Details

Time bar (total: 53.3s)

sample500.0ms

Algorithm
intervals
Results
274.0ms1212×body80nan
88.0ms395×body80valid

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02235
15435
217435
371735
4458035
done500035

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.5b

localize53.0ms

Local error

Found 4 expressions with local error:

6.2b
(/ (* M D) (* 2.0 d))
10.4b
(pow (/ d l) (/ 1.0 2.0))
11.1b
(pow (/ d h) (/ 1.0 2.0))
12.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite133.0ms

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:
16.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(pow (/ d l) (/ 1.0 2.0))
13.0ms
(pow (/ d h) (/ 1.0 2.0))
80.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.2s

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ (* M D) (* 2.0 d))
101.0ms
(pow (/ d l) (/ 1.0 2.0))
92.0ms
(pow (/ d h) (/ 1.0 2.0))
985.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.9s

Counts
179 → 179
Iterations

Useful iterations: 2 (753.0ms)

IterNodesCost
03922931
19532662
234672380
done50002380

prune922.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 11.2b

localize65.0ms

Local error

Found 4 expressions with local error:

4.6b
(* (* (* (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))))
6.2b
(/ (* M D) (* 2.0 d))
10.4b
(pow (/ d l) (/ 1.0 2.0))
12.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite563.0ms

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:
421.0ms
(* (* (* (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))))
23.0ms
(/ (* M D) (* 2.0 d))
15.0ms
(pow (/ d l) (/ 1.0 2.0))
75.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.5s

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))))
45.0ms
(/ (* M D) (* 2.0 d))
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))

simplify1.2s

Counts
318 → 318
Iterations

Useful iterations: done (1.2s)

IterNodesCost
063012762
1141111384
done500110169

prune1.3s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 8.9b

localize98.0ms

Local error

Found 4 expressions with local error:

2.4b
(pow (/ d (cbrt h)) (/ 1.0 2.0))
4.6b
(* (* (* (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))))
6.2b
(/ (* M D) (* 2.0 d))
12.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite1.2s

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:
23.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
685.0ms
(* (* (* (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))))
23.0ms
(/ (* M D) (* 2.0 d))
74.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.7s

Counts
4 → 12
Calls
4 calls:
240.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
1.4s
(* (* (* (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))))
41.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify2.6s

Counts
1551 → 1551
Iterations

Useful iterations: done (2.5s)

IterNodesCost
0182298103
1279779686
done500073388

prune1.8s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 8.5b

localize83.0ms

Local error

Found 4 expressions with local error:

4.6b
(* (* (* (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))))
6.1b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.2b
(/ (* M D) (* 2.0 d))
7.8b
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))

rewrite1.6s

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:
848.0ms
(* (* (* (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))))
55.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
13.0ms
(/ (* M D) (* 2.0 d))
245.0ms
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))

series3.8s

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 (/ 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))))
1.2s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
42.0ms
(/ (* M D) (* 2.0 d))
1.3s
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))

simplify2.3s

Counts
1574 → 1574
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01776102071
1265980395
done500173971

prune1.3s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 8.3b

regimes1.9s

Accuracy

-13.1% (7.9b remaining)

Error of 18.2b against oracle of 10.3b and baseline of 17.3b

bsearch2.3s

Steps
ItersRangePoint
9
1.282747705829506e+283
2.0666300332448816e+291
5.320837894328123e+283
7
3.0776510774548433e+215
2.575279917848011e+217
2.520281039428513e+217
7
6.18366793787593e-218
7.065103514836415e-216
1.4473282588936097e-216
8
-2.85483397411846e-212
-8.110272520166952e-215
-8.719035499619317e-213

simplify23.0ms

Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
086295
1111295
done111295

end0.0ms

sample17.9s

Algorithm
intervals
Results
9.4s37587×body80nan
4.6s12709×body80valid