Details

Time bar (total: 45.1s)

sample288.0ms

Algorithm
intervals
Results
134.0ms1263×body80nan
56.0ms399×body80valid

simplify3.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02235
15435
217435
371735
4458035
done500035

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize47.0ms

Local error

Found 4 expressions with local error:

7.8b
(* (* (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))))
9.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.0b
(pow (/ d h) (/ 1.0 2.0))
12.9b
(pow (/ d l) (/ 1.0 2.0))

rewrite188.0ms

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:
75.0ms
(* (* (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
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
8.0ms
(pow (/ d h) (/ 1.0 2.0))
13.0ms
(pow (/ d l) (/ 1.0 2.0))

series2.2s

Counts
4 → 12
Calls
4 calls:
1.0s
(* (* (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))))
957.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
75.0ms
(pow (/ d h) (/ 1.0 2.0))
92.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify2.6s

Counts
202 → 202
Iterations

Useful iterations: done (2.6s)

IterNodesCost
04635058
111404644
239784180
done50014172

prune1.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.9b

localize51.0ms

Local error

Found 4 expressions with local error:

4.9b
(/ (* M D) (* 2.0 d))
7.8b
(* (* (* (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))))
9.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.9b
(pow (/ d l) (/ 1.0 2.0))

rewrite581.0ms

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:
29.0ms
(/ (* M D) (* 2.0 d))
443.0ms
(* (* (* (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))))
76.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
9.0ms
(pow (/ d l) (/ 1.0 2.0))

series2.0s

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ (* M D) (* 2.0 d))
892.0ms
(* (* (* (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))))
977.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
117.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify971.0ms

Counts
286 → 286
Iterations

Useful iterations: done (951.0ms)

IterNodesCost
057411962
1133310811
done50009346

prune1.1s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 12.0b

localize91.0ms

Local error

Found 4 expressions with local error:

4.1b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
4.9b
(/ (* M D) (* 2.0 d))
7.8b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt 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))))
9.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
6965×add-exp-log
5245×prod-exp
2614×pow-exp
1626×div-exp
789×pow-to-exp
232×rec-exp 1-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 → 1243
Calls
4 calls:
19.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
27.0ms
(/ (* M D) (* 2.0 d))
779.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt 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))))
86.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.7s

Counts
4 → 12
Calls
4 calls:
232.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
42.0ms
(/ (* 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 (/ 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))))
1.0s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify2.0s

Counts
1255 → 1255
Iterations

Useful iterations: done (1.9s)

IterNodesCost
0152084703
1250270377
done500062008

prune1.7s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 11.4b

localize83.0ms

Local error

Found 4 expressions with local error:

4.3b
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))
4.4b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h)))
4.9b
(/ (* M D) (* 2.0 d))
7.8b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt 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 h) l))))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
7347×add-exp-log
5500×prod-exp
2652×pow-exp
1701×div-exp
796×pow-to-exp
232×rec-exp 1-exp
95×add-cbrt-cube
70×cbrt-unprod
26×associate-*r*
23×pow1
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
19×times-frac
17×cbrt-undiv
12×pow-prod-down
9×cbrt-prod
7×associate-*l/
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r/ associate-*l* *-commutative
2×sub-neg div-inv
1×frac-times flip3-- frac-2neg clear-num associate-/r* flip-- associate-/l*
Counts
4 → 1296
Calls
4 calls:
274.0ms
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))
90.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h)))
19.0ms
(/ (* M D) (* 2.0 d))
695.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt 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 h) l))))

series3.7s

Counts
4 → 12
Calls
4 calls:
1.2s
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))
1.0s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h)))
33.0ms
(/ (* 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 (/ 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 h) l))))

simplify2.0s

Counts
1308 → 1308
Iterations

Useful iterations: done (1.9s)

IterNodesCost
0151195586
1248680820
done500167158

prune1.4s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 11.4b

regimes2.2s

Accuracy

0% (5.2b remaining)

Error of 15.9b against oracle of 10.7b and baseline of 15.9b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03773
14873
done4873

end0.0ms

sample11.6s

Algorithm
intervals
Results
5.5s37865×body80nan
2.6s12724×body80valid