Details

Time bar (total: 22.5s)

sample288.0ms

Algorithm
intervals
Results
158.0ms1207×body80nan
66.0ms395×body80valid

simplify200.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 25.1b

Counts
2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

7.5b
(* (* (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))))
10.3b
(pow (/ d h) (/ 1.0 2.0))
11.7b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.4b
(pow (/ d l) (/ 1.0 2.0))

rewrite49.0ms

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:
17.0ms
(* (* (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))
6.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
615.0ms
(* (* (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))))
64.0ms
(pow (/ d h) (/ 1.0 2.0))
713.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
61.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify48.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012282042
150011847

prune676.0ms

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: 13.1b

Counts
189 → 21

localize41.0ms

Local error

Found 4 expressions with local error:

4.5b
(/ (* M D) (* 2.0 d))
7.5b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt 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))
12.4b
(pow (/ d l) (/ 1.0 2.0))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
674×add-exp-log
455×prod-exp
216×pow-exp
171×div-exp
78×pow-to-exp
46×add-cbrt-cube
32×1-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 → 260
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
24.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
15.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
6.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
949.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
731.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
67.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify76.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
016674960
150014530

prune618.0ms

Filtered
272 candidates to 88 candidates (32.4%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New2657272
Fresh51520
Picked101
Done000
Total27122293

Merged error: 12.8b

Counts
293 → 22

localize53.0ms

Local error

Found 4 expressions with local error:

2.6b
(pow (/ (cbrt d) h) (/ 1.0 2.0))
4.5b
(/ (* M D) (* 2.0 d))
7.5b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
11.7b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite296.0ms

Algorithm
rewrite-expression-head
Rules
6373×add-exp-log
4949×prod-exp
2614×pow-exp
1626×div-exp
789×pow-to-exp
528×1-exp
232×rec-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 (/ (cbrt d) h) (/ 1.0 2.0))
6.0ms
(/ (* M D) (* 2.0 d))
73.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
13.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.6s

Counts
4 → 12
Calls
4 calls:
156.0ms
(pow (/ (cbrt d) h) (/ 1.0 2.0))
34.0ms
(/ (* M D) (* 2.0 d))
700.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
733.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify345.0ms

Algorithm
egg-herbie
Counts
1241 → 1241
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0500139395

prune1.2s

Filtered
1241 candidates to 128 candidates (10.3%)
Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New123561241
Fresh31821
Picked101
Done000
Total1239241263

Merged error: 10.9b

Counts
1263 → 24

localize60.0ms

Local error

Found 4 expressions with local error:

2.6b
(pow (/ (cbrt d) h) (/ 1.0 2.0))
4.5b
(/ (* M D) (* 2.0 d))
7.5b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt 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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
7.7b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

rewrite310.0ms

Algorithm
rewrite-expression-head
Rules
6673×add-exp-log
5120×prod-exp
2644×pow-exp
1716×div-exp
795×pow-to-exp
528×1-exp
232×rec-exp
79×add-cbrt-cube
54×cbrt-unprod
29×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
22×unpow-prod-down
21×cbrt-undiv
13×pow-unpow
12×pow1
9×cbrt-prod
8×associate-*r*
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 → 1275
Calls
4 calls:
7.0ms
(pow (/ (cbrt d) h) (/ 1.0 2.0))
6.0ms
(/ (* M D) (* 2.0 d))
76.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt 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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
20.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

series1.4s

Counts
4 → 12
Calls
4 calls:
159.0ms
(pow (/ (cbrt d) h) (/ 1.0 2.0))
27.0ms
(/ (* M D) (* 2.0 d))
689.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt 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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
554.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

simplify433.0ms

Algorithm
egg-herbie
Counts
1287 → 1287
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0500151864

prune1.1s

Filtered
1287 candidates to 131 candidates (10.2%)
Pruning

28 alts after pruning (28 fresh and 0 done)

PrunedKeptTotal
New128161287
Fresh12223
Picked101
Done000
Total1283281311

Merged error: 9.8b

Counts
1311 → 28

regimes1.3s

Accuracy

0% (6.2b remaining)

Error of 16.1b against oracle of 9.9b and baseline of 16.1b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
052134
152134

end0.0ms

sample8.9s

Algorithm
intervals
Results
5.0s39002×body80nan
2.1s12896×body80valid

Profiling

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