Details

Time bar (total: 23.9s)

sample275.0ms

Algorithm
intervals
Results
132.0ms1244×body80nan
57.0ms415×body80valid

simplify195.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05417
117417
271017
3494017
4500217
done500217

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.5b

localize30.0ms

Local error

Found 4 expressions with local error:

6.7b
(* (* (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))))
10.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
10.9b
(pow (/ d l) (/ 1.0 2.0))
12.8b
(pow (/ d h) (/ 1.0 2.0))

rewrite138.0ms

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:
60.0ms
(* (* (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))))
49.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
10.0ms
(pow (/ d l) (/ 1.0 2.0))
8.0ms
(pow (/ d h) (/ 1.0 2.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
673.0ms
(* (* (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))))
758.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
68.0ms
(pow (/ d l) (/ 1.0 2.0))
63.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify41.0ms

Counts
188 → 188
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
012282042
150011847
done50011847

prune679.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 10.6b

localize43.0ms

Local error

Found 4 expressions with local error:

3.9b
(/ (* M D) (* 2.0 d))
6.7b
(* (* (* (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))))
10.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
10.9b
(pow (/ d l) (/ 1.0 2.0))

rewrite404.0ms

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:
13.0ms
(/ (* M D) (* 2.0 d))
311.0ms
(* (* (* (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))))
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))

series1.6s

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (* M D) (* 2.0 d))
724.0ms
(* (* (* (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))))
757.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
71.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify73.0ms

Counts
272 → 272
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
016425552
150025211
done50025211

prune727.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 9.6b

localize56.0ms

Local error

Found 4 expressions with local error:

2.3b
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0))
3.9b
(/ (* M D) (* 2.0 d))
6.7b
(* (* (* (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)) (* (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))))
10.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite772.0ms

Algorithm
rewrite-expression-head
Rules
5947×add-exp-log
4317×prod-exp
1997×pow-exp
1387×div-exp
643×pow-to-exp
55×add-cbrt-cube
27×cbrt-unprod
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
16×associate-*r*
13×pow-unpow
12×pow1
9×cbrt-undiv
5×unpow-prod-down
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 → 983
Calls
4 calls:
17.0ms
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0))
13.0ms
(/ (* M D) (* 2.0 d))
524.0ms
(* (* (* (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)) (* (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:
124.0ms
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0))
42.0ms
(/ (* M D) (* 2.0 d))
676.0ms
(* (* (* (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)) (* (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))))
1.0s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify283.0ms

Counts
995 → 995
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
0408338233
1500138031
done500138031

prune909.0ms

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 8.6b

localize67.0ms

Local error

Found 4 expressions with local error:

3.7b
(/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l)))
3.9b
(/ (* M D) (* 2.0 d))
6.7b
(* (* (* (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)) (* (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)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
7.9b
(* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))

rewrite834.0ms

Algorithm
rewrite-expression-head
Rules
6319×add-exp-log
4478×prod-exp
2032×pow-exp
1549×div-exp
650×pow-to-exp
95×add-cbrt-cube
52×cbrt-unprod
35×cbrt-undiv
27×add-sqr-sqrt
25×associate-*r*
23×times-frac
19×add-cube-cbrt *-un-lft-identity
11×pow1
10×cbrt-prod
6×associate-*l*
4×pow-prod-down div-inv add-log-exp
3×associate-*r/ unswap-sqr
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in associate-*l/ clear-num associate-/r* *-commutative associate-/l*
1×frac-times flip3-- flip-- associate-/l/
Counts
4 → 1056
Calls
4 calls:
25.0ms
(/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l)))
12.0ms
(/ (* M D) (* 2.0 d))
536.0ms
(* (* (* (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)) (* (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)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
79.0ms
(* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))

series2.1s

Counts
4 → 12
Calls
4 calls:
535.0ms
(/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l)))
29.0ms
(/ (* M D) (* 2.0 d))
726.0ms
(* (* (* (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)) (* (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)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
816.0ms
(* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))

simplify338.0ms

Counts
1068 → 1068
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0441644208
1500343802
done500343802

prune962.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 8.6b

regimes1.5s

Accuracy

-19.9% (5.2b remaining)

Error of 15.4b against oracle of 10.2b and baseline of 14.6b

bsearch416.0ms

Steps
ItersRangePoint
6
5.139836535214475e+62
2.688717906628484e+63
1.2014904442691352e+63
8
3.549515307569088e-29
9.514677658063659e-27
9.412867683932309e-27

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0105119
1105119
done105119

end0.0ms

sample8.1s

Algorithm
intervals
Results
3.9s38926×body80nan
1.8s12884×body80valid