Details

Time bar (total: 6.4s)

analyze394.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%50%50%2
0%50%50%3
0%50%50%4
12.5%37.5%50%5
15.6%31.2%53.2%6
17.2%26.5%56.3%7
18%22.6%59.4%8
18.3%19.9%61.8%9
18.5%17.8%63.7%10
18.6%16.3%65.1%11
18.7%15.2%66.1%12
18.7%14.4%66.9%13
18.7%13.8%67.4%14

sample88.0ms

Algorithm
intervals
Results
23.0ms32×body1280nan
22.0ms256×body80valid
12.0ms28×body640nan
11.0ms84×body80overflowed
4.0ms15×body320nan
2.0ms27×body80nan
1.0ms5×body160nan
0.0ms4×body80invalid

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
0498716
1498716

prune10.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.3b

Counts
2 → 2

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
41×add-sqr-sqrt
39×*-un-lft-identity
33×add-cube-cbrt
23×add-exp-log
19×pow-unpow
18×sqrt-prod
11×pow1
8×unpow-prod-down sqr-pow
7×prod-exp add-cbrt-cube
6×pow-exp associate-/r*
5×div-exp associate-/l*
4×pow-prod-down
3×pow-pow associate-*r* associate-*l* distribute-lft-out-- add-log-exp difference-of-squares
2×pow-to-exp div-sub div-inv pow-sub
1×cbrt-undiv frac-2neg clear-num *-commutative cbrt-unprod associate-/l/ unswap-sqr
Counts
3 → 112
Calls
3 calls:
9.0ms
(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))
6.0ms
(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
3.0ms
(* PI n)

series52.0ms

Counts
3 → 9
Calls
3 calls:
15.0ms
(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))
34.0ms
(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
2.0ms
(* PI n)

simplify48.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
050082183

prune234.0ms

Filtered
82 candidates to 121 candidates (-47.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1129121
Fresh011
Picked101
Done000
Total11310123

Merged error: 0.0b

Counts
123 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
124×add-exp-log
65×prod-exp
36×pow-exp
30×div-exp
18×add-sqr-sqrt
17×pow1
16×add-cube-cbrt *-un-lft-identity add-cbrt-cube
14×times-frac
13×pow-unpow
12×pow-to-exp
7×pow-prod-down
6×associate-*l*
5×cbrt-unprod associate-/l*
4×associate-*r* add-log-exp
3×unpow-prod-down pow-pow sqr-pow
2×cbrt-undiv *-commutative div-inv
1×frac-2neg clear-num associate-/r* unswap-sqr
Counts
4 → 118
Calls
4 calls:
6.0ms
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))
9.0ms
(/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (* (sqrt k) (pow (* PI (* 2.0 n)) (/ k 2.0))))
3.0ms
(* PI n)
5.0ms
(* PI (* 2.0 n))

series157.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))
127.0ms
(/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (* (sqrt k) (pow (* PI (* 2.0 n)) (/ k 2.0))))
2.0ms
(* PI n)
3.0ms
(* PI (* 2.0 n))

simplify37.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
050142171

prune213.0ms

Filtered
70 candidates to 130 candidates (-85.7%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1291130
Fresh369
Picked011
Done000
Total1328140

Merged error: 0.0b

Counts
140 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
338×add-exp-log
167×add-sqr-sqrt times-frac
156×prod-exp
146×div-exp
110×pow-exp
75×add-cube-cbrt *-un-lft-identity
61×sqr-pow
60×sqrt-prod
59×unpow-prod-down
58×pow-to-exp
52×associate-*l*
36×unswap-sqr
33×associate-*r*
25×add-cbrt-cube
13×pow1
8×cbrt-unprod
7×associate-/l*
6×associate-/r*
5×cbrt-undiv pow-prod-down
4×add-log-exp
3×*-commutative div-inv
1×frac-times frac-2neg associate-*r/ associate-*l/ clear-num
Counts
4 → 315
Calls
4 calls:
6.0ms
(* PI n)
5.0ms
(* PI (* 2.0 n))
31.0ms
(* (/ (pow 2.0 (/ 1.0 2.0)) (sqrt k)) (/ (pow (* PI n) (/ 1.0 2.0)) (pow (* PI (* 2.0 n)) (/ k 2.0))))
6.0ms
(/ (pow 2.0 (/ 1.0 2.0)) (sqrt k))

series167.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(* PI n)
3.0ms
(* PI (* 2.0 n))
127.0ms
(* (/ (pow 2.0 (/ 1.0 2.0)) (sqrt k)) (/ (pow (* PI n) (/ 1.0 2.0)) (pow (* PI (* 2.0 n)) (/ k 2.0))))
34.0ms
(/ (pow 2.0 (/ 1.0 2.0)) (sqrt k))

simplify79.0ms

Algorithm
egg-herbie
Counts
327 → 327
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
049828545
149828545

prune685.0ms

Filtered
173 candidates to 327 candidates (-89.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New3261327
Fresh156
Picked011
Done011
Total3278335

Merged error: 0b

Counts
335 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
884×add-exp-log
529×prod-exp
351×div-exp
303×pow-exp
225×pow-to-exp
146×times-frac
136×add-sqr-sqrt
89×add-cube-cbrt *-un-lft-identity
80×unpow-prod-down
54×sqrt-prod
47×associate-*l*
46×associate-*r*
40×sqr-pow
32×add-cbrt-cube
21×unswap-sqr
13×pow-unpow
12×cbrt-unprod
7×pow1 cbrt-undiv associate-/l*
6×associate-/r*
4×associate-*l/ div-inv add-log-exp
2×*-commutative
1×frac-times pow-pow frac-2neg associate-*r/ pow-prod-down clear-num
Counts
4 → 459
Calls
4 calls:
21.0ms
(* (* (/ (pow 2.0 (/ 1.0 2.0)) (sqrt k)) (pow PI (/ 1.0 2.0))) (/ (pow n (/ 1.0 2.0)) (pow (* PI (* 2.0 n)) (/ k 2.0))))
17.0ms
(* (/ (pow 2.0 (/ 1.0 2.0)) (sqrt k)) (pow PI (/ 1.0 2.0)))
6.0ms
(/ (pow 2.0 (/ 1.0 2.0)) (sqrt k))
3.0ms
(pow PI (/ 1.0 2.0))

series216.0ms

Counts
4 → 10
Calls
4 calls:
121.0ms
(* (* (/ (pow 2.0 (/ 1.0 2.0)) (sqrt k)) (pow PI (/ 1.0 2.0))) (/ (pow n (/ 1.0 2.0)) (pow (* PI (* 2.0 n)) (/ k 2.0))))
60.0ms
(* (/ (pow 2.0 (/ 1.0 2.0)) (sqrt k)) (pow PI (/ 1.0 2.0)))
34.0ms
(/ (pow 2.0 (/ 1.0 2.0)) (sqrt k))
0.0ms
(pow PI (/ 1.0 2.0))

simplify106.0ms

Algorithm
egg-herbie
Counts
469 → 469
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
0500811888

prune895.0ms

Filtered
183 candidates to 469 candidates (-156.3%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New4690469
Fresh055
Picked011
Done022
Total4698477

Merged error: 0b

Counts
477 → 8

regimes246.0ms

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
02324
12324

end0.0ms

sample2.5s

Algorithm
intervals
Results
703.0ms8000×body80valid
585.0ms967×body1280nan
360.0ms811×body640nan
329.0ms2412×body80overflowed
112.0ms371×body320nan
42.0ms709×body80nan
35.0ms201×body160nan
22.0ms203×body80invalid

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