Details

Time bar (total: 44.0s)

sample544.0ms

Algorithm
intervals
Results
296.0ms1314×body80nan
102.0ms416×body80valid

simplify850.0ms

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: 24.0b

localize35.0ms

Local error

Found 4 expressions with local error:

5.5b
(* (* (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))))
11.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.0b
(pow (/ d l) (/ 1.0 2.0))
12.3b
(pow (/ d h) (/ 1.0 2.0))

rewrite170.0ms

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:
73.0ms
(* (* (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))))
60.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
9.0ms
(pow (/ d l) (/ 1.0 2.0))
15.0ms
(pow (/ d h) (/ 1.0 2.0))

series1.9s

Counts
4 → 12
Calls
4 calls:
824.0ms
(* (* (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))))
943.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
66.0ms
(pow (/ d l) (/ 1.0 2.0))
67.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify635.0ms

Counts
202 → 202
Iterations

Useful iterations: done (627.0ms)

IterNodesCost
04635058
114854743
done50014206

prune1.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.4b

localize110.0ms

Local error

Found 4 expressions with local error:

5.1b
(/ (* M D) (* 2.0 d))
5.5b
(* (* (* (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))))
11.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.0b
(pow (/ d l) (/ 1.0 2.0))

rewrite700.0ms

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×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 → 274
Calls
4 calls:
17.0ms
(/ (* M D) (* 2.0 d))
551.0ms
(* (* (* (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))))
90.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
9.0ms
(pow (/ d l) (/ 1.0 2.0))

series2.0s

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ (* M D) (* 2.0 d))
918.0ms
(* (* (* (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))))
990.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
80.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify933.0ms

Counts
286 → 286
Iterations

Useful iterations: done (915.0ms)

IterNodesCost
057411962
1184911051
done50019396

prune1.4s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 9.6b

localize141.0ms

Local error

Found 4 expressions with local error:

5.1b
(/ (* M D) (* 2.0 d))
5.5b
(* (* (* (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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
5.6b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
12.0b
(pow (/ d l) (/ 1.0 2.0))

rewrite779.0ms

Algorithm
rewrite-expression-head
Rules
1038×add-exp-log
658×prod-exp
261×div-exp
246×pow-exp
84×pow-to-exp
70×add-cbrt-cube
47×cbrt-unprod
22×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
21×cbrt-undiv
20×times-frac
13×unpow-prod-down pow-unpow
9×pow1
8×associate-*r*
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 → 320
Calls
4 calls:
20.0ms
(/ (* M D) (* 2.0 d))
550.0ms
(* (* (* (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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
135.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
17.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.9s

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ (* M D) (* 2.0 d))
923.0ms
(* (* (* (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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
840.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
124.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify1.2s

Counts
332 → 332
Iterations

Useful iterations: done (1.2s)

IterNodesCost
064216693
1218015489
done500111666

prune1.6s

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 9.1b

localize117.0ms

Local error

Found 4 expressions with local error:

3.3b
(pow (/ (cbrt d) l) (/ 1.0 2.0))
5.1b
(/ (* M D) (* 2.0 d))
5.5b
(* (* (* (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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
5.6b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
3361×add-exp-log
2564×prod-exp
1094×pow-exp
647×div-exp
430×pow-to-exp
79×add-cbrt-cube
54×cbrt-unprod
29×times-frac
28×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
22×unpow-prod-down
21×cbrt-undiv
13×pow-unpow
12×pow1
9×cbrt-prod
8×associate-*r*
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 → 709
Calls
4 calls:
21.0ms
(pow (/ (cbrt d) l) (/ 1.0 2.0))
27.0ms
(/ (* M D) (* 2.0 d))
655.0ms
(* (* (* (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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
135.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

series2.4s

Counts
4 → 12
Calls
4 calls:
191.0ms
(pow (/ (cbrt d) l) (/ 1.0 2.0))
40.0ms
(/ (* M D) (* 2.0 d))
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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
771.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

simplify2.8s

Counts
721 → 721
Iterations

Useful iterations: done (2.7s)

IterNodesCost
097551390
1370846379
done500044513

prune2.1s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 8.6b

regimes2.1s

Accuracy

0% (4.8b remaining)

Error of 14.8b against oracle of 10.0b and baseline of 14.8b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03578
14478
done4478

end0.0ms

sample17.4s

Algorithm
intervals
Results
10.1s38250×body80nan
3.6s12752×body80valid