Details

Time bar (total: 46.1s)

sample341.0ms

Algorithm
intervals
Results
150.0ms1263×body80nan
68.0ms399×body80valid

simplify3.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02235
15435
217435
370735
4448135
done500135

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize52.0ms

Local error

Found 4 expressions with local error:

7.8b
(* (* (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))))
9.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.0b
(pow (/ d h) (/ 1.0 2.0))
12.9b
(pow (/ d l) (/ 1.0 2.0))

rewrite243.0ms

Algorithm
rewrite-expression-head
Rules
205×add-exp-log
107×prod-exp
55×div-exp
45×times-frac
40×add-sqr-sqrt add-cube-cbrt *-un-lft-identity pow-exp
30×add-cbrt-cube
26×unpow-prod-down pow-unpow
16×associate-*r*
14×pow-to-exp
13×cbrt-unprod
10×pow1
5×cbrt-undiv div-inv
4×add-log-exp
3×associate-*r/ associate-*l/
2×distribute-rgt-in sub-neg pow-pow distribute-lft-in associate-*l* pow-prod-down *-commutative sqr-pow
1×frac-times flip3-- flip--
Counts
4 → 176
Calls
4 calls:
109.0ms
(* (* (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))))
99.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
9.0ms
(pow (/ d h) (/ 1.0 2.0))
10.0ms
(pow (/ d l) (/ 1.0 2.0))

series2.3s

Counts
4 → 12
Calls
4 calls:
1.0s
(* (* (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))))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
94.0ms
(pow (/ d h) (/ 1.0 2.0))
80.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify2.3s

Counts
188 → 188
Iterations

Useful iterations: 2 (946.0ms)

IterNodesCost
04404376
110813962
237803606
done50003606

prune1.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.9b

localize79.0ms

Local error

Found 4 expressions with local error:

4.9b
(/ (* M D) (* 2.0 d))
7.8b
(* (* (* (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))))
9.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.9b
(pow (/ d l) (/ 1.0 2.0))

rewrite698.0ms

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×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
20×cbrt-unprod
16×associate-*r*
13×unpow-prod-down pow-unpow
9×pow1 cbrt-undiv
4×div-inv add-log-exp
3×associate-*r/ associate-*l/
2×distribute-rgt-in sub-neg distribute-lft-in 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 → 260
Calls
4 calls:
28.0ms
(/ (* M D) (* 2.0 d))
504.0ms
(* (* (* (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))))
94.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
18.0ms
(pow (/ d l) (/ 1.0 2.0))

series2.2s

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ (* M D) (* 2.0 d))
926.0ms
(* (* (* (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))))
1.2s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
109.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify2.9s

Counts
272 → 272
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
055111028
112659877
247898502
done50018502

prune1.1s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 12.0b

localize77.0ms

Local error

Found 4 expressions with local error:

4.1b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
4.9b
(/ (* M D) (* 2.0 d))
7.8b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
9.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite1.4s

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
32×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
4×pow-prod-down div-inv add-log-exp
3×associate-*r/ associate-*l/
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 1229
Calls
4 calls:
21.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
30.0ms
(/ (* M D) (* 2.0 d))
932.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
69.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series3.2s

Counts
4 → 12
Calls
4 calls:
279.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
45.0ms
(/ (* 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 (/ 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))))
1.5s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.9s

Counts
1241 → 1241
Iterations

Useful iterations: done (1.8s)

IterNodesCost
0149783585
1241369259
done500160976

prune1.6s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 11.4b

localize85.0ms

Local error

Found 4 expressions with local error:

4.3b
(* (* (* (cbrt h) (cbrt h)) (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0))) (/ (cbrt h) l))
4.4b
(* (* (cbrt h) (cbrt h)) (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)))
4.9b
(/ (* M D) (* 2.0 d))
7.8b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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 (* (* (* (cbrt h) (cbrt h)) (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0))) (/ (cbrt h) l))))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
7347×add-exp-log
5500×prod-exp
2652×pow-exp
1701×div-exp
796×pow-to-exp
232×rec-exp 1-exp
95×add-cbrt-cube
70×cbrt-unprod
26×associate-*r*
23×pow1
19×times-frac
18×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
17×cbrt-undiv
12×pow-prod-down
9×cbrt-prod
6×associate-*r/
4×associate-*l/ add-log-exp
3×associate-*l* *-commutative
2×distribute-rgt-in sub-neg distribute-lft-in div-inv
1×frac-times flip3-- frac-2neg clear-num associate-/r* flip-- associate-/l*
Counts
4 → 1282
Calls
4 calls:
303.0ms
(* (* (* (cbrt h) (cbrt h)) (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0))) (/ (cbrt h) l))
90.0ms
(* (* (cbrt h) (cbrt h)) (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)))
16.0ms
(/ (* M D) (* 2.0 d))
870.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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 (* (* (* (cbrt h) (cbrt h)) (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0))) (/ (cbrt h) l))))

series2.9s

Counts
4 → 12
Calls
4 calls:
960.0ms
(* (* (* (cbrt h) (cbrt h)) (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0))) (/ (cbrt h) l))
623.0ms
(* (* (cbrt h) (cbrt h)) (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)))
36.0ms
(/ (* M D) (* 2.0 d))
1.3s
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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 (* (* (* (cbrt h) (cbrt h)) (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0))) (/ (cbrt h) l))))

simplify1.9s

Counts
1294 → 1294
Iterations

Useful iterations: done (1.8s)

IterNodesCost
0148594294
1240279528
done500066071

prune1.2s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 11.4b

regimes2.1s

Accuracy

0% (5.2b remaining)

Error of 15.9b against oracle of 10.7b and baseline of 15.9b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03773
14873
done4873

end0.0ms

sample11.1s

Algorithm
intervals
Results
5.1s37865×body80nan
2.4s12724×body80valid