prune4.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
0.2b
(* (sqrt k) (/ 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
0.3b
(* n (* 2 PI))
1.1b
(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
84×add-exp-log
56×add-sqr-sqrt
51×times-frac
40×prod-exp
37×*-un-lft-identity
31×add-cube-cbrt
27×associate-*r*
21×pow-exp
20×div-exp
17×pow1
16×unpow-prod-up add-cbrt-cube
12×sqr-pow
10×rec-exp 1-exp unswap-sqr
9×associate-*l*
8×sub-neg unpow-prod-down sqrt-prod
7×pow-to-exp associate-/r* pow-prod-down
6×pow-unpow
5×cbrt-unprod
4×insert-posit16 add-log-exp
3×pow-pow associate-/l* pow-sub
2×cbrt-undiv associate-/r/ *-commutative div-inv difference-of-squares
1×clear-num frac-2neg associate-*r/ un-div-inv pow-flip distribute-lft-out-- inv-pow
Counts
4 → 178
Calls
4 calls:
26.0ms
(/ 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
53.0ms
(* (sqrt k) (/ 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
13.0ms
(* n (* 2 PI))
21.0ms
(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series834.0ms

Counts
4 → 12
Calls
4 calls:
256.0ms
(/ 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
369.0ms
(* (sqrt k) (/ 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
45.0ms
(* n (* 2 PI))
164.0ms
(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify1.6s

Counts
190 → 190
Iterations
IterNodes
22754
1872
0325

prune2.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (pow n (- 1/2 (/ k 2))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k)))
0.2b
(/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))
0.4b
(pow (* 2 PI) (- 1/2 (/ k 2)))
1.1b
(pow n (- 1/2 (/ k 2)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
98×times-frac
94×add-sqr-sqrt
57×*-un-lft-identity
53×add-exp-log add-cube-cbrt
51×sqrt-prod
46×associate-*r*
32×unpow-prod-up
27×sqr-pow
25×unpow-prod-down
20×prod-exp
16×sub-neg div-exp pow-exp
15×unswap-sqr
12×pow-unpow
11×pow-to-exp add-cbrt-cube
9×associate-*l*
8×pow1
7×associate-/l*
6×associate-/r*
5×pow-sub
4×insert-posit16 add-log-exp difference-of-squares
3×pow-pow
2×cbrt-undiv cbrt-unprod div-inv distribute-lft-out--
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l/
Counts
4 → 219
Calls
4 calls:
23.0ms
(* (pow n (- 1/2 (/ k 2))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k)))
9.0ms
(/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))
12.0ms
(pow (* 2 PI) (- 1/2 (/ k 2)))
12.0ms
(pow n (- 1/2 (/ k 2)))

series1.3s

Counts
4 → 12
Calls
4 calls:
419.0ms
(* (pow n (- 1/2 (/ k 2))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k)))
631.0ms
(/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))
114.0ms
(pow (* 2 PI) (- 1/2 (/ k 2)))
97.0ms
(pow n (- 1/2 (/ k 2)))

simplify1.9s

Counts
231 → 231
Iterations
IterNodes
23486
11054
0387

prune2.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes113.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
216
116
014

end0.0ms

sample7.0s

Algorithm
intervals
Results
3.8s20500×body80nan
2.3s11813×body80valid
1.0ms4×body160nan