Details

Time bar (total: 47.4s)

sample489.0ms

Algorithm
intervals
Results
233.0ms1298×body80nan
120.0ms421×body80valid

simplify940.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02235
15435
217435
372035
done500035

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize66.0ms

Local error

Found 4 expressions with local error:

7.0b
(/ (* M D) (* 2.0 d))
10.4b
(pow (/ d h) (/ 1.0 2.0))
11.5b
(pow (/ d l) (/ 1.0 2.0))
11.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
167×add-exp-log
78×prod-exp
51×div-exp
46×times-frac
39×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
37×add-cbrt-cube
26×unpow-prod-down pow-unpow
24×pow-exp
14×cbrt-unprod
13×associate-*r*
9×cbrt-undiv
8×pow1
6×pow-to-exp div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l/
2×pow-pow sqr-pow
1×frac-times frac-2neg associate-*r/ associate-*l* pow-prod-down clear-num associate-/r* *-commutative associate-/l*
Counts
4 → 167
Calls
4 calls:
13.0ms
(/ (* M D) (* 2.0 d))
8.0ms
(pow (/ d h) (/ 1.0 2.0))
16.0ms
(pow (/ d l) (/ 1.0 2.0))
81.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.2s

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ (* M D) (* 2.0 d))
81.0ms
(pow (/ d h) (/ 1.0 2.0))
70.0ms
(pow (/ d l) (/ 1.0 2.0))
974.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify690.0ms

Counts
179 → 179
Iterations

Useful iterations: done (683.0ms)

IterNodesCost
03922931
112512722
done50002408

prune1.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 13.9b

localize87.0ms

Local error

Found 4 expressions with local error:

6.2b
(* (* (* (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))))
7.0b
(/ (* M D) (* 2.0 d))
11.5b
(pow (/ d l) (/ 1.0 2.0))
11.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite510.0ms

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:
406.0ms
(* (* (* (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))))
13.0ms
(/ (* M D) (* 2.0 d))
8.0ms
(pow (/ d l) (/ 1.0 2.0))
56.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.3s

Counts
4 → 12
Calls
4 calls:
1.3s
(* (* (* (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))))
30.0ms
(/ (* M D) (* 2.0 d))
108.0ms
(pow (/ d l) (/ 1.0 2.0))
886.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify926.0ms

Counts
318 → 318
Iterations

Useful iterations: done (897.0ms)

IterNodesCost
063012762
1203311647
done500010207

prune1.5s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 10.8b

localize99.0ms

Local error

Found 4 expressions with local error:

4.0b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
6.2b
(* (* (* (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))))
7.0b
(/ (* M D) (* 2.0 d))
11.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite1.0s

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))
572.0ms
(* (* (* (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))))
14.0ms
(/ (* M D) (* 2.0 d))
55.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.5s

Counts
4 → 12
Calls
4 calls:
252.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
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))))
31.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.8s

Counts
1551 → 1551
Iterations

Useful iterations: done (1.6s)

IterNodesCost
0182298103
done500083065

prune2.5s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 10.3b

localize115.0ms

Local error

Found 4 expressions with local error:

4.0b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
6.2b
(* (* (* (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)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))))
7.0b
(/ (* M D) (* 2.0 d))
8.5b
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
8361×add-exp-log
6535×prod-exp
3446×pow-exp
1946×div-exp
971×pow-to-exp
592×rec-exp 1-exp
80×add-cbrt-cube
57×cbrt-unprod
46×times-frac
40×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
6×prod-diff
5×distribute-rgt-in distribute-lft-in associate-*l/
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×associate-*r/
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 → 1590
Calls
4 calls:
10.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
726.0ms
(* (* (* (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)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))))
13.0ms
(/ (* M D) (* 2.0 d))
338.0ms
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))

series2.8s

Counts
4 → 12
Calls
4 calls:
275.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
1.3s
(* (* (* (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)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))))
42.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))

simplify1.6s

Counts
1602 → 1602
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01919110400
done500195110

prune2.9s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 10.1b

regimes2.5s

Accuracy

0% (6.1b remaining)

Error of 15.6b against oracle of 9.5b and baseline of 15.6b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03983
15183
done5183

end0.0ms

sample18.0s

Algorithm
intervals
Results
10.7s38583×body80nan
3.5s12782×body80valid