Details

Time bar (total: 49.3s)

sample471.0ms

Algorithm
intervals
Results
248.0ms1195×body80nan
92.0ms419×body80valid

simplify847.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02235
15435
217435
372035
done500035

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize33.0ms

Local error

Found 4 expressions with local error:

8.0b
(* (* (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))))
10.7b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.4b
(pow (/ d l) (/ 1.0 2.0))
12.5b
(pow (/ d h) (/ 1.0 2.0))

rewrite198.0ms

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:
75.0ms
(* (* (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))))
95.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
8.0ms
(pow (/ d l) (/ 1.0 2.0))
8.0ms
(pow (/ d h) (/ 1.0 2.0))

series2.3s

Counts
4 → 12
Calls
4 calls:
841.0ms
(* (* (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))))
1.3s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
71.0ms
(pow (/ d l) (/ 1.0 2.0))
70.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify655.0ms

Counts
202 → 202
Iterations

Useful iterations: done (645.0ms)

IterNodesCost
04635058
114854743
done50014206

prune1.1s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 12.7b

localize77.0ms

Local error

Found 4 expressions with local error:

6.3b
(/ (* M D) (* 2.0 d))
8.0b
(* (* (* (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))))
10.7b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.4b
(pow (/ d l) (/ 1.0 2.0))

rewrite546.0ms

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:
13.0ms
(/ (* M D) (* 2.0 d))
434.0ms
(* (* (* (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))))
65.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
8.0ms
(pow (/ d l) (/ 1.0 2.0))

series2.0s

Counts
4 → 12
Calls
4 calls:
61.0ms
(/ (* M D) (* 2.0 d))
960.0ms
(* (* (* (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))))
919.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
104.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify922.0ms

Counts
286 → 286
Iterations

Useful iterations: done (902.0ms)

IterNodesCost
057411962
1184911051
done50019396

prune1.3s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 11.2b

localize118.0ms

Local error

Found 4 expressions with local error:

2.4b
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
6.3b
(/ (* M D) (* 2.0 d))
8.0b
(* (* (* (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))))
10.7b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite1.3s

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
22×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
20×times-frac
16×associate-*r*
13×pow-unpow
12×pow1
9×cbrt-undiv
6×prod-diff
5×distribute-rgt-in unpow-prod-down 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 → 997
Calls
4 calls:
35.0ms
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
25.0ms
(/ (* M D) (* 2.0 d))
891.0ms
(* (* (* (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))))
74.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.4s

Counts
4 → 12
Calls
4 calls:
169.0ms
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
53.0ms
(/ (* M D) (* 2.0 d))
990.0ms
(* (* (* (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))))
1.2s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify2.3s

Counts
1009 → 1009
Iterations

Useful iterations: done (2.2s)

IterNodesCost
0120572885
1490564016
done500062702

prune2.1s

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 9.7b

localize177.0ms

Local error

Found 4 expressions with local error:

3.7b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ 1 (* (cbrt l) (cbrt l))))
6.3b
(/ (* M D) (* 2.0 d))
6.6b
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))
8.0b
(* (* (* (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)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
7699×add-exp-log
5363×prod-exp
2182×pow-exp
1939×div-exp
680×pow-to-exp
146×add-cbrt-cube
91×cbrt-unprod
90×rec-exp 1-exp
41×cbrt-undiv
32×associate-*r*
22×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
16×pow1
13×associate-*l/
9×cbrt-prod
7×frac-times pow-prod-down
6×associate-*r/ prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l* un-div-inv *-commutative div-inv
2×sub-neg
1×flip3-- frac-2neg clear-num associate-/r* flip-- associate-/l*
Counts
4 → 1311
Calls
4 calls:
100.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ 1 (* (cbrt l) (cbrt l))))
27.0ms
(/ (* M D) (* 2.0 d))
440.0ms
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))
746.0ms
(* (* (* (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)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))))

series3.2s

Counts
4 → 12
Calls
4 calls:
815.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ 1 (* (cbrt l) (cbrt l))))
45.0ms
(/ (* M D) (* 2.0 d))
1.2s
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))
1.1s
(* (* (* (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)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))))

simplify1.2s

Counts
1323 → 1323
Iterations

Useful iterations: done (1.0s)

IterNodesCost
0150692107
done500181672

prune2.7s

Pruning

36 alts after pruning (36 fresh and 0 done)

Merged error: 9.3b

regimes3.0s

Accuracy

0% (6.9b remaining)

Error of 15.9b against oracle of 9.0b and baseline of 15.9b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03780
14780
done4780

end0.0ms

sample18.8s

Algorithm
intervals
Results
10.6s38799×body80nan
4.3s12928×body80valid