Details

Time bar (total: 26.1s)

sample232.0ms

Algorithm
intervals
Results
115.0ms1127×body80nan
56.0ms418×body80valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02235
15435
217035
365135
4408935
done500035

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.7b

localize30.0ms

Local error

Found 4 expressions with local error:

8.9b
(* (* (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))))
9.8b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.8b
(pow (/ d h) (/ 1.0 2.0))
13.5b
(pow (/ d l) (/ 1.0 2.0))

rewrite74.0ms

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:
35.0ms
(* (* (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))))
22.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
4.0ms
(pow (/ d h) (/ 1.0 2.0))
4.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
628.0ms
(* (* (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))))
725.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
64.0ms
(pow (/ d h) (/ 1.0 2.0))
65.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify1.5s

Counts
188 → 188
Iterations

Useful iterations: 2 (560.0ms)

IterNodesCost
04404376
112283962
243433606
done50003606

prune693.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.8b

localize40.0ms

Local error

Found 4 expressions with local error:

4.5b
(/ (* M D) (* 2.0 d))
8.9b
(* (* (pow (/ d 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))))
9.8b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.8b
(pow (/ d h) (/ 1.0 2.0))

rewrite181.0ms

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 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 → 292
Calls
4 calls:
4.0ms
(/ (* M D) (* 2.0 d))
125.0ms
(* (* (pow (/ d 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))))
22.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
4.0ms
(pow (/ d h) (/ 1.0 2.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
975.0ms
(* (* (pow (/ d 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))))
722.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
62.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify508.0ms

Counts
304 → 304
Iterations

Useful iterations: done (496.0ms)

IterNodesCost
061011899
1184710522
done50009770

prune702.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 11.8b

localize51.0ms

Local error

Found 4 expressions with local error:

3.8b
(pow (/ (cbrt d) h) (/ 1.0 2.0))
4.5b
(/ (* M D) (* 2.0 d))
8.9b
(* (* (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) 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))))
9.8b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite358.0ms

Algorithm
rewrite-expression-head
Rules
3529×add-exp-log
2893×prod-exp
1396×pow-exp
623×div-exp
522×pow-to-exp
136×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 → 785
Calls
4 calls:
6.0ms
(pow (/ (cbrt d) h) (/ 1.0 2.0))
4.0ms
(/ (* M D) (* 2.0 d))
226.0ms
(* (* (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) 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))))
22.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.8s

Counts
4 → 12
Calls
4 calls:
158.0ms
(pow (/ (cbrt d) h) (/ 1.0 2.0))
34.0ms
(/ (* M D) (* 2.0 d))
704.0ms
(* (* (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) 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))))
910.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify859.0ms

Counts
797 → 797
Iterations

Useful iterations: done (814.0ms)

IterNodesCost
0101045973
1338737956
done500037952

prune1.0s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 10.8b

localize56.0ms

Local error

Found 4 expressions with local error:

3.8b
(pow (/ (cbrt d) h) (/ 1.0 2.0))
4.5b
(/ (* M D) (* 2.0 d))
5.6b
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))
8.9b
(* (* (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) 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)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))))

rewrite449.0ms

Algorithm
rewrite-expression-head
Rules
3769×add-exp-log
3059×prod-exp
1416×pow-exp
669×div-exp
526×pow-to-exp
136×rec-exp 1-exp
80×add-cbrt-cube
57×cbrt-unprod
46×times-frac
38×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
25×associate-*r*
22×unpow-prod-down
19×pow1
18×cbrt-prod
15×cbrt-undiv
13×pow-unpow
9×pow-prod-down
5×associate-*l/
4×div-inv add-log-exp
3×associate-*r/
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 → 836
Calls
4 calls:
6.0ms
(pow (/ (cbrt d) h) (/ 1.0 2.0))
4.0ms
(/ (* M D) (* 2.0 d))
101.0ms
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))
228.0ms
(* (* (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) 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)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))))

series1.7s

Counts
4 → 12
Calls
4 calls:
166.0ms
(pow (/ (cbrt d) h) (/ 1.0 2.0))
27.0ms
(/ (* M D) (* 2.0 d))
783.0ms
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))
760.0ms
(* (* (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) 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)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))))

simplify950.0ms

Counts
848 → 848
Iterations

Useful iterations: 1 (628.0ms)

IterNodesCost
0111052936
1378044610
done500044610

prune1.1s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 10.5b

regimes1.4s

Accuracy

0% (5.5b remaining)

Error of 15.5b against oracle of 10.0b and baseline of 15.5b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03979
15179
done5179

end0.0ms

sample7.3s

Algorithm
intervals
Results
3.9s38641×body80nan
1.7s12773×body80valid