Details

Time bar (total: 13.3s)

sample163.0ms

Algorithm
intervals
Results
57.0ms796×body80nan
25.0ms62×body1280nan
23.0ms335×body80valid
14.0ms47×body640nan
7.0ms31×body320nan
2.0ms14×body160nan

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0298
1598
21198
33258
410448
550018

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.7b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.2b
(* (* 2.0 PI) n)
0.3b
(/ 1.0 (sqrt k))
0.4b
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
55×times-frac
49×*-un-lft-identity
46×add-exp-log
43×add-cube-cbrt
23×associate-*l* sqrt-prod
22×prod-exp
19×pow-unpow
16×add-cbrt-cube
15×pow1
9×pow-exp
8×associate-*r*
6×div-exp pow-prod-down associate-/r* unswap-sqr
5×cbrt-unprod sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp pow-pow div-sub div-inv associate-/l* distribute-lft-out-- pow-sub difference-of-squares
2×cbrt-undiv unpow-prod-down *-commutative
1×frac-times frac-2neg associate-*r/ associate-*l/ clear-num
Counts
4 → 157
Calls
4 calls:
11.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
5.0ms
(* (* 2.0 PI) n)
4.0ms
(/ 1.0 (sqrt k))
10.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series554.0ms

Counts
4 → 12
Calls
4 calls:
328.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
38.0ms
(* (* 2.0 PI) n)
39.0ms
(/ 1.0 (sqrt k))
149.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify105.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
09811502
140211398
250031383

prune463.0ms

Filtered
169 candidates to 119 candidates (70.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New15811169
Fresh000
Picked101
Done000
Total15911170

Merged error: 0.0b

Counts
170 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
0.3b
(/ 1.0 (sqrt k))
0.3b
(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
0.7b
(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
110×add-exp-log
68×prod-exp
63×add-sqr-sqrt
55×times-frac
50×*-un-lft-identity
44×add-cube-cbrt
27×pow-exp
23×associate-*l* sqrt-prod
20×add-cbrt-cube
19×pow-unpow
18×pow-to-exp
17×div-exp
12×associate-*r*
11×div-sub pow-sub
7×pow1 cbrt-unprod
6×frac-times associate-*l/ associate-/r* unswap-sqr sqr-pow
5×unpow-prod-down
4×expm1-log1p-u associate-*r/ log1p-expm1-u add-log-exp
3×cbrt-undiv div-inv associate-/l* distribute-lft-out-- difference-of-squares
2×pow-pow *-commutative
1×frac-2neg pow-prod-down clear-num
Counts
4 → 188
Calls
4 calls:
12.0ms
(* (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
5.0ms
(/ 1.0 (sqrt k))
11.0ms
(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
7.0ms
(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

series992.0ms

Counts
4 → 12
Calls
4 calls:
581.0ms
(* (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
44.0ms
(/ 1.0 (sqrt k))
287.0ms
(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
80.0ms
(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify138.0ms

Algorithm
egg-herbie
Counts
200 → 200
Iterations

Useful iterations: 2 (111.0ms)

IterNodesCost
011622113
149311915
250011887

prune489.0ms

Filtered
200 candidates to 127 candidates (63.5%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1982200
Fresh3710
Picked011
Done000
Total20110211

Merged error: 0.0b

Counts
211 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)))) (pow n (/ (- 1.0 k) 2.0)))
0.3b
(/ 1.0 (sqrt k))
0.3b
(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
0.7b
(pow PI (/ (- 1.0 k) 2.0))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
276×add-exp-log
215×prod-exp
70×pow-to-exp pow-exp
51×times-frac
50×add-sqr-sqrt *-un-lft-identity
44×add-cube-cbrt
41×div-exp
36×add-cbrt-cube
33×div-sub pow-sub
23×associate-*l*
22×frac-times
21×sqrt-prod
19×pow-unpow
17×cbrt-unprod
16×associate-*r/ associate-*l/
8×associate-*r*
7×pow1
6×unpow-prod-down associate-/r*
5×cbrt-undiv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×div-inv associate-/l* distribute-lft-out-- difference-of-squares
2×*-commutative sqr-pow
1×pow-pow frac-2neg pow-prod-down clear-num
Counts
4 → 243
Calls
4 calls:
17.0ms
(* (* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)))) (pow n (/ (- 1.0 k) 2.0)))
4.0ms
(/ 1.0 (sqrt k))
13.0ms
(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
6.0ms
(pow PI (/ (- 1.0 k) 2.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
868.0ms
(* (* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)))) (pow n (/ (- 1.0 k) 2.0)))
45.0ms
(/ 1.0 (sqrt k))
696.0ms
(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
53.0ms
(pow PI (/ (- 1.0 k) 2.0))

simplify72.0ms

Algorithm
egg-herbie
Counts
255 → 255
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
015333387
150012977

prune598.0ms

Filtered
255 candidates to 138 candidates (54.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2523255
Fresh358
Picked101
Done011
Total2569265

Merged error: 0b

Counts
265 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow PI (/ k 2.0))
0.3b
(/ (* (* 1.0 (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ 1.0 2.0)))) (pow n (/ 1.0 2.0))) (* (* (sqrt k) (pow PI (/ k 2.0))) (pow n (/ k 2.0))))
0.3b
(* (* 1.0 (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ 1.0 2.0)))) (pow n (/ 1.0 2.0)))
1.0b
(pow PI (/ 1.0 2.0))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
2253×add-exp-log
1974×prod-exp
646×pow-to-exp pow-exp
442×div-exp
67×add-cbrt-cube
36×cbrt-unprod
26×pow-unpow
22×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
19×times-frac
12×cbrt-undiv
9×unpow-prod-down
7×associate-*r*
6×pow1
4×expm1-log1p-u associate-*l/ log1p-expm1-u add-log-exp
3×div-inv sqr-pow
2×pow-pow div-sub associate-*r/ pow-sub
1×frac-2neg associate-*l* clear-num associate-/r* *-commutative associate-/l/ associate-/l*
Counts
4 → 583
Calls
4 calls:
4.0ms
(pow PI (/ k 2.0))
24.0ms
(/ (* (* 1.0 (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ 1.0 2.0)))) (pow n (/ 1.0 2.0))) (* (* (sqrt k) (pow PI (/ k 2.0))) (pow n (/ k 2.0))))
16.0ms
(* (* 1.0 (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ 1.0 2.0)))) (pow n (/ 1.0 2.0)))
4.0ms
(pow PI (/ 1.0 2.0))

series1.8s

Counts
4 → 10
Calls
4 calls:
32.0ms
(pow PI (/ k 2.0))
1.3s
(/ (* (* 1.0 (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ 1.0 2.0)))) (pow n (/ 1.0 2.0))) (* (* (sqrt k) (pow PI (/ k 2.0))) (pow n (/ k 2.0))))
447.0ms
(* (* 1.0 (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ 1.0 2.0)))) (pow n (/ 1.0 2.0)))
0.0ms
(pow PI (/ 1.0 2.0))

simplify142.0ms

Algorithm
egg-herbie
Counts
593 → 593
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0165910634
1500110349

prune559.0ms

Filtered
593 candidates to 100 candidates (16.9%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New5930593
Fresh077
Picked011
Done011
Total5939602

Merged error: 0b

Counts
602 → 9

regimes156.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02618
12618

end0.0ms

sample5.1s

Algorithm
intervals
Results
1.8s27028×body80nan
891.0ms2114×body1280nan
795.0ms10703×body80valid
508.0ms1669×body640nan
184.0ms857×body320nan
55.0ms411×body160nan