Details

Time bar (total: 24.9s)

sample305.0ms

Algorithm
intervals
Results
152.0ms1173×body80nan
56.0ms414×body80valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02235
15435
217035
365135
4410735
done500035

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.9b

Counts
2 → 1

localize30.0ms

Local error

Found 4 expressions with local error:

6.5b
(* (* (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))))
11.8b
(pow (/ d l) (/ 1.0 2.0))
13.8b
(pow (/ d h) (/ 1.0 2.0))
14.7b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite51.0ms

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:
15.0ms
(* (* (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))))
6.0ms
(pow (/ d l) (/ 1.0 2.0))
7.0ms
(pow (/ d h) (/ 1.0 2.0))
14.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series589.0ms

Counts
4 → 12
Calls
4 calls:
298.0ms
(* (* (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
(pow (/ d l) (/ 1.0 2.0))
14.0ms
(pow (/ d h) (/ 1.0 2.0))
263.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.7s

Counts
188 → 188
Iterations

Useful iterations: 2 (985.0ms)

IterNodesCost
05304650
115194191
247483771
done50003771

prune595.0ms

Filtered
107 candidates to 188 candidates (-75.7%)
Pruning

23 alts after pruning (23 fresh and 0 done)

PrunedKeptTotal
New16523188
Fresh000
Picked101
Done000
Total16623189

Merged error: 14.3b

Counts
189 → 23

localize33.0ms

Local error

Found 4 expressions with local error:

5.0b
(/ (* M D) (* 2.0 d))
6.5b
(* (* (* (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))))
11.8b
(pow (/ d l) (/ 1.0 2.0))
14.7b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite88.0ms

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:
7.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(* (* (* (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))))
6.0ms
(pow (/ d l) (/ 1.0 2.0))
16.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series610.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
340.0ms
(* (* (* (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))))
14.0ms
(pow (/ d l) (/ 1.0 2.0))
250.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify598.0ms

Counts
304 → 304
Iterations

Useful iterations: done (584.0ms)

IterNodesCost
068712149
1206510730
done500110552

prune607.0ms

Filtered
90 candidates to 304 candidates (-237.8%)
Pruning

29 alts after pruning (29 fresh and 0 done)

PrunedKeptTotal
New29113304
Fresh61622
Picked101
Done000
Total29829327

Merged error: 13.3b

Counts
327 → 29

localize41.0ms

Local error

Found 4 expressions with local error:

3.8b
(pow (/ d (cbrt h)) (/ 1.0 2.0))
5.0b
(/ (* M D) (* 2.0 d))
6.5b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
14.7b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite368.0ms

Algorithm
rewrite-expression-head
Rules
3529×add-exp-log
2893×prod-exp
1396×pow-exp
623×div-exp
522×pow-to-exp
136×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 → 785
Calls
4 calls:
7.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
6.0ms
(/ (* M D) (* 2.0 d))
54.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt 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))

series602.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
6.0ms
(/ (* M D) (* 2.0 d))
300.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
255.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify972.0ms

Counts
797 → 797
Iterations

Useful iterations: done (926.0ms)

IterNodesCost
0110146232
1360138174
done500138146

prune753.0ms

Filtered
106 candidates to 797 candidates (-651.9%)
Pruning

29 alts after pruning (29 fresh and 0 done)

PrunedKeptTotal
New78710797
Fresh91928
Picked101
Done000
Total79729826

Merged error: 11.9b

Counts
826 → 29

localize42.0ms

Local error

Found 4 expressions with local error:

5.0b
(/ (* M D) (* 2.0 d))
6.5b
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.5b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
7.0b
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
3500×add-exp-log
2885×prod-exp
1389×pow-exp
607×div-exp
520×pow-to-exp
136×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 → 738
Calls
4 calls:
7.0ms
(/ (* M D) (* 2.0 d))
8.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
59.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
12.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

series796.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
233.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
305.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
252.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

simplify897.0ms

Counts
750 → 750
Iterations

Useful iterations: done (845.0ms)

IterNodesCost
097045597
1327537599
done500137459

prune351.0ms

Filtered
67 candidates to 750 candidates (-1019.4%)
Pruning

30 alts after pruning (30 fresh and 0 done)

PrunedKeptTotal
New7464750
Fresh22628
Picked101
Done000
Total74930779

Merged error: 11.9b

Counts
779 → 30

regimes2.3s

Accuracy

3.7% (5.3b remaining)

Error of 16.7b against oracle of 11.4b and baseline of 16.9b

bsearch429.0ms

Steps
ItersRangePoint
8
1.1216373519901905e+282
3.110509378487501e+284
7.680515421182015e+283
8
1.4841189549473678e+197
2.2499158756864882e+201
6.604748430151654e+200
9
-6.5485710084279506e+122
-1.5328177591333543e+116
-2.3201941826751998e+117

simplify9.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
090244
1117238
done117238

end0.0ms

sample9.6s

Algorithm
intervals
Results
4.8s38287×body80nan
1.8s12960×body80valid

Profiling

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