Details

Time bar (total: 1.4m)

sample553.0ms

Algorithm
intervals
Results
317.0ms1362×body80nan
111.0ms430×body80valid

simplify3.6s

Counts
1 → 1
Iterations
IterNodes
done5000
43841
3645
2170
154
022

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize56.0ms

Local error

Found 4 expressions with local error:

9.2b
(* (* (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))))
9.5b
(pow (/ d h) (/ 1.0 2.0))
10.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.0b
(pow (/ d l) (/ 1.0 2.0))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
205×add-exp-log
107×prod-exp
55×div-exp
45×times-frac
40×add-sqr-sqrt *-un-lft-identity pow-exp add-cube-cbrt
30×add-cbrt-cube
26×pow-unpow unpow-prod-down
16×associate-*r*
14×pow-to-exp
13×cbrt-unprod
10×pow1
5×cbrt-undiv div-inv
4×add-log-exp
3×associate-*l/ associate-*r/
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:
73.0ms
(* (* (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))))
14.0ms
(pow (/ d h) (/ 1.0 2.0))
66.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
7.0ms
(pow (/ d l) (/ 1.0 2.0))

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))))
101.0ms
(pow (/ d h) (/ 1.0 2.0))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
86.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify3.0s

Counts
188 → 188
Iterations
IterNodes
done5001
24318
11322
0437

prune1.8s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 13.0b

localize159.0ms

Local error

Found 4 expressions with local error:

4.8b
(/ (* M D) (* 2.0 d))
9.2b
(* (* (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))))
9.5b
(pow (/ d h) (/ 1.0 2.0))
10.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite440.0ms

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 *-un-lft-identity add-cube-cbrt
20×cbrt-unprod
16×associate-*r*
13×pow-unpow unpow-prod-down
9×pow1 cbrt-undiv
4×div-inv add-log-exp
3×associate-*l/ associate-*r/
2×distribute-rgt-in sub-neg distribute-lft-in 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 → 292
Calls
4 calls:
12.0ms
(/ (* M D) (* 2.0 d))
292.0ms
(* (* (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))))
13.0ms
(pow (/ d h) (/ 1.0 2.0))
76.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.6s

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ (* M D) (* 2.0 d))
1.4s
(* (* (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))))
89.0ms
(pow (/ d h) (/ 1.0 2.0))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify2.2s

Counts
304 → 304
Iterations
IterNodes
done5000
11686
0608

prune1.7s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 12.0b

localize176.0ms

Local error

Found 4 expressions with local error:

2.9b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
4.8b
(/ (* M D) (* 2.0 d))
9.2b
(* (* (* (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))))
10.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite1.3s

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
32×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
4×pow-prod-down div-inv add-log-exp
3×associate-*l/ associate-*r/
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* *-commutative
1×frac-times clear-num associate-/r* pow-pow frac-2neg flip3-- flip-- associate-/l* sqr-pow
Counts
4 → 1525
Calls
4 calls:
18.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
20.0ms
(/ (* M D) (* 2.0 d))
504.0ms
(* (* (* (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)) (/ h l))))
68.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.6s

Counts
4 → 12
Calls
4 calls:
255.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
37.0ms
(/ (* 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 (/ 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))))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify14.0s

Counts
1537 → 1537
Iterations
IterNodes
done5000
01798

prune3.0s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 10.8b

localize220.0ms

Local error

Found 4 expressions with local error:

4.8b
(/ (* M D) (* 2.0 d))
6.0b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.9b
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))
9.2b
(* (* (* (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) (/ 1 l))))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
8382×add-exp-log
6544×prod-exp
3454×pow-exp
1961×div-exp
972×pow-to-exp
608×rec-exp 1-exp
75×add-cbrt-cube
40×cbrt-unprod
19×associate-*r*
16×pow1
13×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
11×cbrt-undiv
10×times-frac
7×pow-prod-down associate-*l/
4×add-log-exp
3×associate-*l* associate-*r/ *-commutative
2×distribute-rgt-in sub-neg distribute-lft-in div-inv
1×frac-times clear-num associate-/r* frac-2neg flip3-- un-div-inv flip-- associate-/l*
Counts
4 → 1548
Calls
4 calls:
20.0ms
(/ (* M D) (* 2.0 d))
49.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
198.0ms
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))
613.0ms
(* (* (* (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)) h) (/ 1 l))))

series3.3s

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
1.1s
(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))
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) (/ 1 l))))

simplify18.3s

Counts
1560 → 1560
Iterations
IterNodes
done5002
13878
01749

prune1.5s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 10.2b

regimes3.3s

Accuracy

24% (6.7b remaining)

Error of 15.4b against oracle of 8.8b and baseline of 17.5b

bsearch3.0ms

simplify16.0ms

Iterations
IterNodes
done67
167
049

end0.0ms

sample16.7s

Algorithm
intervals
Results
9.3s38075×body80nan
4.6s12747×body80valid