Details

Time bar (total: 8.8s)

sample241.0ms

Algorithm
intervals
Results
71.0ms970×body80nan
48.0ms82×body1280nan
33.0ms355×body80valid
29.0ms67×body640nan
13.0ms32×body320nan
3.0ms19×body160nan

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
0499216
1499216

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

rewrite22.0ms

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:
6.0ms
(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
9.0ms
(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))
3.0ms
(* PI n)

series53.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
16.0ms
(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))
2.0ms
(* PI n)

simplify50.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
049752183
149752183

prune224.0ms

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

localize22.0ms

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)) (* (pow (* PI (* 2.0 n)) (/ k 2.0)) (sqrt k)))
0.3b
(* PI n)
0.3b
(* 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)) (* (pow (* PI (* 2.0 n)) (/ k 2.0)) (sqrt k)))
4.0ms
(* PI n)
5.0ms
(* PI (* 2.0 n))

series160.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))
128.0ms
(/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (* (pow (* PI (* 2.0 n)) (/ k 2.0)) (sqrt k)))
2.0ms
(* PI n)
3.0ms
(* PI (* 2.0 n))

simplify48.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
050122003

prune205.0ms

Filtered
69 candidates to 130 candidates (-88.4%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1273130
Fresh369
Picked011
Done000
Total13010140

Merged error: 0b

Counts
140 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
39×times-frac
32×add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity
20×pow1
18×sqrt-prod
16×add-cbrt-cube
13×pow-unpow
12×prod-exp
9×pow-prod-down
8×unpow-prod-down sqr-pow
6×associate-*l* pow-exp associate-/r* cbrt-unprod
5×div-exp associate-/l*
4×add-log-exp
3×pow-pow
2×pow-to-exp associate-*r* *-commutative div-inv
1×cbrt-undiv frac-2neg clear-num
Counts
4 → 122
Calls
4 calls:
7.0ms
(pow (* PI (* 2.0 n)) (/ 1.0 2.0))
5.0ms
(* PI (* 2.0 n))
5.0ms
(* PI (* 2.0 n))
6.0ms
(/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (sqrt k))

series112.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(pow (* PI (* 2.0 n)) (/ 1.0 2.0))
3.0ms
(* PI (* 2.0 n))
3.0ms
(* PI (* 2.0 n))
82.0ms
(/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (sqrt k))

simplify43.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
052241792

prune225.0ms

Filtered
83 candidates to 134 candidates (-61.4%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1340134
Fresh088
Picked011
Done011
Total13410144

Merged error: 0b

Counts
144 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
34×pow1
31×add-sqr-sqrt
21×add-exp-log associate-*l* add-cbrt-cube
20×times-frac
19×add-cube-cbrt *-un-lft-identity
15×associate-*r*
14×swap-sqr
12×pow-prod-down
10×prod-exp cbrt-unprod
8×sqrt-pow1 pow1/2
5×pow-prod-up
4×unpow-prod-down sqrt-div *-commutative div-inv add-log-exp unswap-sqr sqr-pow
3×pow-sqr
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ associate-*l/ rem-square-sqrt
Counts
4 → 124
Calls
4 calls:
5.0ms
(* PI (* 2.0 n))
5.0ms
(* PI (* 2.0 n))
5.0ms
(* PI (* 2.0 n))
17.0ms
(* (sqrt (/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (* (sqrt k) (pow (* PI (* 2.0 n)) (/ k 2.0))))) (sqrt (/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (* (sqrt k) (pow (* PI (* 2.0 n)) (/ k 2.0))))))

series140.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* PI (* 2.0 n))
3.0ms
(* PI (* 2.0 n))
3.0ms
(* PI (* 2.0 n))
130.0ms
(* (sqrt (/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (* (sqrt k) (pow (* PI (* 2.0 n)) (/ k 2.0))))) (sqrt (/ (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) (* (sqrt k) (pow (* PI (* 2.0 n)) (/ k 2.0))))))

simplify52.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
050442751

prune278.0ms

Filtered
76 candidates to 136 candidates (-78.9%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1360136
Fresh077
Picked011
Done022
Total13610146

Merged error: 0b

Counts
146 → 10

regimes266.0ms

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
02226
12226

end0.0ms

sample6.4s

Algorithm
intervals
Results
2.1s26966×body80nan
1.2s2004×body1280nan
904.0ms10767×body80valid
756.0ms1692×body640nan
256.0ms840×body320nan
81.0ms442×body160nan

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