Details

Time bar (total: 14.2s)

analyze1.9s

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%81.1%18.9%7
0%68.6%31.4%8
0%59.2%40.8%9
0%59.2%40.8%10
0%59.2%40.8%11
0.4%49.5%50.1%12
0.8%44.4%54.8%13
1.4%39.9%58.7%14

sample133.0ms

Algorithm
intervals
Results
48.0ms256×body80valid
33.0ms240×body80nan
22.0ms126×body80invalid

simplify20.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (18.0ms)

IterNodesCost
0540135

prune18.0ms

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: 25.7b

Counts
2 → 2

localize35.0ms

Local error

Found 4 expressions with local error:

6.5b
(* M (/ D (* d 2.0)))
8.8b
(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
11.4b
(pow (/ d l) (/ 1.0 2.0))
13.2b
(pow (/ d h) (/ 1.0 2.0))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
92×add-exp-log
41×prod-exp
39×times-frac
38×add-sqr-sqrt
36×add-cube-cbrt *-un-lft-identity
31×add-cbrt-cube
27×div-exp
26×unpow-prod-down pow-unpow
13×pow1 cbrt-unprod
12×pow-exp
8×associate-*r*
6×cbrt-undiv associate-*l*
5×associate-*r/ div-inv
4×pow-to-exp pow-prod-down add-log-exp
2×pow-pow *-commutative sqr-pow
1×frac-times associate-*l/ unswap-sqr
Counts
4 → 140
Calls
4 calls:
7.0ms
(* M (/ D (* d 2.0)))
11.0ms
(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
6.0ms
(pow (/ d l) (/ 1.0 2.0))
5.0ms
(pow (/ d h) (/ 1.0 2.0))

series222.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(* M (/ D (* d 2.0)))
190.0ms
(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
13.0ms
(pow (/ d l) (/ 1.0 2.0))
13.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify36.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
052701921

prune532.0ms

Filtered
100 candidates to 152 candidates (-52.0%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New12725152
Fresh011
Picked101
Done000
Total12826154

Merged error: 12.9b

Counts
154 → 26

localize43.0ms

Local error

Found 4 expressions with local error:

5.6b
(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
6.5b
(* M (/ D (* d 2.0)))
8.8b
(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
11.4b
(pow (/ d l) (/ 1.0 2.0))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
106×add-exp-log
45×prod-exp
36×times-frac
34×add-sqr-sqrt div-exp
33×add-cbrt-cube
32×add-cube-cbrt *-un-lft-identity
17×unpow-prod-down
14×pow-exp
13×pow-unpow cbrt-unprod
12×pow1
8×associate-*r*
7×cbrt-undiv
6×associate-*l*
5×associate-*r/ associate-/l* sqr-pow
4×pow-to-exp pow-prod-down div-inv add-log-exp
3×associate-/r*
2×*-commutative
1×frac-times pow-pow frac-2neg associate-*l/ clear-num unswap-sqr
Counts
4 → 142
Calls
4 calls:
5.0ms
(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
9.0ms
(* M (/ D (* d 2.0)))
11.0ms
(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
6.0ms
(pow (/ d l) (/ 1.0 2.0))

series385.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
6.0ms
(* M (/ D (* d 2.0)))
189.0ms
(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
13.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify39.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
053222198

prune628.0ms

Filtered
103 candidates to 154 candidates (-49.5%)
Pruning

32 alts after pruning (32 fresh and 0 done)

PrunedKeptTotal
New14311154
Fresh42125
Picked101
Done000
Total14832180

Merged error: 11.2b

Counts
180 → 32

localize57.0ms

Local error

Found 4 expressions with local error:

5.4b
(* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0))) (- 1.0 (* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l))))))
5.6b
(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
6.5b
(* M (/ D (* d 2.0)))
8.8b
(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))

rewrite282.0ms

Algorithm
rewrite-expression-head
Rules
7016×add-exp-log
5284×prod-exp
2638×pow-exp
1632×div-exp
798×pow-to-exp
232×rec-exp 1-exp
54×add-cbrt-cube
28×cbrt-unprod
20×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity times-frac
16×pow1
9×associate-*r/ associate-*r*
7×cbrt-undiv associate-*l* pow-prod-down
5×associate-/l*
4×distribute-rgt-in sub-neg unpow-prod-down distribute-lft-in add-log-exp sqr-pow
3×associate-/r* *-commutative
2×div-inv
1×frac-times flip3-- frac-2neg associate-*l/ clear-num flip-- unswap-sqr
Counts
4 → 1230
Calls
4 calls:
46.0ms
(* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0))) (- 1.0 (* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l))))))
5.0ms
(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
7.0ms
(* M (/ D (* d 2.0)))
11.0ms
(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))

series717.0ms

Counts
4 → 12
Calls
4 calls:
335.0ms
(* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0))) (- 1.0 (* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l))))))
180.0ms
(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
6.0ms
(* M (/ D (* d 2.0)))
196.0ms
(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))

simplify411.0ms

Algorithm
egg-herbie
Counts
1242 → 1242
Iterations

Useful iterations: 0 (147.0ms)

IterNodesCost
0503653351

prune687.0ms

Filtered
92 candidates to 1242 candidates (-1250.0%)
Pruning

29 alts after pruning (29 fresh and 0 done)

PrunedKeptTotal
New123571242
Fresh92231
Picked101
Done000
Total1245291274

Merged error: 8.6b

Counts
1274 → 29

localize62.0ms

Local error

Found 4 expressions with local error:

8.8b
(* h (* (/ 1.0 2.0) (* (* (cbrt (/ (pow (* M (/ D (* 2.0 d))) 2.0) l)) (cbrt (/ (pow (* M (/ D (* 2.0 d))) 2.0) l))) (cbrt (/ (pow (* M (/ D (* 2.0 d))) 2.0) l)))))
25.3b
(cbrt (/ (pow (* M (/ D (* 2.0 d))) 2.0) l))
25.3b
(cbrt (/ (pow (* M (/ D (* 2.0 d))) 2.0) l))
25.3b
(cbrt (/ (pow (* M (/ D (* 2.0 d))) 2.0) l))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
57×cbrt-prod
45×times-frac
33×add-exp-log
32×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
28×associate-*r/
27×cbrt-div
25×add-cbrt-cube
19×prod-exp cbrt-unprod
18×pow1
17×frac-times
11×associate-*l/
10×pow-prod-down
9×unpow-prod-down sqr-pow
4×add-log-exp
3×cbrt-undiv pow1/3 div-exp associate-*l* div-inv
1×associate-*r* *-commutative
Counts
4 → 129
Calls
4 calls:
24.0ms
(* h (* (/ 1.0 2.0) (* (* (cbrt (/ (pow (* M (/ D (* 2.0 d))) 2.0) l)) (cbrt (/ (pow (* M (/ D (* 2.0 d))) 2.0) l))) (cbrt (/ (pow (* M (/ D (* 2.0 d))) 2.0) l)))))
3.0ms
(cbrt (/ (pow (* M (/ D (* 2.0 d))) 2.0) l))
5.0ms
(cbrt (/ (pow (* M (/ D (* 2.0 d))) 2.0) l))
3.0ms
(cbrt (/ (pow (* M (/ D (* 2.0 d))) 2.0) l))

series604.0ms

Counts
4 → 12
Calls
4 calls:
197.0ms
(* h (* (/ 1.0 2.0) (* (* (cbrt (/ (pow (* M (/ D (* 2.0 d))) 2.0) l)) (cbrt (/ (pow (* M (/ D (* 2.0 d))) 2.0) l))) (cbrt (/ (pow (* M (/ D (* 2.0 d))) 2.0) l)))))
137.0ms
(cbrt (/ (pow (* M (/ D (* 2.0 d))) 2.0) l))
135.0ms
(cbrt (/ (pow (* M (/ D (* 2.0 d))) 2.0) l))
135.0ms
(cbrt (/ (pow (* M (/ D (* 2.0 d))) 2.0) l))

simplify78.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
049303245
149303245

prune808.0ms

Filtered
107 candidates to 141 candidates (-31.8%)
Pruning

30 alts after pruning (29 fresh and 1 done)

PrunedKeptTotal
New1392141
Fresh12728
Picked011
Done000
Total14030170

Merged error: 8.6b

Counts
170 → 30

regimes2.2s

Accuracy

28.4% (5.3b remaining)

Error of 13.3b against oracle of 8.0b and baseline of 15.5b

bsearch5.0ms

simplify6.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0286468
1286468

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.4s8000×body80valid
1.1s8067×body80nan
836.0ms4732×body80invalid

Profiling

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