Details

Time bar (total: 11.1s)

sample147.0ms

Algorithm
intervals
Results
49.0ms809×body80nan
23.0ms64×body1280nan
21.0ms325×body80valid
16.0ms59×body640nan
5.0ms24×body320nan
2.0ms17×body160nan

simplify36.0ms

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: 0.4b

Counts
2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

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

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:
2.0ms
(/ 1.0 (sqrt k))
6.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
4.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
3.0ms
(* (* 2.0 PI) n)

series541.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(/ 1.0 (sqrt k))
321.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
145.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
32.0ms
(* (* 2.0 PI) n)

simplify59.0ms

Algorithm
egg-herbie
Counts
40 → 40
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0605495
12255461
25001442

prune165.0ms

Filtered
40 candidates to 38 candidates (95.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New33740
Fresh000
Picked101
Done000
Total34741

Merged error: 0.0b

Counts
41 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
21×div-sub pow-sub
16×frac-times associate-*l/
6×frac-2neg associate-*l* clear-num *-commutative
5×associate-*r*
4×unpow-prod-down associate-*r/ sqr-pow
3×div-inv
1×pow-to-exp pow-unpow
Counts
4 → 40
Calls
4 calls:
3.0ms
(pow (* PI n) (/ (- 1.0 k) 2.0))
8.0ms
(* (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* PI n) (/ (- 1.0 k) 2.0)))
2.0ms
(* PI n)
4.0ms
(* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))

series878.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(pow (* PI n) (/ (- 1.0 k) 2.0))
568.0ms
(* (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* PI n) (/ (- 1.0 k) 2.0)))
25.0ms
(* PI n)
183.0ms
(* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))

simplify86.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
0848809
13470760
25001731

prune235.0ms

Filtered
52 candidates to 49 candidates (94.2%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New47552
Fresh426
Picked101
Done000
Total52759

Merged error: 0.0b

Counts
59 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
33×sqr-pow
28×times-frac
26×associate-*l*
22×*-commutative
14×unpow-prod-down associate-*r*
12×div-inv
7×associate-/l*
6×unswap-sqr
5×associate-*l/
4×associate-/r*
3×pow-to-exp pow-unpow div-sub associate-/r/ pow-sub
2×frac-2neg clear-num
1×pow-prod-down prod-exp associate-/l/
Counts
4 → 62
Calls
4 calls:
3.0ms
(pow (* PI n) (/ (- 1.0 k) 2.0))
12.0ms
(/ (* (pow (* PI n) (/ (- 1.0 k) 2.0)) (pow 2.0 (/ 1.0 2.0))) (* (/ (sqrt k) 1.0) (pow 2.0 (/ k 2.0))))
2.0ms
(* PI n)
7.0ms
(* (pow (* PI n) (/ (- 1.0 k) 2.0)) (pow 2.0 (/ 1.0 2.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
104.0ms
(pow (* PI n) (/ (- 1.0 k) 2.0))
771.0ms
(/ (* (pow (* PI n) (/ (- 1.0 k) 2.0)) (pow 2.0 (/ 1.0 2.0))) (* (/ (sqrt k) 1.0) (pow 2.0 (/ k 2.0))))
20.0ms
(* PI n)
310.0ms
(* (pow (* PI n) (/ (- 1.0 k) 2.0)) (pow 2.0 (/ 1.0 2.0)))

simplify106.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
09011320
140001269
250011203

prune359.0ms

Filtered
74 candidates to 71 candidates (95.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New70474
Fresh426
Picked101
Done000
Total75681

Merged error: 0b

Counts
81 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
0.2b
(/ (* (* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))) (pow 2.0 (/ 1.0 2.0))) (* (/ (sqrt k) 1.0) (pow 2.0 (/ k 2.0))))
0.3b
(* (* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))) (pow 2.0 (/ 1.0 2.0)))
0.6b
(pow PI (/ (- 1.0 k) 2.0))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
63×sqr-pow
47×associate-*l*
36×times-frac
23×associate-*r* *-commutative
19×unswap-sqr
17×div-inv
13×div-sub pow-sub
12×associate-*l/
9×associate-/l*
6×pow-to-exp pow-unpow
4×pow-prod-down associate-/r*
3×frac-times associate-*r/ prod-exp associate-/r/ associate-/l/
2×frac-2neg clear-num
Counts
4 → 85
Calls
4 calls:
8.0ms
(* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
23.0ms
(/ (* (* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))) (pow 2.0 (/ 1.0 2.0))) (* (/ (sqrt k) 1.0) (pow 2.0 (/ k 2.0))))
11.0ms
(* (* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))) (pow 2.0 (/ 1.0 2.0)))
3.0ms
(pow PI (/ (- 1.0 k) 2.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
189.0ms
(* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
1.1s
(/ (* (* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))) (pow 2.0 (/ 1.0 2.0))) (* (/ (sqrt k) 1.0) (pow 2.0 (/ k 2.0))))
407.0ms
(* (* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))) (pow 2.0 (/ 1.0 2.0)))
47.0ms
(pow PI (/ (- 1.0 k) 2.0))

simplify50.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011571820
150011771

prune614.0ms

Filtered
97 candidates to 95 candidates (97.9%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New96197
Fresh145
Picked011
Done000
Total976103

Merged error: 0b

Counts
103 → 6

regimes95.0ms

Accuracy

0% (0.5b 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
02216
12216

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.6s27202×body80nan
747.0ms2044×body1280nan
694.0ms10624×body80valid
476.0ms1711×body640nan
168.0ms839×body320nan
51.0ms427×body160nan