Details

Time bar (total: 17.6s)

sample364.0ms

Algorithm
intervals
Results
184.0ms1395×body80nan
73.0ms431×body80valid

simplify199.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05417
117417
271017
3494017
4500217

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.1b

Counts
2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

6.7b
(/ (* M D) (* 2.0 d))
9.8b
(pow (/ d h) (/ 1.0 2.0))
14.3b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
14.8b
(pow (/ d l) (/ 1.0 2.0))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
167×add-exp-log
78×prod-exp
51×div-exp
46×times-frac
39×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
37×add-cbrt-cube
26×unpow-prod-down pow-unpow
24×pow-exp
14×cbrt-unprod
13×associate-*r*
9×cbrt-undiv
8×pow1
6×pow-to-exp div-inv
4×add-log-exp
3×associate-*l/
2×pow-pow sqr-pow
1×frac-times frac-2neg associate-*r/ associate-*l* pow-prod-down clear-num associate-/r* *-commutative associate-/l*
Counts
4 → 159
Calls
4 calls:
5.0ms
(/ (* M D) (* 2.0 d))
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))
8.0ms
(pow (/ d l) (/ 1.0 2.0))

series260.0ms

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

simplify107.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012131383
149971229
250021229

prune449.0ms

Filtered
104 candidates to 171 candidates (-64.4%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New15417171
Fresh000
Picked101
Done000
Total15517172

Merged error: 13.3b

Counts
172 → 17

localize45.0ms

Local error

Found 4 expressions with local error:

6.3b
(* (* (* (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))))
6.7b
(/ (* M D) (* 2.0 d))
14.3b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
14.8b
(pow (/ d l) (/ 1.0 2.0))

rewrite75.0ms

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:
33.0ms
(* (* (* (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))))
5.0ms
(/ (* M D) (* 2.0 d))
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))

series520.0ms

Counts
4 → 12
Calls
4 calls:
270.0ms
(* (* (* (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))))
6.0ms
(/ (* M D) (* 2.0 d))
231.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify78.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
019345729
150025433

prune513.0ms

Filtered
96 candidates to 272 candidates (-183.3%)
Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New2666272
Fresh11516
Picked101
Done000
Total26821289

Merged error: 12.1b

Counts
289 → 21

localize44.0ms

Local error

Found 4 expressions with local error:

5.5b
(* (/ M 2.0) (/ D d))
6.3b
(* (* (* (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 2.0) (/ D d)) 2.0)) (/ h l))))
14.3b
(* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (/ h l))
14.8b
(pow (/ d l) (/ 1.0 2.0))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
738×add-exp-log
487×prod-exp
216×pow-exp
171×div-exp
78×pow-to-exp
52×add-sqr-sqrt
49×times-frac
46×add-cbrt-cube
40×add-cube-cbrt *-un-lft-identity
29×associate-*r*
20×cbrt-unprod
15×associate-*l*
13×unpow-prod-down pow-unpow
11×pow1
9×cbrt-undiv
5×div-inv
4×associate-*r/ associate-*l/ add-log-exp unswap-sqr
3×pow-prod-down *-commutative
2×distribute-rgt-in frac-times sub-neg distribute-lft-in
1×flip3-- pow-pow flip-- sqr-pow
Counts
4 → 289
Calls
4 calls:
10.0ms
(* (/ M 2.0) (/ D d))
32.0ms
(* (* (* (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 2.0) (/ D d)) 2.0)) (/ h l))))
12.0ms
(* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (/ h l))
6.0ms
(pow (/ d l) (/ 1.0 2.0))

series516.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(* (/ M 2.0) (/ D d))
264.0ms
(* (* (* (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 2.0) (/ D d)) 2.0)) (/ h l))))
233.0ms
(* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (/ h l))
13.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify81.0ms

Algorithm
egg-herbie
Counts
301 → 301
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
020825883
150015584

prune636.0ms

Filtered
118 candidates to 301 candidates (-155.1%)
Pruning

23 alts after pruning (22 fresh and 1 done)

PrunedKeptTotal
New2983301
Fresh11920
Picked011
Done000
Total29923322

Merged error: 11.8b

Counts
322 → 23

localize57.0ms

Local error

Found 4 expressions with local error:

3.5b
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
5.5b
(* (/ M 2.0) (/ D d))
6.3b
(* (* (* (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 2.0) (/ D d)) 2.0)) (/ h l))))
14.3b
(* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (/ h l))

rewrite269.0ms

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
46×add-sqr-sqrt
41×times-frac
34×add-cube-cbrt *-un-lft-identity
29×associate-*r*
27×cbrt-unprod
15×associate-*l*
14×pow1
13×pow-unpow
9×cbrt-undiv
5×unpow-prod-down pow-prod-down div-inv
4×associate-*r/ associate-*l/ add-log-exp unswap-sqr
3×*-commutative
2×distribute-rgt-in frac-times sub-neg distribute-lft-in
1×flip3-- pow-pow flip-- sqr-pow
Counts
4 → 1012
Calls
4 calls:
11.0ms
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
10.0ms
(* (/ M 2.0) (/ D d))
73.0ms
(* (* (* (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 2.0) (/ D d)) 2.0)) (/ h l))))
12.0ms
(* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (/ h l))

series530.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
6.0ms
(* (/ M 2.0) (/ D d))
270.0ms
(* (* (* (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 2.0) (/ D d)) 2.0)) (/ h l))))
224.0ms
(* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (/ h l))

simplify335.0ms

Algorithm
egg-herbie
Counts
1024 → 1024
Iterations

Useful iterations: 1 (42.0ms)

IterNodesCost
0452138563
1500138382

prune621.0ms

Filtered
117 candidates to 1024 candidates (-775.2%)
Pruning

25 alts after pruning (24 fresh and 1 done)

PrunedKeptTotal
New102131024
Fresh02121
Picked101
Done011
Total1022251047

Merged error: 10.4b

Counts
1047 → 25

regimes1.5s

Accuracy

17.8% (4.1b remaining)

Error of 15.1b against oracle of 11.0b and baseline of 16.0b

bsearch237.0ms

Steps
ItersRangePoint
10
-5.821729671012748e+36
-1.3350198522982622e+22
-5.357794897230685e+30

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05682
15682

end0.0ms

sample10.0s

Algorithm
intervals
Results
5.1s38193×body80nan
2.2s12769×body80valid

Profiling

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