Details

Time bar (total: 5.9s)

analyze403.0ms

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

sample81.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
19.0ms33×body1280nan
10.0ms76×body80overflowed
10.0ms23×body640nan
3.0ms12×body320nan
1.0ms27×body80nan
1.0ms8×body160nan
0.0ms4×body80invalid

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
0555316

prune15.0ms

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: 0.4b

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

rewrite24.0ms

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)

series55.0ms

Counts
3 → 9
Calls
3 calls:
19.0ms
(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))
33.0ms
(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
3.0ms
(* PI n)

simplify43.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
050482248

prune275.0ms

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

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New10912121
Fresh101
Picked101
Done000
Total11112123

Merged error: 0b

Counts
123 → 12

localize20.0ms

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))))
0.3b
(* PI n)
0.3b
(* PI (* 2.0 n))

rewrite29.0ms

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))

series162.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))
131.0ms
(/ (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))

simplify45.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
051512145

prune234.0ms

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

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1300130
Fresh01111
Picked011
Done000
Total13012142

Merged error: 0b

Counts
142 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
358×times-frac
150×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
117×add-exp-log
90×sqrt-prod
71×unpow-prod-down sqr-pow
51×div-exp
39×prod-exp
33×pow-exp
29×associate-/l*
20×pow1
19×add-cbrt-cube
13×pow-unpow
11×pow-to-exp
9×pow-prod-down div-inv
6×associate-*l* associate-/r* cbrt-unprod
4×add-log-exp
3×cbrt-undiv pow-pow
2×associate-*r* *-commutative
1×frac-2neg clear-num associate-/l/
Counts
4 → 313
Calls
4 calls:
7.0ms
(pow (* PI (* 2.0 n)) (/ 1.0 2.0))
15.0ms
(/ (/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (pow (* PI (* 2.0 n)) (/ k 2.0))) (sqrt k))
5.0ms
(* PI (* 2.0 n))
5.0ms
(* PI (* 2.0 n))

series162.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(pow (* PI (* 2.0 n)) (/ 1.0 2.0))
131.0ms
(/ (/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (pow (* PI (* 2.0 n)) (/ k 2.0))) (sqrt k))
3.0ms
(* PI (* 2.0 n))
3.0ms
(* PI (* 2.0 n))

simplify87.0ms

Algorithm
egg-herbie
Counts
325 → 325
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
0576310497

prune922.0ms

Filtered
204 candidates to 325 candidates (-59.3%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New3250325
Fresh01010
Picked011
Done011
Total32512337

Merged error: 0b

Counts
337 → 12

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))
0.3b
(/ (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))

rewrite39.0ms

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:
14.0ms
(pow (* 2.0 (* (* PI (sqrt n)) (sqrt n))) (/ (- 1.0 k) 2.0))
8.0ms
(/ (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))

series77.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(pow (* 2.0 (* (* PI (sqrt n)) (sqrt n))) (/ (- 1.0 k) 2.0))
41.0ms
(/ (pow (* 2.0 (* (* PI (sqrt n)) (sqrt n))) (/ (- 1.0 k) 2.0)) (sqrt k))
4.0ms
(* PI (sqrt n))
4.0ms
(* (* PI (sqrt n)) (sqrt n))

simplify55.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
055862591

prune230.0ms

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

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New1520152
Fresh099
Picked011
Done022
Total15212164

Merged error: 0b

Counts
164 → 12

regimes161.0ms

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 (1.0ms)

IterNodesCost
06324
16324

end0.0ms

sample2.6s

Algorithm
intervals
Results
727.0ms8000×body80valid
603.0ms994×body1280nan
410.0ms906×body640nan
331.0ms2403×body80overflowed
133.0ms440×body320nan
41.0ms732×body80nan
40.0ms226×body160nan
24.0ms260×body80invalid

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