Details

Time bar (total: 47.6s)

sample480.0ms

Algorithm
intervals
Results
287.0ms1301×body80nan
94.0ms427×body80valid

simplify775.0ms

Counts
1 → 1
Iterations
IterNodes
done5001
3710
2174
154
022

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.2b

localize66.0ms

Local error

Found 4 expressions with local error:

5.6b
(* (* (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))))
9.4b
(pow (/ d h) (/ 1.0 2.0))
14.8b
(pow (/ d l) (/ 1.0 2.0))
14.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
205×add-exp-log
107×prod-exp
55×div-exp
45×times-frac
40×add-sqr-sqrt *-un-lft-identity pow-exp add-cube-cbrt
30×add-cbrt-cube
26×pow-unpow unpow-prod-down
16×associate-*r*
14×pow-to-exp
13×cbrt-unprod
10×pow1
5×cbrt-undiv div-inv
4×add-log-exp
3×associate-*l/ associate-*r/
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:
72.0ms
(* (* (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))))
9.0ms
(pow (/ d h) (/ 1.0 2.0))
6.0ms
(pow (/ d l) (/ 1.0 2.0))
60.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.9s

Counts
4 → 12
Calls
4 calls:
821.0ms
(* (* (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))))
87.0ms
(pow (/ d h) (/ 1.0 2.0))
76.0ms
(pow (/ d l) (/ 1.0 2.0))
917.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify896.0ms

Counts
188 → 188
Iterations
IterNodes
done5001
11404
0437

prune1.4s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 11.1b

localize119.0ms

Local error

Found 4 expressions with local error:

5.1b
(/ (* M D) (* 2.0 d))
5.6b
(* (* (* (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))))
14.8b
(pow (/ d l) (/ 1.0 2.0))
14.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite400.0ms

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×times-frac
26×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
20×cbrt-unprod
16×associate-*r*
13×pow-unpow unpow-prod-down
9×pow1 cbrt-undiv
4×div-inv add-log-exp
3×associate-*l/ associate-*r/
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* pow-prod-down *-commutative
1×frac-times clear-num associate-/r* pow-pow frac-2neg flip3-- flip-- associate-/l* sqr-pow
Counts
4 → 292
Calls
4 calls:
13.0ms
(/ (* M D) (* 2.0 d))
292.0ms
(* (* (* (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))))
9.0ms
(pow (/ d l) (/ 1.0 2.0))
55.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.1s

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (* (* (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))))
80.0ms
(pow (/ d l) (/ 1.0 2.0))
878.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify679.0ms

Counts
304 → 304
Iterations
IterNodes
done5001
11953
0606

prune1.3s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 9.7b

localize145.0ms

Local error

Found 4 expressions with local error:

3.4b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
5.1b
(/ (* M D) (* 2.0 d))
5.6b
(* (* (* (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))))
14.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite824.0ms

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
32×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
27×cbrt-unprod
22×unpow-prod-down
16×associate-*r*
13×pow-unpow
12×pow1
9×cbrt-prod cbrt-undiv
4×pow-prod-down div-inv add-log-exp
3×associate-*l/ associate-*r/
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* *-commutative
1×frac-times clear-num associate-/r* pow-pow frac-2neg flip3-- flip-- associate-/l* sqr-pow
Counts
4 → 1525
Calls
4 calls:
8.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
10.0ms
(/ (* M D) (* 2.0 d))
493.0ms
(* (* (* (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))))
42.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.4s

Counts
4 → 12
Calls
4 calls:
234.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
43.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (* (* (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))))
951.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify938.0ms

Counts
1537 → 1537
Iterations
IterNodes
done5001
01798

prune2.3s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 7.3b

localize215.0ms

Local error

Found 4 expressions with local error:

5.1b
(* (/ M 2.0) (/ D d))
5.5b
(* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (/ 1 (* (cbrt l) (cbrt l))))
5.6b
(* (* (* (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 2.0) (/ D d)) 2.0)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))))
9.1b
(* (* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
9883×add-exp-log
7419×prod-exp
3614×pow-exp
2455×div-exp
1004×pow-to-exp
682×rec-exp 1-exp
146×add-cbrt-cube
91×cbrt-unprod
46×add-sqr-sqrt
45×associate-*r*
43×times-frac
41×cbrt-undiv
34×*-un-lft-identity add-cube-cbrt
18×pow1
16×associate-*l*
14×associate-*l/
9×cbrt-prod
8×frac-times pow-prod-down
7×associate-*r/
4×*-commutative div-inv add-log-exp unswap-sqr
3×un-div-inv
2×distribute-rgt-in sub-neg distribute-lft-in
1×flip3-- flip--
Counts
4 → 1854
Calls
4 calls:
18.0ms
(* (/ M 2.0) (/ D d))
59.0ms
(* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (/ 1 (* (cbrt l) (cbrt l))))
530.0ms
(* (* (* (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 2.0) (/ D d)) 2.0)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))))
269.0ms
(* (* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))

series3.2s

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (/ M 2.0) (/ D d))
701.0ms
(* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (/ 1 (* (cbrt l) (cbrt l))))
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 2.0) (/ D d)) 2.0)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))))
1.1s
(* (* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))

simplify1.2s

Counts
1866 → 1866
Iterations
IterNodes
done5000
02078

prune3.3s

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 6.8b

regimes3.1s

Accuracy

10.4% (7.2b remaining)

Error of 15.4b against oracle of 8.2b and baseline of 16.2b

bsearch1.3s

Steps
ItersRangePoint
8
5.533435193588874e+20
3.739078058005972e+23
3.3446969069902763e+21
7
-3.7848911868249716e+80
-1.8966182186078663e+78
-7.890146375208439e+78
9
-5.353626350749262e+250
-3.627888600219891e+242
-2.0998200135116775e+249

simplify16.0ms

Iterations
IterNodes
done97
197
073

end0.0ms

sample17.2s

Algorithm
intervals
Results
10.4s38741×body80nan
4.3s12885×body80valid