Details

Time bar (total: 11.5s)

sample153.0ms

Algorithm
intervals
Results
59.0ms1021×body80nan
21.0ms348×body80valid
18.0ms54×body1280nan
13.0ms52×body640nan
5.0ms27×body320nan
2.0ms21×body160nan

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0298
1598
21198
33258
410348
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: 0.4b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
8×unpow-prod-down
7×associate-*l* *-commutative
5×div-sub associate-*r* pow-sub
3×frac-times frac-2neg associate-*l/ clear-num div-inv
2×sqr-pow
1×pow-to-exp pow-unpow associate-*r/
Counts
4 → 28
Calls
4 calls:
4.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
3.0ms
(* (* 2.0 PI) n)
7.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
2.0ms
(/ 1.0 (sqrt k))

series543.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
36.0ms
(* (* 2.0 PI) n)
321.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
44.0ms
(/ 1.0 (sqrt k))

simplify56.0ms

Algorithm
egg-herbie
Counts
40 → 40
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0582496
12170463
25002455

prune159.0ms

Filtered
40 candidates to 38 candidates (95.0%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New34640
Fresh000
Picked101
Done000
Total35641

Merged error: 0.0b

Counts
41 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
0.3b
(* (* 2.0 PI) n)
0.3b
(* (* 2.0 PI) n)
0.3b
(/ (* (- 1.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (- (sqrt k)) (pow (* (* 2.0 PI) n) (/ k 2.0))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
90×associate-*r*
76×unpow-prod-down
64×times-frac
60×associate-*l* *-commutative
19×sqr-pow
18×neg-mul-1
8×associate-/r* associate-/l*
2×div-inv
1×distribute-lft-neg-out pow-to-exp pow-unpow frac-2neg distribute-frac-neg clear-num
Counts
4 → 97
Calls
4 calls:
3.0ms
(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
3.0ms
(* (* 2.0 PI) n)
3.0ms
(* (* 2.0 PI) n)
15.0ms
(/ (* (- 1.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (- (sqrt k)) (pow (* (* 2.0 PI) n) (/ k 2.0))))

series1.2s

Counts
4 → 12
Calls
4 calls:
260.0ms
(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
38.0ms
(* (* 2.0 PI) n)
32.0ms
(* (* 2.0 PI) n)
905.0ms
(/ (* (- 1.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (- (sqrt k)) (pow (* (* 2.0 PI) n) (/ k 2.0))))

simplify92.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
09711627
142611596
250021596

prune456.0ms

Filtered
109 candidates to 104 candidates (95.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1063109
Fresh325
Picked101
Done000
Total1105115

Merged error: 0.0b

Counts
115 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (* (- (sqrt k)) (pow (* (* 2.0 PI) n) (/ k 2.0))))
0.3b
(* (* 2.0 PI) n)
0.3b
(* (* 2.0 PI) n)
0.3b
(* (* (- 1.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (/ 1 (* (- (sqrt k)) (pow (* (* 2.0 PI) n) (/ k 2.0)))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
21×associate-*l*
16×associate-*r* associate-/r*
14×*-commutative
12×unpow-prod-down
11×associate-*r/
3×neg-mul-1 clear-num sqr-pow
2×distribute-lft-neg-out frac-2neg un-div-inv div-inv
1×inv-pow
Counts
4 → 42
Calls
4 calls:
6.0ms
(/ 1 (* (- (sqrt k)) (pow (* (* 2.0 PI) n) (/ k 2.0))))
3.0ms
(* (* 2.0 PI) n)
3.0ms
(* (* 2.0 PI) n)
12.0ms
(* (* (- 1.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (/ 1 (* (- (sqrt k)) (pow (* (* 2.0 PI) n) (/ k 2.0)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
203.0ms
(/ 1 (* (- (sqrt k)) (pow (* (* 2.0 PI) n) (/ k 2.0))))
32.0ms
(* (* 2.0 PI) n)
38.0ms
(* (* 2.0 PI) n)
893.0ms
(* (* (- 1.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (/ 1 (* (- (sqrt k)) (pow (* (* 2.0 PI) n) (/ k 2.0)))))

simplify79.0ms

Algorithm
egg-herbie
Counts
54 → 54
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
0722696
13212643
25001643

prune226.0ms

Filtered
54 candidates to 46 candidates (85.2%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New54054
Fresh044
Picked011
Done000
Total54559

Merged error: 0.0b

Counts
59 → 5

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (pow (* PI n) (/ 1.0 2.0)) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
0.3b
(* PI n)
0.3b
(* (* 2.0 PI) n)
0.3b
(* (/ (* (- 1.0) (pow 2.0 (/ 1.0 2.0))) -1) (/ (pow (* PI n) (/ 1.0 2.0)) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
111×associate-*r*
106×unpow-prod-down
91×frac-times
86×*-commutative
83×associate-/l*
63×associate-/r*
52×sqr-pow
47×associate-*l*
42×times-frac
24×clear-num
23×frac-2neg
14×neg-mul-1
13×associate-*r/
7×associate-*l/
3×div-inv
2×distribute-lft-neg-out
1×distribute-frac-neg un-div-inv
Counts
4 → 175
Calls
4 calls:
9.0ms
(/ (pow (* PI n) (/ 1.0 2.0)) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
2.0ms
(* PI n)
3.0ms
(* (* 2.0 PI) n)
17.0ms
(* (/ (* (- 1.0) (pow 2.0 (/ 1.0 2.0))) -1) (/ (pow (* PI n) (/ 1.0 2.0)) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))))

series1.7s

Counts
4 → 12
Calls
4 calls:
660.0ms
(/ (pow (* PI n) (/ 1.0 2.0)) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
20.0ms
(* PI n)
39.0ms
(* (* 2.0 PI) n)
1.0s
(* (/ (* (- 1.0) (pow 2.0 (/ 1.0 2.0))) -1) (/ (pow (* PI n) (/ 1.0 2.0)) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))))

simplify70.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
015913102
150013030

prune880.0ms

Filtered
187 candidates to 179 candidates (95.7%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1834187
Fresh303
Picked011
Done011
Total1866192

Merged error: 0b

Counts
192 → 6

regimes104.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03015
14215
24715
34915
44915

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.5s27204×body80nan
669.0ms1931×body1280nan
654.0ms10627×body80valid
427.0ms1628×body640nan
143.0ms789×body320nan
45.0ms399×body160nan