Details

Time bar (total: 49.1s)

sample922.0ms

Algorithm
intervals
Results
672.0ms1130×body80nan
106.0ms382×body80valid

simplify936.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
3720
2174
154
022

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.8b

localize73.0ms

Local error

Found 4 expressions with local error:

6.0b
(* (* (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))))
9.2b
(pow (/ d h) (/ 1.0 2.0))
12.0b
(pow (/ d l) (/ 1.0 2.0))
12.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite214.0ms

Algorithm
rewrite-expression-head
Rules
205×add-exp-log
107×prod-exp
55×div-exp
45×times-frac
42×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
40×pow-exp
30×add-cbrt-cube
26×pow-unpow unpow-prod-down
16×associate-*r*
14×pow-to-exp
13×cbrt-unprod
10×pow1
6×prod-diff
5×distribute-rgt-in cbrt-undiv distribute-lft-in div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l/ associate-*r/
2×sub-neg pow-pow associate-*l* pow-prod-down *-commutative sqr-pow
1×frac-times flip3-- flip--
Counts
4 → 190
Calls
4 calls:
89.0ms
(* (* (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))))
12.0ms
(pow (/ d h) (/ 1.0 2.0))
13.0ms
(pow (/ d l) (/ 1.0 2.0))
93.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.2s

Counts
4 → 12
Calls
4 calls:
998.0ms
(* (* (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))))
75.0ms
(pow (/ d h) (/ 1.0 2.0))
104.0ms
(pow (/ d l) (/ 1.0 2.0))
1.0s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify761.0ms

Counts
202 → 202
Iterations
IterNodes
done5001
11468
0460

prune1.8s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 11.5b

localize130.0ms

Local error

Found 4 expressions with local error:

3.5b
(/ (* M D) (* 2.0 d))
6.0b
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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))))
12.0b
(pow (/ d l) (/ 1.0 2.0))
12.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite456.0ms

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 *-un-lft-identity times-frac add-cube-cbrt
20×cbrt-unprod
16×associate-*r*
13×pow-unpow unpow-prod-down
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-*l/ associate-*r/
2×sub-neg 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 → 274
Calls
4 calls:
10.0ms
(/ (* M D) (* 2.0 d))
336.0ms
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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))))
13.0ms
(pow (/ d l) (/ 1.0 2.0))
79.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.1s

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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
(pow (/ d l) (/ 1.0 2.0))
983.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify999.0ms

Counts
286 → 286
Iterations
IterNodes
done5000
11833
0567

prune1.8s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 11.0b

localize126.0ms

Local error

Found 4 expressions with local error:

3.5b
(/ (* M D) (* 2.0 d))
3.5b
(pow (/ (cbrt d) l) (/ 1.0 2.0))
6.0b
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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)) (/ h l))))
12.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite712.0ms

Algorithm
rewrite-expression-head
Rules
3061×add-exp-log
2393×prod-exp
1064×pow-exp
557×div-exp
424×pow-to-exp
55×add-cbrt-cube
37×times-frac
34×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
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-*l/ associate-*r/
2×sub-neg associate-*l* *-commutative
1×frac-times clear-num associate-/r* pow-pow frac-2neg flip3-- flip-- associate-/l* sqr-pow
Counts
4 → 663
Calls
4 calls:
10.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(pow (/ (cbrt d) l) (/ 1.0 2.0))
519.0ms
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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)) (/ h l))))
80.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.8s

Counts
4 → 12
Calls
4 calls:
33.0ms
(/ (* M D) (* 2.0 d))
220.0ms
(pow (/ (cbrt d) l) (/ 1.0 2.0))
1.4s
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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)) (/ h l))))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.9s

Counts
675 → 675
Iterations
IterNodes
done5000
13384
0905

prune2.4s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 9.5b

localize126.0ms

Local error

Found 4 expressions with local error:

6.5b
(/ (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ 1.0 2.0)) h) l)
6.5b
(/ (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ 1.0 2.0)) h) l)
18.1b
(sqrt (/ (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ 1.0 2.0)) h) l))
18.1b
(sqrt (/ (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ 1.0 2.0)) h) l))

rewrite209.0ms

Algorithm
rewrite-expression-head
Rules
168×add-exp-log
74×prod-exp
62×div-exp
32×add-cbrt-cube
20×pow-exp
14×add-sqr-sqrt sqrt-prod
12×*-un-lft-identity times-frac add-cube-cbrt
10×cbrt-undiv cbrt-unprod
6×pow1 associate-/r*
4×expm1-log1p-u pow-to-exp log1p-expm1-u div-inv add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 sqrt-div associate-*l/ associate-*r/ associate-/l* associate-/l/
Counts
4 → 120
Calls
4 calls:
73.0ms
(/ (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ 1.0 2.0)) h) l)
64.0ms
(/ (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ 1.0 2.0)) h) l)
30.0ms
(sqrt (/ (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ 1.0 2.0)) h) l))
32.0ms
(sqrt (/ (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ 1.0 2.0)) h) l))

series4.3s

Counts
4 → 12
Calls
4 calls:
1.2s
(/ (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ 1.0 2.0)) h) l)
1.1s
(/ (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ 1.0 2.0)) h) l)
1.0s
(sqrt (/ (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ 1.0 2.0)) h) l))
971.0ms
(sqrt (/ (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ 1.0 2.0)) h) l))

simplify1.1s

Counts
132 → 132
Iterations
IterNodes
done5002
22306
1525
0194

prune1.5s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 9.5b

regimes2.6s

Accuracy

-4.9% (7.0b remaining)

Error of 16.8b against oracle of 9.8b and baseline of 16.4b

bsearch814.0ms

Steps
ItersRangePoint
8
2.278240458059081e-110
7.710292087168796e-106
6.910995874866272e-109

simplify13.0ms

Iterations
IterNodes
done69
369
267
165
052

end0.0ms

sample18.1s

Algorithm
intervals
Results
10.6s38852×body80nan
3.5s12890×body80valid