Details

Time bar (total: 48.6s)

sample550.0ms

Algorithm
intervals
Results
271.0ms1359×body80nan
144.0ms411×body80valid

simplify4.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02235
15435
217435
371735
4458035
done500035

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.1b

localize61.0ms

Local error

Found 4 expressions with local error:

5.3b
(* (* (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))))
9.8b
(pow (/ d h) (/ 1.0 2.0))
12.0b
(pow (/ d l) (/ 1.0 2.0))
12.1b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
205×add-exp-log
107×prod-exp
55×div-exp
45×times-frac
42×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
40×pow-exp
30×add-cbrt-cube
26×unpow-prod-down pow-unpow
16×associate-*r*
14×pow-to-exp
13×cbrt-unprod
10×pow1
6×prod-diff
5×cbrt-undiv distribute-rgt-in distribute-lft-in div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r/ associate-*l/
2×sub-neg pow-pow associate-*l* pow-prod-down *-commutative sqr-pow
1×frac-times flip3-- flip--
Counts
4 → 190
Calls
4 calls:
102.0ms
(* (* (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))))
8.0ms
(pow (/ d h) (/ 1.0 2.0))
8.0ms
(pow (/ d l) (/ 1.0 2.0))
74.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.0s

Counts
4 → 12
Calls
4 calls:
940.0ms
(* (* (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))))
81.0ms
(pow (/ d h) (/ 1.0 2.0))
81.0ms
(pow (/ d l) (/ 1.0 2.0))
931.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify2.3s

Counts
202 → 202
Iterations

Useful iterations: done (2.3s)

IterNodesCost
04635058
111404644
239784180
done50014172

prune995.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.0b

localize102.0ms

Local error

Found 4 expressions with local error:

4.0b
(/ (* M D) (* 2.0 d))
5.3b
(* (* (* (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))))
12.0b
(pow (/ d l) (/ 1.0 2.0))
12.1b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite515.0ms

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×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
20×cbrt-unprod
16×associate-*r*
13×unpow-prod-down pow-unpow
9×pow1 cbrt-undiv
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×associate-*r/ associate-*l/
2×sub-neg 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 → 274
Calls
4 calls:
13.0ms
(/ (* M D) (* 2.0 d))
384.0ms
(* (* (* (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))))
8.0ms
(pow (/ d l) (/ 1.0 2.0))
89.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.0s

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ (* M D) (* 2.0 d))
999.0ms
(* (* (* (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))))
72.0ms
(pow (/ d l) (/ 1.0 2.0))
895.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify865.0ms

Counts
286 → 286
Iterations

Useful iterations: done (849.0ms)

IterNodesCost
057411962
1133310811
done50009346

prune1.0s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 8.8b

localize128.0ms

Local error

Found 4 expressions with local error:

3.9b
(pow (/ (cbrt d) l) (/ 1.0 2.0))
4.0b
(/ (* M D) (* 2.0 d))
5.3b
(* (* (* (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)) (/ 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))))
12.1b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite958.0ms

Algorithm
rewrite-expression-head
Rules
3061×add-exp-log
2393×prod-exp
1064×pow-exp
557×div-exp
424×pow-to-exp
55×add-cbrt-cube
37×times-frac
34×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
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u pow-prod-down log1p-expm1-u div-inv add-log-exp
3×associate-*r/ associate-*l/
2×sub-neg associate-*l* *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 663
Calls
4 calls:
19.0ms
(pow (/ (cbrt d) l) (/ 1.0 2.0))
25.0ms
(/ (* M D) (* 2.0 d))
670.0ms
(* (* (* (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)) (/ 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))))
106.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.9s

Counts
4 → 12
Calls
4 calls:
234.0ms
(pow (/ (cbrt d) l) (/ 1.0 2.0))
33.0ms
(/ (* M D) (* 2.0 d))
1.5s
(* (* (* (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)) (/ 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))))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.1s

Counts
675 → 675
Iterations

Useful iterations: done (1.1s)

IterNodesCost
091041283
1186134977
done500030166

prune1.5s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 8.0b

localize99.0ms

Local error

Found 4 expressions with local error:

3.9b
(pow (/ (cbrt d) l) (/ 1.0 2.0))
4.0b
(/ (* M D) (* 2.0 d))
5.3b
(* (* (* (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)) (/ 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)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))))
9.4b
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
3301×add-exp-log
2559×prod-exp
1084×pow-exp
603×div-exp
428×pow-to-exp
80×add-cbrt-cube
57×cbrt-unprod
46×times-frac
40×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
25×associate-*r*
22×unpow-prod-down
19×pow1
18×cbrt-prod
15×cbrt-undiv
13×pow-unpow
9×pow-prod-down
6×prod-diff
5×distribute-rgt-in distribute-lft-in associate-*l/
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×associate-*r/
2×sub-neg associate-*l* *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 714
Calls
4 calls:
20.0ms
(pow (/ (cbrt d) l) (/ 1.0 2.0))
18.0ms
(/ (* M D) (* 2.0 d))
693.0ms
(* (* (* (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)) (/ 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)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))))
394.0ms
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))

series2.9s

Counts
4 → 12
Calls
4 calls:
259.0ms
(pow (/ (cbrt d) l) (/ 1.0 2.0))
39.0ms
(/ (* M D) (* 2.0 d))
1.4s
(* (* (* (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)) (/ 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)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))))
1.2s
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))

simplify1.4s

Counts
726 → 726
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0100447448
1208640833
done500133244

prune1.7s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 8.0b

regimes2.2s

Accuracy

0% (5.3b remaining)

Error of 16.4b against oracle of 11.1b and baseline of 16.4b

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03584
14484
done4484

end0.0ms

sample17.7s

Algorithm
intervals
Results
10.1s38252×body80nan
3.8s12825×body80valid