Details

Time bar (total: 1.0m)

sample598.0ms

Algorithm
intervals
Results
261.0ms1301×body80nan
133.0ms427×body80valid

simplify1.9s

Counts
1 → 1
Iterations
IterNodes
done5000
3720
2174
154
022

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize70.0ms

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))

rewrite192.0ms

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:
85.0ms
(* (* (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))))
10.0ms
(pow (/ d h) (/ 1.0 2.0))
7.0ms
(pow (/ d l) (/ 1.0 2.0))
75.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.3s

Counts
4 → 12
Calls
4 calls:
1.0s
(* (* (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))))
124.0ms
(pow (/ d h) (/ 1.0 2.0))
120.0ms
(pow (/ d l) (/ 1.0 2.0))
1.0s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.4s

Counts
202 → 202
Iterations
IterNodes
done5001
11468
0460

prune2.0s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 10.9b

localize165.0ms

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))

rewrite538.0ms

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×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 → 306
Calls
4 calls:
11.0ms
(/ (* M D) (* 2.0 d))
405.0ms
(* (* (* (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))))
7.0ms
(pow (/ d l) (/ 1.0 2.0))
80.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.5s

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ (* M D) (* 2.0 d))
1.3s
(* (* (* (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))))
96.0ms
(pow (/ d l) (/ 1.0 2.0))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify2.4s

Counts
318 → 318
Iterations
IterNodes
done5001
12038
0629

prune2.1s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 9.4b

localize193.0ms

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))

rewrite1.5s

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
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 → 1539
Calls
4 calls:
9.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
11.0ms
(/ (* 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))))
75.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.6s

Counts
4 → 12
Calls
4 calls:
263.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
36.0ms
(/ (* M D) (* 2.0 d))
1.2s
(* (* (* (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))))
1.0s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify4.0s

Counts
1551 → 1551
Iterations
IterNodes
done5001
01821

prune2.9s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 7.3b

localize278.0ms

Local error

Found 4 expressions with local error:

3.4b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h)))
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)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))))
8.3b
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
8503×add-exp-log
6624×prod-exp
3464×pow-exp
1975×div-exp
974×pow-to-exp
592×rec-exp 1-exp
95×add-cbrt-cube
70×cbrt-unprod
26×associate-*r*
23×pow1
20×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
19×times-frac
17×cbrt-undiv
12×pow-prod-down
9×cbrt-prod
7×associate-*l/
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l* associate-*r/ *-commutative
2×sub-neg div-inv
1×frac-times clear-num associate-/r* frac-2neg flip3-- flip-- associate-/l*
Counts
4 → 1592
Calls
4 calls:
86.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h)))
11.0ms
(/ (* M D) (* 2.0 d))
641.0ms
(* (* (* (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)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))))
303.0ms
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))

series3.3s

Counts
4 → 12
Calls
4 calls:
684.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h)))
39.0ms
(/ (* M D) (* 2.0 d))
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 D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))))
1.1s
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))

simplify4.6s

Counts
1604 → 1604
Iterations
IterNodes
done5000
01810

prune2.7s

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 6.8b

regimes3.6s

Accuracy

0% (7.4b remaining)

Error of 15.5b against oracle of 8.1b and baseline of 15.5b

bsearch0.0ms

simplify11.0ms

Iterations
IterNodes
done49
149
037

end0.0ms

sample18.4s

Algorithm
intervals
Results
10.7s38741×body80nan
3.4s12885×body80valid