Details

Time bar (total: 23.3s)

sample300.0ms

Algorithm
intervals
Results
160.0ms1276×body80nan
72.0ms416×body80valid

simplify192.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05417
117417
271017
3494017
4500217

prune4.0ms

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: 26.7b

Counts
2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

7.0b
(* (* (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))))
11.7b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.8b
(pow (/ d h) (/ 1.0 2.0))
12.6b
(pow (/ d l) (/ 1.0 2.0))

rewrite47.0ms

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))))
13.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
6.0ms
(pow (/ d h) (/ 1.0 2.0))
6.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
622.0ms
(* (* (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))))
729.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
68.0ms
(pow (/ d h) (/ 1.0 2.0))
69.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify48.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012282042
150011847

prune688.0ms

Filtered
188 candidates to 109 candidates (58.0%)
Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New16721188
Fresh000
Picked101
Done000
Total16821189

Merged error: 12.3b

Counts
189 → 21

localize45.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (* M D) (* 2.0 d))
7.0b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
11.7b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.6b
(pow (/ d l) (/ 1.0 2.0))

rewrite80.0ms

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))
26.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
12.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
6.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
859.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
727.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
67.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify84.0ms

Algorithm
egg-herbie
Counts
304 → 304
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
018025799
150015527

prune717.0ms

Filtered
304 candidates to 95 candidates (31.3%)
Pruning

28 alts after pruning (28 fresh and 0 done)

PrunedKeptTotal
New29212304
Fresh41620
Picked101
Done000
Total29728325

Merged error: 11.4b

Counts
325 → 28

localize55.0ms

Local error

Found 4 expressions with local error:

3.6b
(pow (/ d (cbrt h)) (/ 1.0 2.0))
4.6b
(/ (* M D) (* 2.0 d))
7.0b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
11.7b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite330.0ms

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:
13.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
6.0ms
(/ (* M D) (* 2.0 d))
76.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
12.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.8s

Counts
4 → 12
Calls
4 calls:
179.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
27.0ms
(/ (* M D) (* 2.0 d))
872.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
736.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify383.0ms

Algorithm
egg-herbie
Counts
1241 → 1241
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
0500145022

prune1.2s

Filtered
1241 candidates to 130 candidates (10.5%)
Pruning

31 alts after pruning (31 fresh and 0 done)

PrunedKeptTotal
New123561241
Fresh22527
Picked101
Done000
Total1238311269

Merged error: 8.5b

Counts
1269 → 31

localize61.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (* M D) (* 2.0 d))
5.2b
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
5.4b
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
7.0b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

rewrite313.0ms

Algorithm
rewrite-expression-head
Rules
6936×add-exp-log
5237×prod-exp
2607×pow-exp
1610×div-exp
787×pow-to-exp
232×rec-exp 1-exp
60×add-cbrt-cube
29×cbrt-unprod
11×pow1
10×cbrt-undiv
8×add-sqr-sqrt *-un-lft-identity associate-*r*
6×add-cube-cbrt
4×pow-prod-down add-log-exp
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in times-frac associate-*r/ associate-*l* clear-num associate-/r* *-commutative div-inv associate-/l*
1×flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 1182
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
7.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
10.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
77.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

series2.6s

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
715.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
735.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
1.1s
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

simplify384.0ms

Algorithm
egg-herbie
Counts
1194 → 1194
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0476243189
1500343007

prune560.0ms

Filtered
1194 candidates to 70 candidates (5.9%)
Pruning

31 alts after pruning (31 fresh and 0 done)

PrunedKeptTotal
New119221194
Fresh12930
Picked101
Done000
Total1194311225

Merged error: 8.5b

Counts
1225 → 31

regimes1.5s

Accuracy

6.1% (6.3b remaining)

Error of 15.4b against oracle of 9.0b and baseline of 15.8b

bsearch4.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06883
16883

end0.0ms

sample8.7s

Algorithm
intervals
Results
4.8s38111×body80nan
2.1s12707×body80valid

Profiling

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