Details

Time bar (total: 48.3s)

sample666.0ms

Algorithm
intervals
Results
383.0ms1295×body80nan
123.0ms441×body80valid

simplify946.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
3720
2174
154
022

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.3b

localize80.0ms

Local error

Found 4 expressions with local error:

6.9b
(* (* (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))))
10.3b
(pow (/ d h) (/ 1.0 2.0))
12.2b
(pow (/ d l) (/ 1.0 2.0))
14.2b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite236.0ms

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:
99.0ms
(* (* (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))))
13.0ms
(pow (/ d h) (/ 1.0 2.0))
23.0ms
(pow (/ d l) (/ 1.0 2.0))
85.0ms
(* (* (/ 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))))
91.0ms
(pow (/ d h) (/ 1.0 2.0))
113.0ms
(pow (/ d l) (/ 1.0 2.0))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify640.0ms

Counts
202 → 202
Iterations
IterNodes
done5001
11468
0460

prune1.6s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 10.6b

localize106.0ms

Local error

Found 4 expressions with local error:

3.9b
(/ (* M D) (* 2.0 d))
6.9b
(* (* (* (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))))
12.2b
(pow (/ d l) (/ 1.0 2.0))
14.2b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite445.0ms

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:
16.0ms
(/ (* M D) (* 2.0 d))
342.0ms
(* (* (* (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))))
6.0ms
(pow (/ d l) (/ 1.0 2.0))
55.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.6s

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ (* 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))))
116.0ms
(pow (/ d l) (/ 1.0 2.0))
1.2s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.2s

Counts
318 → 318
Iterations
IterNodes
done5001
12038
0629

prune1.9s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 8.8b

localize142.0ms

Local error

Found 4 expressions with local error:

2.7b
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
3.9b
(/ (* M D) (* 2.0 d))
6.9b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
14.2b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
6975×add-exp-log
5249×prod-exp
2617×pow-exp
1629×div-exp
789×pow-to-exp
232×rec-exp 1-exp
55×add-cbrt-cube
27×cbrt-unprod
22×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
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-*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 → 1229
Calls
4 calls:
29.0ms
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
11.0ms
(/ (* M D) (* 2.0 d))
679.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
85.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.7s

Counts
4 → 12
Calls
4 calls:
169.0ms
(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
57.0ms
(/ (* 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 (/ (* (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))))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify938.0ms

Counts
1241 → 1241
Iterations
IterNodes
done5000
01455

prune2.5s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 6.8b

localize150.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (* (cbrt h) (cbrt h))) (* (cbrt l) (cbrt l)))
5.3b
(* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (* (cbrt h) (cbrt h)))
5.7b
(* (/ M 2.0) (/ D d))
6.9b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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 2.0) (/ D d)) 2.0)) (* (cbrt h) (cbrt h))) (* (cbrt l) (cbrt l))) (/ (cbrt h) (cbrt l)))))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
7347×add-exp-log
5469×prod-exp
2652×pow-exp
1732×div-exp
796×pow-to-exp
232×rec-exp 1-exp
88×add-cbrt-cube
63×cbrt-unprod
33×add-sqr-sqrt
24×cbrt-undiv
23×times-frac
21×*-un-lft-identity add-cube-cbrt
17×associate-*r*
16×pow1
15×associate-*l*
7×pow-prod-down
6×prod-diff
5×distribute-rgt-in distribute-lft-in associate-*l/
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×associate-*r/ *-commutative div-inv
2×sub-neg
1×frac-times clear-num associate-/r* frac-2neg flip3-- flip-- associate-/l* associate-/l/
Counts
4 → 1302
Calls
4 calls:
103.0ms
(/ (* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (* (cbrt h) (cbrt h))) (* (cbrt l) (cbrt l)))
69.0ms
(* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (* (cbrt h) (cbrt h)))
18.0ms
(* (/ M 2.0) (/ D d))
616.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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 2.0) (/ D d)) 2.0)) (* (cbrt h) (cbrt h))) (* (cbrt l) (cbrt l))) (/ (cbrt h) (cbrt l)))))

series3.0s

Counts
4 → 12
Calls
4 calls:
797.0ms
(/ (* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (* (cbrt h) (cbrt h))) (* (cbrt l) (cbrt l)))
753.0ms
(* (* (/ 1.0 2.0) (pow (* (/ M 2.0) (/ D d)) 2.0)) (* (cbrt h) (cbrt h)))
36.0ms
(* (/ M 2.0) (/ D d))
1.4s
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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 2.0) (/ D d)) 2.0)) (* (cbrt h) (cbrt h))) (* (cbrt l) (cbrt l))) (/ (cbrt h) (cbrt l)))))

simplify1.3s

Counts
1314 → 1314
Iterations
IterNodes
done5001
01529

prune2.6s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 6.6b

regimes2.8s

Accuracy

0% (6.3b remaining)

Error of 14.6b against oracle of 8.3b and baseline of 14.6b

bsearch0.0ms

simplify10.0ms

Iterations
IterNodes
done48
148
038

end0.0ms

sample17.4s

Algorithm
intervals
Results
9.8s37752×body80nan
4.0s12750×body80valid