Details

Time bar (total: 51.3s)

sample580.0ms

Algorithm
intervals
Results
334.0ms1359×body80nan
98.0ms411×body80valid

simplify4.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02235
15435
217435
370735
4448135
done500135

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.1b

localize78.0ms

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))

rewrite232.0ms

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:
88.0ms
(* (* (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))
109.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.3s

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))))
109.0ms
(pow (/ d h) (/ 1.0 2.0))
98.0ms
(pow (/ d l) (/ 1.0 2.0))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify2.7s

Counts
188 → 188
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
04404376
110813962
237683606
done50003606

prune1.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.0b

localize103.0ms

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))

rewrite615.0ms

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×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 → 260
Calls
4 calls:
13.0ms
(/ (* M D) (* 2.0 d))
475.0ms
(* (* (* (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))))
14.0ms
(pow (/ d l) (/ 1.0 2.0))
82.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.3s

Counts
4 → 12
Calls
4 calls:
41.0ms
(/ (* M D) (* 2.0 d))
964.0ms
(* (* (* (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))))
102.0ms
(pow (/ d l) (/ 1.0 2.0))
1.2s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify2.4s

Counts
272 → 272
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
055111028
112659877
247928502
done50008502

prune1.3s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 8.8b

localize161.0ms

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))

rewrite1.0s

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
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 → 649
Calls
4 calls:
21.0ms
(pow (/ (cbrt d) l) (/ 1.0 2.0))
25.0ms
(/ (* M D) (* 2.0 d))
756.0ms
(* (* (* (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))))
91.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series3.1s

Counts
4 → 12
Calls
4 calls:
252.0ms
(pow (/ (cbrt d) l) (/ 1.0 2.0))
34.0ms
(/ (* M D) (* 2.0 d))
1.8s
(* (* (* (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))))
1.0s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.1s

Counts
661 → 661
Iterations

Useful iterations: done (1.1s)

IterNodesCost
088740193
1178733887
done500129641

prune1.3s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 8.0b

localize140.0ms

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

rewrite1.2s

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
38×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
5×associate-*r/
4×div-inv add-log-exp
3×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 → 700
Calls
4 calls:
19.0ms
(pow (/ (cbrt d) l) (/ 1.0 2.0))
22.0ms
(/ (* M D) (* 2.0 d))
676.0ms
(* (* (* (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 (* (* (* (cbrt h) (cbrt h)) (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0))) (/ (cbrt h) l))))
290.0ms
(* (* (* (cbrt h) (cbrt h)) (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0))) (/ (cbrt h) l))

series3.0s

Counts
4 → 12
Calls
4 calls:
252.0ms
(pow (/ (cbrt d) l) (/ 1.0 2.0))
63.0ms
(/ (* M D) (* 2.0 d))
1.7s
(* (* (* (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 (* (* (* (cbrt h) (cbrt h)) (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0))) (/ (cbrt h) l))))
1.1s
(* (* (* (cbrt h) (cbrt h)) (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0))) (/ (cbrt h) l))

simplify1.4s

Counts
712 → 712
Iterations

Useful iterations: done (1.3s)

IterNodesCost
098146212
1202139597
done500032673

prune1.6s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 8.0b

regimes2.3s

Accuracy

0% (4.7b remaining)

Error of 15.6b against oracle of 10.9b and baseline of 15.6b

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03884
15084
done5084

end0.0ms

sample17.0s

Algorithm
intervals
Results
9.2s38252×body80nan
4.3s12825×body80valid