Details

Time bar (total: 5.1s)

analyze412.0ms (8.1%)

Algorithm
1×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

sample92.0ms (1.8%)

Algorithm
1×intervals
Results
23.0ms256×body80valid
19.0ms31×body1280nan
18.0ms31×body640nan
11.0ms76×body80overflowed
4.0ms12×body320nan
2.0ms31×body80nan
1.0ms8×body160nan
1.0ms8×body80invalid

simplify43.0ms (0.8%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
0498716
1498716

prune11.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.9b

Counts
2 → 2

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.2b
(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
0.3b
(* PI n)
0.8b
(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))

rewrite26.0ms (0.5%)

Algorithm
1×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)

series50.0ms (1%)

Counts
3 → 9
Calls

3 calls:

31.0ms
(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
17.0ms
(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))
2.0ms
(* PI n)

simplify49.0ms (1%)

Algorithm
1×egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
050082183

prune316.0ms (6.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1129121
Fresh011
Picked101
Done000
Total11310123

Merged error: 0.5b

Counts
123 → 10

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b
(* PI n)
0.3b
(* PI n)
0.5b
(pow (* 2.0 (* PI n)) (/ k 2.0))
0.6b
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))

rewrite22.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
26×add-sqr-sqrt pow-unpow
22×add-cube-cbrt *-un-lft-identity
20×pow1 add-exp-log
18×times-frac
8×pow-prod-down prod-exp add-cbrt-cube
6×pow-pow associate-*r* associate-*l* pow-exp
4×add-log-exp
2×pow-to-exp unpow-prod-down *-commutative cbrt-unprod div-inv unswap-sqr sqr-pow
Counts
4 → 94
Calls

4 calls:

6.0ms
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))
6.0ms
(pow (* 2.0 (* PI n)) (/ k 2.0))
4.0ms
(* PI n)
3.0ms
(* PI n)

series44.0ms (0.9%)

Counts
4 → 12
Calls

4 calls:

26.0ms
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))
13.0ms
(pow (* 2.0 (* PI n)) (/ k 2.0))
3.0ms
(* PI n)
2.0ms
(* PI n)

simplify48.0ms (1%)

Algorithm
1×egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
05003873

prune274.0ms (5.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1033106
Fresh369
Picked101
Done000
Total1079116

Merged error: 0.5b

Counts
116 → 9

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b
(* PI n)
0.3b
(* PI n)
0.5b
(pow (* 2.0 (* PI n)) (/ k 2.0))
0.6b
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))

rewrite23.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
26×add-sqr-sqrt pow-unpow
22×add-cube-cbrt *-un-lft-identity
20×pow1 add-exp-log
18×times-frac
8×pow-prod-down prod-exp add-cbrt-cube
6×pow-pow associate-*r* associate-*l* pow-exp
4×add-log-exp
2×pow-to-exp unpow-prod-down *-commutative cbrt-unprod div-inv unswap-sqr sqr-pow
Counts
4 → 94
Calls

4 calls:

7.0ms
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))
6.0ms
(pow (* 2.0 (* PI n)) (/ k 2.0))
3.0ms
(* PI n)
3.0ms
(* PI n)

series43.0ms (0.8%)

Counts
4 → 12
Calls

4 calls:

25.0ms
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))
14.0ms
(pow (* 2.0 (* PI n)) (/ k 2.0))
2.0ms
(* PI n)
2.0ms
(* PI n)

simplify53.0ms (1%)

Algorithm
1×egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
05003873

prune259.0ms (5.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1060106
Fresh088
Picked011
Done000
Total1069115

Merged error: 0.5b

Counts
115 → 9

localize23.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b
(* PI n)
0.3b
(/ PI (/ -1 n))
0.5b
(pow (* 2.0 (* PI n)) (/ k 2.0))
0.6b
(pow (* -2.0 (/ PI (/ -1 n))) 0.5)

rewrite29.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
84×times-frac
58×add-sqr-sqrt
56×add-cube-cbrt *-un-lft-identity
27×add-exp-log
16×pow-unpow
15×pow1
13×associate-/r*
11×add-cbrt-cube
7×pow-exp prod-exp
6×div-exp div-inv
5×pow-pow pow-prod-down
4×add-log-exp
3×cbrt-undiv associate-*r* associate-*l* associate-/l*
2×pow-to-exp unpow-prod-down sqr-pow
1×frac-2neg clear-num associate-/r/ *-commutative cbrt-unprod unswap-sqr
Counts
4 → 136
Calls

4 calls:

8.0ms
(pow (* -2.0 (/ PI (/ -1 n))) 0.5)
7.0ms
(pow (* 2.0 (* PI n)) (/ k 2.0))
6.0ms
(/ PI (/ -1 n))
3.0ms
(* PI n)

series46.0ms (0.9%)

Counts
4 → 12
Calls

4 calls:

26.0ms
(pow (* -2.0 (/ PI (/ -1 n))) 0.5)
14.0ms
(pow (* 2.0 (* PI n)) (/ k 2.0))
3.0ms
(/ PI (/ -1 n))
2.0ms
(* PI n)

simplify46.0ms (0.9%)

Algorithm
1×egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
049651405
149651405

prune337.0ms (6.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1480148
Fresh077
Picked011
Done011
Total1489157

Merged error: 0.5b

Counts
157 → 9

regimes137.0ms (2.7%)

Accuracy

Total 0.3b remaining (78.7%)

Threshold costs 0.3b (78.7%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01824
11824

end0.0ms (0%)

sample2.6s (51.9%)

Algorithm
1×intervals
Results
728.0ms8000×body80valid
618.0ms978×body1280nan
405.0ms891×body640nan
348.0ms2455×body80overflowed
134.0ms422×body320nan
44.0ms763×body80nan
44.0ms219×body160nan
22.0ms229×body80invalid

Profiling

Loading profile data...