Details

Time bar (total: 31.1s)

sample283.0ms

Algorithm
intervals
Results
132.0ms1303×body80nan
59.0ms426×body80valid

simplify2.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02235
15435
217435
371735
4458035
done500035

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.8b

localize30.0ms

Local error

Found 4 expressions with local error:

7.4b
(* (* (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))))
12.6b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.9b
(pow (/ d l) (/ 1.0 2.0))
14.6b
(pow (/ d h) (/ 1.0 2.0))

rewrite139.0ms

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:
62.0ms
(* (* (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))))
52.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
7.0ms
(pow (/ d l) (/ 1.0 2.0))
8.0ms
(pow (/ d h) (/ 1.0 2.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
683.0ms
(* (* (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))))
957.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
63.0ms
(pow (/ d l) (/ 1.0 2.0))
71.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify1.7s

Counts
202 → 202
Iterations

Useful iterations: done (1.7s)

IterNodesCost
04635058
111404644
239824180
done50004172

prune763.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 12.3b

localize47.0ms

Local error

Found 4 expressions with local error:

5.2b
(/ (* M D) (* 2.0 d))
7.4b
(* (* (* (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))))
12.6b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.9b
(pow (/ d l) (/ 1.0 2.0))

rewrite362.0ms

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:
12.0ms
(/ (* M D) (* 2.0 d))
264.0ms
(* (* (* (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))))
52.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
8.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (* M D) (* 2.0 d))
903.0ms
(* (* (* (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))))
752.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
70.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify615.0ms

Counts
318 → 318
Iterations

Useful iterations: done (602.0ms)

IterNodesCost
063012762
1141111384
done500010169

prune789.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 11.2b

localize57.0ms

Local error

Found 4 expressions with local error:

2.7b
(pow (/ d (cbrt h)) (/ 1.0 2.0))
5.2b
(/ (* M D) (* 2.0 d))
7.4b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
12.6b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite790.0ms

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 h)) (/ 1.0 2.0))
12.0ms
(/ (* M D) (* 2.0 d))
495.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt 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))

series1.9s

Counts
4 → 12
Calls
4 calls:
185.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
29.0ms
(/ (* M D) (* 2.0 d))
935.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
763.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.2s

Counts
1255 → 1255
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0151984720
1249970393
done500062024

prune1.1s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 10.1b

localize57.0ms

Local error

Found 4 expressions with local error:

4.9b
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
5.2b
(/ (* M D) (* 2.0 d))
5.6b
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
7.4b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

rewrite813.0ms

Algorithm
rewrite-expression-head
Rules
6936×add-exp-log
5237×prod-exp
2607×pow-exp
1610×div-exp
787×pow-to-exp
232×rec-exp 1-exp
60×add-cbrt-cube
30×prod-diff
29×cbrt-unprod
24×add-sqr-sqrt *-un-lft-identity
22×add-cube-cbrt
17×distribute-rgt-in distribute-lft-in
11×pow1
10×cbrt-undiv
8×times-frac associate-*r* div-inv
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp
2×sub-neg frac-2neg associate-*r/ associate-*l* clear-num associate-/r* *-commutative associate-/l*
1×flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 1220
Calls
4 calls:
38.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
12.0ms
(/ (* M D) (* 2.0 d))
33.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
517.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

series2.7s

Counts
4 → 12
Calls
4 calls:
760.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
28.0ms
(/ (* M D) (* 2.0 d))
767.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
1.1s
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

simplify1.2s

Counts
1232 → 1232
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0144588845
1234673534
done500164691

prune706.0ms

Pruning

31 alts after pruning (30 fresh and 1 done)

Merged error: 9.4b

regimes1.6s

Accuracy

14% (5.0b remaining)

Error of 14.4b against oracle of 9.4b and baseline of 15.2b

bsearch106.0ms

Steps
ItersRangePoint
3
17388065660229.82
24261170235186.168
23818843675239.758

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
053151
170151
done70151

end0.0ms

sample8.0s

Algorithm
intervals
Results
3.8s39049×body80nan
1.7s12853×body80valid