Details

Time bar (total: 6.5s)

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

sample90.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
22.0ms38×body1280nan
11.0ms26×body640nan
11.0ms81×body80overflowed
5.0ms16×body320nan
2.0ms31×body80nan
1.0ms6×body160nan
1.0ms10×body80invalid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
0505216

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

localize14.0ms

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))
4.0ms
(* PI n)

series53.0ms

Counts
3 → 9
Calls
3 calls:
16.0ms
(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))
35.0ms
(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
2.0ms
(* PI n)

simplify34.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
050032191

prune231.0ms

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

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New11110121
Fresh101
Picked101
Done000
Total11310123

Merged error: 0.0b

Counts
123 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
270×times-frac
143×add-sqr-sqrt *-un-lft-identity
137×add-cube-cbrt
78×sqrt-prod
72×add-exp-log
40×associate-/r*
32×unpow-prod-down div-exp sqr-pow
19×pow-unpow
18×prod-exp
16×pow1 add-cbrt-cube
15×pow-exp
9×associate-/l*
7×div-inv
6×rec-exp 1-exp div-sub pow-prod-down associate-/r/ pow-sub
5×pow-to-exp
4×cbrt-undiv add-log-exp
3×pow-pow associate-*l* cbrt-unprod distribute-lft-out-- difference-of-squares
2×frac-2neg clear-num
1×pow-flip associate-*r* *-commutative inv-pow
Counts
4 → 288
Calls
4 calls:
12.0ms
(/ 1 (/ (sqrt k) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))))
9.0ms
(pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))
7.0ms
(/ (sqrt k) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))
5.0ms
(* PI (* 2.0 n))

series135.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ 1 (/ (sqrt k) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))))
16.0ms
(pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))
64.0ms
(/ (sqrt k) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))
3.0ms
(* PI (* 2.0 n))

simplify75.0ms

Algorithm
egg-herbie
Counts
300 → 300
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
054107228

prune474.0ms

Filtered
163 candidates to 300 candidates (-84.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2982300
Fresh369
Picked101
Done000
Total3028310

Merged error: 0.0b

Counts
310 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
45×times-frac
43×*-un-lft-identity
38×add-exp-log
37×add-cube-cbrt
25×sqrt-prod
21×pow1
19×pow-unpow
16×prod-exp
13×add-cbrt-cube
12×associate-*r*
10×pow-prod-down
8×unpow-prod-down pow-exp sqr-pow
6×div-exp associate-/r*
5×associate-/l*
4×pow-pow associate-*l* cbrt-unprod add-log-exp
3×distribute-lft-out-- difference-of-squares
2×pow-to-exp div-sub *-commutative div-inv pow-sub unswap-sqr
1×cbrt-undiv frac-2neg clear-num associate-/l/
Counts
4 → 140
Calls
4 calls:
13.0ms
(pow (* 2.0 (* (* PI (sqrt n)) (sqrt n))) (/ (- 1.0 k) 2.0))
10.0ms
(/ (pow (* 2.0 (* (* PI (sqrt n)) (sqrt n))) (/ (- 1.0 k) 2.0)) (sqrt k))
5.0ms
(* PI (sqrt n))
7.0ms
(* (* PI (sqrt n)) (sqrt n))

series72.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(pow (* 2.0 (* (* PI (sqrt n)) (sqrt n))) (/ (- 1.0 k) 2.0))
36.0ms
(/ (pow (* 2.0 (* (* PI (sqrt n)) (sqrt n))) (/ (- 1.0 k) 2.0)) (sqrt k))
4.0ms
(* PI (sqrt n))
3.0ms
(* (* PI (sqrt n)) (sqrt n))

simplify69.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049682508
149682508

prune218.0ms

Filtered
98 candidates to 152 candidates (-55.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1520152
Fresh077
Picked011
Done000
Total1528160

Merged error: 0.0b

Counts
160 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
530×times-frac
250×add-sqr-sqrt
248×*-un-lft-identity
242×add-cube-cbrt
164×unpow-prod-down
138×sqrt-prod
92×sqr-pow
54×add-exp-log
40×associate-/r*
31×div-exp
19×pow-unpow
15×pow-exp
13×add-cbrt-cube associate-/l*
11×div-sub div-inv pow-sub
10×pow-to-exp associate-/r/
9×pow1
6×prod-exp
4×cbrt-undiv add-log-exp
3×associate-*r* associate-*l* distribute-lft-out-- difference-of-squares
2×pow-pow frac-2neg pow-prod-down clear-num
1×*-commutative cbrt-unprod associate-/l/ unswap-sqr
Counts
4 → 425
Calls
4 calls:
7.0ms
(pow (* PI n) (/ (- 1.0 k) 2.0))
3.0ms
(* PI n)
6.0ms
(/ (sqrt k) (pow (* PI n) (/ (- 1.0 k) 2.0)))
16.0ms
(/ (pow 2.0 (/ (- 1.0 k) 2.0)) (/ (sqrt k) (pow (* PI n) (/ (- 1.0 k) 2.0))))

series162.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(pow (* PI n) (/ (- 1.0 k) 2.0))
2.0ms
(* PI n)
48.0ms
(/ (sqrt k) (pow (* PI n) (/ (- 1.0 k) 2.0)))
96.0ms
(/ (pow 2.0 (/ (- 1.0 k) 2.0)) (/ (sqrt k) (pow (* PI n) (/ (- 1.0 k) 2.0))))

simplify122.0ms

Algorithm
egg-herbie
Counts
437 → 437
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
0500014442

prune1.1s

Filtered
269 candidates to 437 candidates (-62.5%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New4361437
Fresh066
Picked011
Done011
Total4369445

Merged error: 0b

Counts
445 → 9

regimes119.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01920
11920

end0.0ms

analyze392.0ms

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

sample2.5s

Algorithm
intervals
Results
711.0ms8000×body80valid
619.0ms1026×body1280nan
360.0ms831×body640nan
354.0ms2506×body80overflowed
124.0ms420×body320nan
40.0ms209×body160nan
37.0ms670×body80nan
22.0ms238×body80invalid

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