Details

Time bar (total: 6.8s)

analyze404.0ms

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

sample89.0ms

Algorithm
intervals
Results
24.0ms32×body1280nan
23.0ms256×body80valid
12.0ms28×body640nan
12.0ms85×body80overflowed
1.0ms22×body80nan
1.0ms4×body320nan
1.0ms5×body160nan
1.0ms8×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: 0.6b

Counts
2 → 2

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b
(* PI n)
0.3b
(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
0.5b
(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))

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:
3.0ms
(* PI n)
7.0ms
(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
10.0ms
(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))

series56.0ms

Counts
3 → 9
Calls
3 calls:
2.0ms
(* PI n)
32.0ms
(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
21.0ms
(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))

simplify34.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
050032191

prune240.0ms

Filtered
80 candidates to 121 candidates (-51.3%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New11110121
Fresh011
Picked101
Done000
Total11211123

Merged error: 0.0b

Counts
123 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
367×times-frac
159×add-sqr-sqrt
157×add-cube-cbrt *-un-lft-identity
115×add-exp-log
90×sqrt-prod
72×unpow-prod-down sqr-pow
51×div-exp
37×prod-exp
36×pow-exp
29×associate-/l*
26×pow-unpow
18×pow1
12×pow-to-exp
11×add-cbrt-cube
10×div-inv
7×pow-prod-down
6×pow-pow associate-/r*
4×add-log-exp
3×cbrt-undiv associate-*r* associate-*l*
1×frac-2neg clear-num *-commutative cbrt-unprod associate-/l/ unswap-sqr
Counts
4 → 324
Calls
4 calls:
3.0ms
(* PI n)
7.0ms
(pow (* 2.0 (* PI n)) (/ k 2.0))
16.0ms
(/ (/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (pow (* 2.0 (* PI n)) (/ k 2.0))) (sqrt k))
7.0ms
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))

series176.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(* PI n)
14.0ms
(pow (* 2.0 (* PI n)) (/ k 2.0))
130.0ms
(/ (/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (pow (* 2.0 (* PI n)) (/ k 2.0))) (sqrt k))
29.0ms
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))

simplify138.0ms

Algorithm
egg-herbie
Counts
336 → 336
Iterations

Useful iterations: 0 (83.0ms)

IterNodesCost
0499010709
1499010709

prune834.0ms

Filtered
215 candidates to 336 candidates (-56.3%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New3324336
Fresh4610
Picked011
Done000
Total33611347

Merged error: 0.0b

Counts
347 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (pow (* 2.0 (* PI n)) (/ k 2.0))) (/ 1 (sqrt k)))
0.2b
(pow (* 2.0 (* PI n)) (/ k 2.0))
0.3b
(/ 1 (sqrt k))
0.4b
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
434×add-exp-log
230×prod-exp
154×div-exp
126×pow-exp
119×times-frac
117×add-sqr-sqrt
67×*-un-lft-identity
57×add-cube-cbrt
42×pow-to-exp
32×sqr-pow
31×sqrt-prod
29×associate-*l*
27×rec-exp 1-exp
26×pow-unpow
25×unswap-sqr
22×associate-*r*
20×pow1
18×add-cbrt-cube
12×unpow-prod-down
7×pow-prod-down
6×pow-pow associate-/r*
5×cbrt-undiv div-inv
4×cbrt-unprod add-log-exp
3×pow-flip associate-/l*
1×frac-times frac-2neg sqrt-pow1 pow1/2 associate-*r/ associate-*l/ clear-num un-div-inv *-commutative inv-pow
Counts
4 → 300
Calls
4 calls:
27.0ms
(* (/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (pow (* 2.0 (* PI n)) (/ k 2.0))) (/ 1 (sqrt k)))
7.0ms
(pow (* 2.0 (* PI n)) (/ k 2.0))
4.0ms
(/ 1 (sqrt k))
7.0ms
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))

series181.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(* (/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (pow (* 2.0 (* PI n)) (/ k 2.0))) (/ 1 (sqrt k)))
18.0ms
(pow (* 2.0 (* PI n)) (/ k 2.0))
7.0ms
(/ 1 (sqrt k))
25.0ms
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))

simplify87.0ms

Algorithm
egg-herbie
Counts
312 → 312
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
050146146

prune426.0ms

Filtered
135 candidates to 312 candidates (-131.1%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New3111312
Fresh369
Picked011
Done011
Total3149323

Merged error: 0.0b

Counts
323 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* PI n)
0.2b
(* (/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (pow (* 2.0 (* PI n)) (/ k 2.0))) (pow k -1/2))
0.2b
(pow (* 2.0 (* PI n)) (/ k 2.0))
0.4b
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
283×add-exp-log
175×prod-exp
122×pow-exp
75×div-exp
60×add-sqr-sqrt
58×pow-to-exp
55×times-frac
33×add-cube-cbrt *-un-lft-identity
32×associate-*l*
30×sqr-pow
26×pow-unpow
20×unpow-prod-down
18×pow1
16×unswap-sqr
11×add-cbrt-cube
10×associate-*r*
7×pow-prod-down
6×pow-pow
4×add-log-exp
3×cbrt-unprod div-inv
2×*-commutative
1×cbrt-undiv associate-*l/
Counts
4 → 216
Calls
4 calls:
3.0ms
(* PI n)
16.0ms
(* (/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (pow (* 2.0 (* PI n)) (/ k 2.0))) (pow k -1/2))
7.0ms
(pow (* 2.0 (* PI n)) (/ k 2.0))
7.0ms
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))

series178.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(* PI n)
132.0ms
(* (/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (pow (* 2.0 (* PI n)) (/ k 2.0))) (pow k -1/2))
19.0ms
(pow (* 2.0 (* PI n)) (/ k 2.0))
25.0ms
(pow (* 2.0 (* PI n)) (/ 1.0 2.0))

simplify57.0ms

Algorithm
egg-herbie
Counts
228 → 228
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
051374581

prune439.0ms

Filtered
120 candidates to 228 candidates (-90.0%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New2280228
Fresh066
Picked011
Done022
Total2289237

Merged error: 0.0b

Counts
237 → 9

regimes132.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02025
12025

end0.0ms

analyze408.0ms

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

sample2.6s

Algorithm
intervals
Results
734.0ms8000×body80valid
615.0ms984×body1280nan
382.0ms847×body640nan
366.0ms2527×body80overflowed
134.0ms441×body320nan
44.0ms765×body80nan
37.0ms210×body160nan
24.0ms242×body80invalid

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