Details

Time bar (total: 18.8s)

sample331.0ms

Algorithm
intervals
Results
167.0ms1274×body80nan
67.0ms384×body80valid

simplify29.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
0564135

prune16.0ms

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: 24.0b

Counts
2 → 2

localize32.0ms

Local error

Found 4 expressions with local error:

6.7b
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
9.7b
(pow (/ d h) (/ 1.0 2.0))
12.5b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
13.0b
(pow (/ d l) (/ 1.0 2.0))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
205×add-exp-log
107×prod-exp
55×div-exp
45×times-frac
40×add-sqr-sqrt add-cube-cbrt *-un-lft-identity pow-exp
30×add-cbrt-cube
26×unpow-prod-down pow-unpow
16×associate-*r*
14×pow-to-exp
13×cbrt-unprod
10×pow1
5×cbrt-undiv div-inv
4×add-log-exp
3×associate-*r/ associate-*l/
2×distribute-rgt-in sub-neg pow-pow distribute-lft-in associate-*l* pow-prod-down *-commutative sqr-pow
1×frac-times flip3-- flip--
Counts
4 → 176
Calls
4 calls:
13.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
5.0ms
(pow (/ d h) (/ 1.0 2.0))
12.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
5.0ms
(pow (/ d l) (/ 1.0 2.0))

series527.0ms

Counts
4 → 12
Calls
4 calls:
268.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
12.0ms
(pow (/ d h) (/ 1.0 2.0))
233.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
13.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify56.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
053803792

prune541.0ms

Filtered
111 candidates to 188 candidates (-69.4%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New16721188
Fresh011
Picked101
Done000
Total16822190

Merged error: 11.4b

Counts
190 → 22

localize41.0ms

Local error

Found 4 expressions with local error:

5.6b
(/ (* M D) (* 2.0 d))
6.7b
(* (* (pow (/ d 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 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
9.7b
(pow (/ d h) (/ 1.0 2.0))
12.5b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
818×add-exp-log
567×prod-exp
280×pow-exp
187×div-exp
94×pow-to-exp
46×add-cbrt-cube
32×rec-exp 1-exp
28×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
20×cbrt-unprod
16×associate-*r*
13×unpow-prod-down pow-unpow
9×pow1 cbrt-undiv
4×div-inv add-log-exp
3×associate-*r/ associate-*l/
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* pow-prod-down *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 292
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
30.0ms
(* (* (pow (/ d 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 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
6.0ms
(pow (/ d h) (/ 1.0 2.0))
12.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series575.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
327.0ms
(* (* (pow (/ d 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 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
12.0ms
(pow (/ d h) (/ 1.0 2.0))
229.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify84.0ms

Algorithm
egg-herbie
Counts
304 → 304
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
050429487

prune498.0ms

Filtered
92 candidates to 304 candidates (-230.4%)
Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New2995304
Fresh21921
Picked101
Done000
Total30224326

Merged error: 10.3b

Counts
326 → 24

localize56.0ms

Local error

Found 4 expressions with local error:

3.7b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
5.6b
(/ (* M D) (* 2.0 d))
6.7b
(* (* (* (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 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
12.5b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite305.0ms

Algorithm
rewrite-expression-head
Rules
6965×add-exp-log
5245×prod-exp
2614×pow-exp
1626×div-exp
789×pow-to-exp
232×rec-exp 1-exp
55×add-cbrt-cube
37×times-frac
32×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
27×cbrt-unprod
22×unpow-prod-down
16×associate-*r*
13×pow-unpow
12×pow1
9×cbrt-undiv cbrt-prod
4×pow-prod-down div-inv add-log-exp
3×associate-*r/ associate-*l/
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 1229
Calls
4 calls:
14.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
5.0ms
(/ (* M D) (* 2.0 d))
77.0ms
(* (* (* (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 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
12.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series588.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
6.0ms
(/ (* M D) (* 2.0 d))
321.0ms
(* (* (* (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 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
227.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify371.0ms

Algorithm
egg-herbie
Counts
1241 → 1241
Iterations

Useful iterations: 0 (121.0ms)

IterNodesCost
0513252601

prune667.0ms

Filtered
102 candidates to 1241 candidates (-1116.7%)
Pruning

27 alts after pruning (27 fresh and 0 done)

PrunedKeptTotal
New123381241
Fresh41923
Picked101
Done000
Total1238271265

Merged error: 9.2b

Counts
1265 → 27

localize53.0ms

Local error

Found 4 expressions with local error:

5.5b
(/ (* 1.0 (* (pow (* (/ M 2.0) (/ D d)) 2.0) h)) (* 2.0 l))
5.9b
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
6.7b
(* (* (* (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 (/ (* 1.0 (* (pow (* (/ M 2.0) (/ D d)) 2.0) h)) (* 2.0 l))))
6.8b
(* (/ M 2.0) (/ D d))

rewrite290.0ms

Algorithm
rewrite-expression-head
Rules
6927×add-exp-log
5229×prod-exp
2607×pow-exp
1610×div-exp
787×pow-to-exp
232×rec-exp 1-exp
57×add-cbrt-cube
38×add-sqr-sqrt
27×cbrt-unprod
23×*-un-lft-identity times-frac
21×add-cube-cbrt associate-*r*
19×associate-*l*
11×pow1
10×cbrt-undiv
6×unswap-sqr
4×pow-prod-down add-log-exp
3×associate-*r/ *-commutative div-inv
2×distribute-rgt-in sub-neg distribute-lft-in sqr-pow
1×frac-times unpow-prod-down flip3-- frac-2neg associate-*l/ clear-num associate-/r* flip-- associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 1214
Calls
4 calls:
9.0ms
(/ (* 1.0 (* (pow (* (/ M 2.0) (/ D d)) 2.0) h)) (* 2.0 l))
5.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
75.0ms
(* (* (* (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 (/ (* 1.0 (* (pow (* (/ M 2.0) (/ D d)) 2.0) h)) (* 2.0 l))))
11.0ms
(* (/ M 2.0) (/ D d))

series757.0ms

Counts
4 → 12
Calls
4 calls:
220.0ms
(/ (* 1.0 (* (pow (* (/ M 2.0) (/ D d)) 2.0) h)) (* 2.0 l))
199.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
333.0ms
(* (* (* (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 (/ (* 1.0 (* (pow (* (/ M 2.0) (/ D d)) 2.0) h)) (* 2.0 l))))
6.0ms
(* (/ M 2.0) (/ D d))

simplify354.0ms

Algorithm
egg-herbie
Counts
1226 → 1226
Iterations

Useful iterations: 0 (110.0ms)

IterNodesCost
0501352273

prune443.0ms

Filtered
94 candidates to 1226 candidates (-1204.3%)
Pruning

27 alts after pruning (26 fresh and 1 done)

PrunedKeptTotal
New122421226
Fresh22426
Picked011
Done000
Total1226271253

Merged error: 7.7b

Counts
1253 → 27

regimes1.6s

Accuracy

0.3% (5.9b remaining)

Error of 14.6b against oracle of 8.7b and baseline of 14.6b

bsearch320.0ms

Steps
ItersRangePoint
11
-4.758284248083552e+113
-8.89129579431458e+92
-1.0654141621624213e+100

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
073145
173145

end0.0ms

sample10.1s

Algorithm
intervals
Results
5.2s38428×body80nan
2.2s12737×body80valid

Profiling

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