Details

Time bar (total: 25.0s)

sample261.0ms

Algorithm
intervals
Results
122.0ms1263×body80nan
54.0ms399×body80valid

simplify29.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05417
117417
272017
3500117
done500117

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize32.0ms

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))

rewrite141.0ms

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:
63.0ms
(* (* (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))))
50.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
10.0ms
(pow (/ d h) (/ 1.0 2.0))
8.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
675.0ms
(* (* (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))))
757.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
68.0ms
(pow (/ d h) (/ 1.0 2.0))
63.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify44.0ms

Counts
202 → 202
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
012872382
150012125
done50012125

prune750.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.9b

localize47.0ms

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))

rewrite414.0ms

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))
319.0ms
(* (* (* (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))))
53.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
8.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (* M D) (* 2.0 d))
688.0ms
(* (* (* (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))))
742.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
68.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify77.0ms

Counts
286 → 286
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
017106060
150015717
done50015717

prune837.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 12.0b

localize59.0ms

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))

rewrite803.0ms

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:
10.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
12.0ms
(/ (* M D) (* 2.0 d))
519.0ms
(* (* (* (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))))
53.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.0s

Counts
4 → 12
Calls
4 calls:
181.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
36.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (* (* (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))))
749.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify329.0ms

Counts
1255 → 1255
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
0500145180
done500145180

prune1.6s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 10.6b

localize69.0ms

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
(* (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))))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
7251×add-exp-log
5438×prod-exp
2642×pow-exp
1681×div-exp
794×pow-to-exp
232×rec-exp 1-exp
87×add-cbrt-cube
58×cbrt-unprod
26×associate-*r*
24×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
20×times-frac
17×cbrt-undiv
14×pow1
11×associate-*l*
9×cbrt-prod
6×unpow-prod-down prod-diff pow-prod-down
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r/ associate-*l/ *-commutative div-inv unswap-sqr
2×sub-neg sqr-pow
1×frac-times flip3-- frac-2neg clear-num associate-/r* flip-- associate-/l*
Counts
4 → 1283
Calls
4 calls:
253.0ms
(* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))
38.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))
12.0ms
(/ (* M D) (* 2.0 d))
521.0ms
(* (* (* (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))))

series2.3s

Counts
4 → 12
Calls
4 calls:
781.0ms
(* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))
463.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))
28.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (* (* (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))))

simplify380.0ms

Counts
1295 → 1295
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
0500152101
done500152101

prune1.3s

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 9.0b

regimes1.6s

Accuracy

0% (5.2b remaining)

Error of 14.4b against oracle of 9.2b and baseline of 14.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05149
15149
done5149

end0.0ms

sample7.7s

Algorithm
intervals
Results
3.7s37865×body80nan
1.7s12724×body80valid