Details

Time bar (total: 12.3s)

sample145.0ms

Algorithm
intervals
Results
51.0ms863×body80nan
22.0ms65×body1280nan
20.0ms324×body80valid
13.0ms50×body640nan
6.0ms33×body320nan
2.0ms14×body160nan

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0298
1598
21198
33258
410448
550018

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

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
(* (* 2.0 PI) n)
3.0ms
(/ 1.0 (sqrt k))
9.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
17.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))

series532.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* (* 2.0 PI) n)
37.0ms
(/ 1.0 (sqrt k))
141.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
317.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))

simplify99.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
09811502
140211398
250011383

prune474.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
0.2b
(* (* 2.0 PI) n)
0.2b
(* (* 2.0 PI) n)
0.2b
(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
176×add-exp-log
105×prod-exp
39×pow-exp
36×div-exp
26×add-cbrt-cube
20×pow1
13×add-sqr-sqrt pow-to-exp add-cube-cbrt pow-unpow *-un-lft-identity
10×times-frac cbrt-unprod
9×pow-prod-down
6×associate-*r*
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-pow
2×associate-*l* *-commutative div-inv
1×unpow-prod-down frac-2neg clear-num associate-/r* associate-/l* sqr-pow
Counts
4 → 126
Calls
4 calls:
7.0ms
(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
11.0ms
(* (* 2.0 PI) n)
7.0ms
(* (* 2.0 PI) n)
10.0ms
(/ (* 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:
254.0ms
(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
37.0ms
(* (* 2.0 PI) n)
31.0ms
(* (* 2.0 PI) n)
876.0ms
(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))

simplify99.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
09351406
140121247
250011237

prune313.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
678×add-exp-log
390×prod-exp
218×div-exp
144×pow-exp
48×pow-to-exp
44×add-cbrt-cube
37×rec-exp 1-exp
20×times-frac
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
15×pow1
14×cbrt-unprod
13×cbrt-undiv
6×associate-*r* pow-prod-down associate-/r* div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
2×frac-2neg associate-*l* clear-num *-commutative
1×pow-flip associate-/r/ inv-pow
Counts
4 → 249
Calls
4 calls:
18.0ms
(/ 1 (/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))))
10.0ms
(/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))
6.0ms
(* (* 2.0 PI) n)
6.0ms
(* (* 2.0 PI) n)

series1.7s

Counts
4 → 12
Calls
4 calls:
776.0ms
(/ 1 (/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))))
822.0ms
(/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))
31.0ms
(* (* 2.0 PI) n)
39.0ms
(* (* 2.0 PI) n)

simplify60.0ms

Algorithm
egg-herbie
Counts
261 → 261
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
014063861
150023567

prune394.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 2.0 PI) n)
0.2b
(/ (* 1.0 (* (pow (* 2.0 PI) (/ 1.0 2.0)) (pow n (/ 1.0 2.0)))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
0.5b
(* (pow (* 2.0 PI) (/ 1.0 2.0)) (pow n (/ 1.0 2.0)))
1.0b
(pow (* 2.0 PI) (/ 1.0 2.0))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
424×add-exp-log
299×prod-exp
114×pow-exp
84×div-exp
64×pow-to-exp
32×add-cbrt-cube
22×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
13×pow-unpow cbrt-unprod
12×pow1
10×times-frac associate-*r*
8×sqr-pow
7×unpow-prod-down
6×cbrt-undiv associate-*l* unswap-sqr
5×pow-prod-down
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-pow *-commutative div-inv
1×frac-2neg clear-num associate-/r* associate-/l*
Counts
4 → 196
Calls
4 calls:
10.0ms
(* (* 2.0 PI) n)
16.0ms
(/ (* 1.0 (* (pow (* 2.0 PI) (/ 1.0 2.0)) (pow n (/ 1.0 2.0)))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
8.0ms
(* (pow (* 2.0 PI) (/ 1.0 2.0)) (pow n (/ 1.0 2.0)))
3.0ms
(pow (* 2.0 PI) (/ 1.0 2.0))

series2.1s

Counts
4 → 10
Calls
4 calls:
31.0ms
(* (* 2.0 PI) n)
967.0ms
(/ (* 1.0 (* (pow (* 2.0 PI) (/ 1.0 2.0)) (pow n (/ 1.0 2.0)))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
1.1s
(* (pow (* 2.0 PI) (/ 1.0 2.0)) (pow n (/ 1.0 2.0)))
0.0ms
(pow (* 2.0 PI) (/ 1.0 2.0))

simplify55.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011552568
150012352

prune373.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes104.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02313
12313

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.5s26685×body80nan
710.0ms1982×body1280nan
687.0ms10557×body80valid
469.0ms1720×body640nan
163.0ms833×body320nan
51.0ms437×body160nan