Details

Time bar (total: 49.2s)

sample568.0ms

Algorithm
intervals
Results
279.0ms1213×body80nan
138.0ms412×body80valid

simplify3.6s

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: 29.1b

localize59.0ms

Local error

Found 4 expressions with local error:

7.1b
(* (* (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 h) (/ 1.0 2.0))
14.7b
(pow (/ d l) (/ 1.0 2.0))
15.8b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite239.0ms

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:
100.0ms
(* (* (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))))
16.0ms
(pow (/ d h) (/ 1.0 2.0))
18.0ms
(pow (/ d l) (/ 1.0 2.0))
87.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.1s

Counts
4 → 12
Calls
4 calls:
917.0ms
(* (* (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))))
72.0ms
(pow (/ d h) (/ 1.0 2.0))
93.0ms
(pow (/ d l) (/ 1.0 2.0))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify2.0s

Counts
188 → 188
Iterations

Useful iterations: 2 (758.0ms)

IterNodesCost
04404376
110813962
237683606
done50003606

prune1.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.7b

localize80.0ms

Local error

Found 4 expressions with local error:

5.6b
(/ (* M D) (* 2.0 d))
7.1b
(* (* (* (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))))
14.7b
(pow (/ d l) (/ 1.0 2.0))
15.8b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite586.0ms

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:
20.0ms
(/ (* M D) (* 2.0 d))
450.0ms
(* (* (* (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))
69.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.2s

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ (* M D) (* 2.0 d))
977.0ms
(* (* (* (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))))
81.0ms
(pow (/ d l) (/ 1.0 2.0))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify3.0s

Counts
272 → 272
Iterations

Useful iterations: 2 (1.5s)

IterNodesCost
055111028
112659877
247928502
done50008502

prune1.1s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 11.7b

localize162.0ms

Local error

Found 4 expressions with local error:

5.6b
(/ (* M D) (* 2.0 d))
5.9b
(pow (/ (cbrt d) l) (/ 1.0 2.0))
7.1b
(* (* (* (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))))
15.8b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite876.0ms

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
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:
14.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(pow (/ (cbrt d) l) (/ 1.0 2.0))
619.0ms
(* (* (* (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))))
87.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.8s

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ (* M D) (* 2.0 d))
271.0ms
(pow (/ (cbrt d) l) (/ 1.0 2.0))
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)) (/ h l))))
1.0s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.0s

Counts
661 → 661
Iterations

Useful iterations: done (970.0ms)

IterNodesCost
088740193
1178733887
done500029641

prune1.2s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 10.1b

localize92.0ms

Local error

Found 4 expressions with local error:

5.6b
(/ (* M D) (* 2.0 d))
5.9b
(pow (/ (cbrt d) l) (/ 1.0 2.0))
7.1b
(* (* (* (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) (/ 1 l))))
7.7b
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
3260×add-exp-log
2531×prod-exp
1084×pow-exp
604×div-exp
428×pow-to-exp
66×add-cbrt-cube
37×times-frac
35×cbrt-unprod
32×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
22×unpow-prod-down
16×rec-exp 1-exp associate-*r*
15×pow1
13×pow-unpow
10×cbrt-undiv
9×cbrt-prod
6×pow-prod-down
5×associate-*l/
4×div-inv add-log-exp
3×associate-*r/
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* un-div-inv flip-- associate-/l* sqr-pow
Counts
4 → 687
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
18.0ms
(pow (/ (cbrt d) l) (/ 1.0 2.0))
757.0ms
(* (* (* (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) (/ 1 l))))
213.0ms
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))

series3.1s

Counts
4 → 12
Calls
4 calls:
33.0ms
(/ (* M D) (* 2.0 d))
225.0ms
(pow (/ (cbrt d) l) (/ 1.0 2.0))
1.6s
(* (* (* (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) (/ 1 l))))
1.3s
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))

simplify1.3s

Counts
699 → 699
Iterations

Useful iterations: done (1.2s)

IterNodesCost
094542369
1188334631
done500130305

prune1.0s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 9.8b

regimes1.8s

Accuracy

-7.4% (5.2b remaining)

Error of 15.6b against oracle of 10.4b and baseline of 15.2b

bsearch5.0ms

simplify18.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
059170
179170
done79170

end0.0ms

sample18.1s

Algorithm
intervals
Results
10.5s38803×body80nan
3.8s12790×body80valid