Details

Time bar (total: 24.7s)

sample322.0ms

Algorithm
intervals
Results
155.0ms1173×body80nan
63.0ms414×body80valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02235
15435
217035
365535
4429035
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

localize25.0ms

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))

rewrite59.0ms

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))
21.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series613.0ms

Counts
4 → 12
Calls
4 calls:
311.0ms
(* (* (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))))
17.0ms
(pow (/ d l) (/ 1.0 2.0))
14.0ms
(pow (/ d h) (/ 1.0 2.0))
270.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify441.0ms

Counts
188 → 188
Iterations

Useful iterations: done (434.0ms)

IterNodesCost
05304650
115304307
done50004229

prune686.0ms

Filtered
125 candidates to 188 candidates (-50.4%)
Pruning

25 alts after pruning (25 fresh and 0 done)

PrunedKeptTotal
New16325188
Fresh000
Picked101
Done000
Total16425189

Merged error: 13.8b

Counts
189 → 25

localize36.0ms

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))

rewrite89.0ms

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))
29.0ms
(* (* (* (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))
14.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series648.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(/ (* M D) (* 2.0 d))
362.0ms
(* (* (* (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))))
15.0ms
(pow (/ d l) (/ 1.0 2.0))
264.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify559.0ms

Counts
304 → 304
Iterations

Useful iterations: done (545.0ms)

IterNodesCost
068712149
1207911109
done500110800

prune739.0ms

Filtered
126 candidates to 304 candidates (-141.3%)
Pruning

29 alts after pruning (29 fresh and 0 done)

PrunedKeptTotal
New29212304
Fresh71724
Picked101
Done000
Total30029329

Merged error: 12.6b

Counts
329 → 29

localize43.0ms

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))

rewrite218.0ms

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:
8.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
7.0ms
(/ (* M D) (* 2.0 d))
63.0ms
(* (* (* (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))))
14.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series635.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
7.0ms
(/ (* M D) (* 2.0 d))
322.0ms
(* (* (* (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))))
264.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify942.0ms

Counts
797 → 797
Iterations

Useful iterations: done (886.0ms)

IterNodesCost
0110146232
1361740817
done500139790

prune1.1s

Filtered
157 candidates to 797 candidates (-407.6%)
Pruning

34 alts after pruning (34 fresh and 0 done)

PrunedKeptTotal
New78512797
Fresh62228
Picked101
Done000
Total79234826

Merged error: 11.0b

Counts
826 → 34

localize43.0ms

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))

rewrite212.0ms

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))
9.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
63.0ms
(* (* (* (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))

series843.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(/ (* M D) (* 2.0 d))
244.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
327.0ms
(* (* (* (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))))
265.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

simplify1.3s

Counts
750 → 750
Iterations

Useful iterations: done (1.2s)

IterNodesCost
097045597
1328039594
done500137619

prune553.0ms

Filtered
101 candidates to 750 candidates (-642.6%)
Pruning

35 alts after pruning (35 fresh and 0 done)

PrunedKeptTotal
New7446750
Fresh42933
Picked101
Done000
Total74935784

Merged error: 10.5b

Counts
784 → 35

regimes2.4s

Accuracy

2.4% (6.6b remaining)

Error of 16.8b against oracle of 10.2b and baseline of 16.9b

bsearch454.0ms

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

simplify16.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
089244
1116238
2122238
done122238

end0.0ms

sample10.2s

Algorithm
intervals
Results
5.1s38287×body80nan
1.9s12960×body80valid

Profiling

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