Details

Time bar (total: 25.0s)

sample303.0ms

Algorithm
intervals
Results
138.0ms1125×body80nan
69.0ms401×body80valid

simplify194.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05417
117417
271017
3494017
4500217

prune7.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.2b

Counts
2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

8.9b
(* (* (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))))
12.8b
(pow (/ d l) (/ 1.0 2.0))
14.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
15.1b
(pow (/ d h) (/ 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 l) (/ 1.0 2.0))
12.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
5.0ms
(pow (/ d h) (/ 1.0 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
620.0ms
(* (* (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))))
68.0ms
(pow (/ d l) (/ 1.0 2.0))
746.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
70.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify45.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
012282042
150011847

prune1.1s

Filtered
188 candidates to 109 candidates (58.0%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New16622188
Fresh000
Picked101
Done000
Total16722189

Merged error: 14.0b

Counts
189 → 22

localize45.0ms

Local error

Found 4 expressions with local error:

5.8b
(/ (* M D) (* 2.0 d))
8.9b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt 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))))
12.8b
(pow (/ d l) (/ 1.0 2.0))
14.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
738×add-exp-log
487×prod-exp
216×pow-exp
171×div-exp
78×pow-to-exp
46×add-cbrt-cube
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 → 260
Calls
4 calls:
5.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt 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))))
8.0ms
(pow (/ d l) (/ 1.0 2.0))
12.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.6s

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (* M D) (* 2.0 d))
616.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt 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))))
66.0ms
(pow (/ d l) (/ 1.0 2.0))
930.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify71.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
016425552
150025211

prune994.0ms

Filtered
272 candidates to 88 candidates (32.4%)
Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New2675272
Fresh21921
Picked101
Done000
Total27024294

Merged error: 13.5b

Counts
294 → 24

localize56.0ms

Local error

Found 4 expressions with local error:

3.1b
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
5.8b
(/ (* M D) (* 2.0 d))
8.9b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
14.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
5947×add-exp-log
4317×prod-exp
1997×pow-exp
1387×div-exp
643×pow-to-exp
55×add-cbrt-cube
27×cbrt-unprod
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
16×associate-*r*
13×pow-unpow
12×pow1
9×cbrt-undiv
5×unpow-prod-down
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 → 983
Calls
4 calls:
11.0ms
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
6.0ms
(/ (* M D) (* 2.0 d))
71.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
14.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
122.0ms
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
34.0ms
(/ (* M D) (* 2.0 d))
631.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
754.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify320.0ms

Algorithm
egg-herbie
Counts
995 → 995
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0408038233
1500238031

prune1.2s

Filtered
995 candidates to 89 candidates (8.9%)
Pruning

23 alts after pruning (23 fresh and 0 done)

PrunedKeptTotal
New9914995
Fresh41923
Picked101
Done000
Total996231019

Merged error: 12.9b

Counts
1019 → 23

localize59.0ms

Local error

Found 4 expressions with local error:

4.7b
(/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l)))
5.8b
(/ (* M D) (* 2.0 d))
8.9b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
9.2b
(* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))

rewrite277.0ms

Algorithm
rewrite-expression-head
Rules
6319×add-exp-log
4478×prod-exp
2032×pow-exp
1549×div-exp
650×pow-to-exp
95×add-cbrt-cube
52×cbrt-unprod
35×cbrt-undiv
27×add-sqr-sqrt
25×associate-*r*
23×times-frac
19×add-cube-cbrt *-un-lft-identity
11×pow1
10×cbrt-prod
6×associate-*l*
4×pow-prod-down div-inv add-log-exp
3×associate-*r/ unswap-sqr
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in associate-*l/ clear-num associate-/r* *-commutative associate-/l*
1×frac-times flip3-- flip-- associate-/l/
Counts
4 → 1056
Calls
4 calls:
12.0ms
(/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l)))
6.0ms
(/ (* M D) (* 2.0 d))
70.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
23.0ms
(* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))

series2.0s

Counts
4 → 12
Calls
4 calls:
526.0ms
(/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l)))
29.0ms
(/ (* M D) (* 2.0 d))
667.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
803.0ms
(* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))

simplify358.0ms

Algorithm
egg-herbie
Counts
1068 → 1068
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0441644208
1500343802

prune1.2s

Filtered
1068 candidates to 105 candidates (9.8%)
Pruning

24 alts after pruning (23 fresh and 1 done)

PrunedKeptTotal
New106711068
Fresh02222
Picked011
Done000
Total1067241091

Merged error: 12.9b

Counts
1091 → 24

regimes2.1s

Accuracy

13.3% (4.2b remaining)

Error of 14.9b against oracle of 10.6b and baseline of 15.5b

bsearch4.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06967
16967

end0.0ms

sample9.6s

Algorithm
intervals
Results
4.7s38006×body80nan
2.1s12847×body80valid

Profiling

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