Details

Time bar (total: 44.6s)

sample245.0ms

Algorithm
intervals
Results
125.0ms1184×body80nan
55.0ms387×body80valid

simplify2.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02235
15435
217035
366535
4438235
done500035

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.4b

localize31.0ms

Local error

Found 4 expressions with local error:

7.2b
(* (* (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))))
11.1b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.4b
(pow (/ d l) (/ 1.0 2.0))
12.6b
(pow (/ d h) (/ 1.0 2.0))

rewrite92.0ms

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:
40.0ms
(* (* (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))))
24.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
4.0ms
(pow (/ d l) (/ 1.0 2.0))
9.0ms
(pow (/ d h) (/ 1.0 2.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
706.0ms
(* (* (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))))
801.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
70.0ms
(pow (/ d l) (/ 1.0 2.0))
74.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify857.0ms

Counts
202 → 202
Iterations

Useful iterations: done (840.0ms)

IterNodesCost
04635058
113014644
done50014404

prune851.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.2b

localize41.0ms

Local error

Found 4 expressions with local error:

6.5b
(/ (* M D) (* 2.0 d))
7.2b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
11.1b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.4b
(pow (/ d l) (/ 1.0 2.0))

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
818×add-exp-log
567×prod-exp
280×pow-exp
187×div-exp
94×pow-to-exp
46×add-cbrt-cube
32×rec-exp 1-exp
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 → 306
Calls
4 calls:
4.0ms
(/ (* M D) (* 2.0 d))
186.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
28.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
5.0ms
(pow (/ d l) (/ 1.0 2.0))

series2.0s

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
823.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
71.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify1.2s

Counts
318 → 318
Iterations

Useful iterations: done (1.2s)

IterNodesCost
063012762
1188911384
done500011232

prune911.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 11.1b

localize69.0ms

Local error

Found 4 expressions with local error:

3.6b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
6.5b
(/ (* M D) (* 2.0 d))
7.2b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
11.1b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite676.0ms

Algorithm
rewrite-expression-head
Rules
8121×add-exp-log
6369×prod-exp
3426×pow-exp
1900×div-exp
967×pow-to-exp
592×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 → 1539
Calls
4 calls:
10.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
5.0ms
(/ (* M D) (* 2.0 d))
312.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
27.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.4s

Counts
4 → 12
Calls
4 calls:
294.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
35.0ms
(/ (* M D) (* 2.0 d))
1.2s
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
900.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify834.0ms

Counts
1551 → 1551
Iterations

Useful iterations: 0 (199.0ms)

IterNodesCost
0182298103
done500098103

prune8.1s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 9.5b

localize66.0ms

Local error

Found 4 expressions with local error:

5.7b
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))
6.1b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.5b
(/ (* M D) (* 2.0 d))
7.2b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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) (/ 1 l))))

rewrite805.0ms

Algorithm
rewrite-expression-head
Rules
8382×add-exp-log
6544×prod-exp
3454×pow-exp
1961×div-exp
972×pow-to-exp
608×rec-exp 1-exp
75×add-cbrt-cube
40×cbrt-unprod
19×associate-*r*
16×pow1
15×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
11×cbrt-undiv
10×times-frac
7×pow-prod-down 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* un-div-inv flip-- associate-/l*
Counts
4 → 1562
Calls
4 calls:
88.0ms
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))
23.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
5.0ms
(/ (* M D) (* 2.0 d))
356.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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) (/ 1 l))))

series2.7s

Counts
4 → 12
Calls
4 calls:
888.0ms
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))
801.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
28.0ms
(/ (* M D) (* 2.0 d))
942.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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) (/ 1 l))))

simplify714.0ms

Counts
1574 → 1574
Iterations

Useful iterations: done (566.0ms)

IterNodesCost
01776102071
done5000102055

prune8.2s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 9.3b

regimes1.2s

Accuracy

3.8% (6.5b remaining)

Error of 15.8b against oracle of 9.3b and baseline of 16.1b

bsearch6.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
044152
158152
done58152

end0.0ms

sample8.1s

Algorithm
intervals
Results
4.2s38505×body80nan
1.9s12768×body80valid