Details

Time bar (total: 31.0s)

sample253.0ms

Algorithm
intervals
Results
117.0ms1171×body80nan
55.0ms410×body80valid

simplify2.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02235
15435
217435
371735
4458035
done500035

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.7b

localize35.0ms

Local error

Found 4 expressions with local error:

5.8b
(* (* (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))))
12.7b
(pow (/ d h) (/ 1.0 2.0))
13.0b
(pow (/ d l) (/ 1.0 2.0))
13.1b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite138.0ms

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:
61.0ms
(* (* (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))))
7.0ms
(pow (/ d h) (/ 1.0 2.0))
7.0ms
(pow (/ d l) (/ 1.0 2.0))
53.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.6s

Counts
4 → 12
Calls
4 calls:
698.0ms
(* (* (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))))
72.0ms
(pow (/ d h) (/ 1.0 2.0))
64.0ms
(pow (/ d l) (/ 1.0 2.0))
769.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.7s

Counts
202 → 202
Iterations

Useful iterations: done (1.7s)

IterNodesCost
04635058
111404644
239784180
done50014172

prune769.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.5b

localize42.0ms

Local error

Found 4 expressions with local error:

5.2b
(/ (* M D) (* 2.0 d))
5.8b
(* (* (* (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))))
13.0b
(pow (/ d l) (/ 1.0 2.0))
13.1b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite362.0ms

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 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 → 306
Calls
4 calls:
12.0ms
(/ (* M D) (* 2.0 d))
267.0ms
(* (* (* (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))
52.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.8s

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (* M D) (* 2.0 d))
920.0ms
(* (* (* (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))))
63.0ms
(pow (/ d l) (/ 1.0 2.0))
771.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify601.0ms

Counts
318 → 318
Iterations

Useful iterations: done (582.0ms)

IterNodesCost
063012762
1141111384
done500010169

prune751.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.5b

localize56.0ms

Local error

Found 4 expressions with local error:

2.8b
(pow (/ d (cbrt h)) (/ 1.0 2.0))
5.2b
(/ (* M D) (* 2.0 d))
5.8b
(* (* (* (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))))
13.1b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite770.0ms

Algorithm
rewrite-expression-head
Rules
6965×add-exp-log
5245×prod-exp
2614×pow-exp
1626×div-exp
789×pow-to-exp
232×rec-exp 1-exp
55×add-cbrt-cube
37×times-frac
34×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
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-*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 → 1243
Calls
4 calls:
9.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
12.0ms
(/ (* M D) (* 2.0 d))
487.0ms
(* (* (* (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))))
52.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.9s

Counts
4 → 12
Calls
4 calls:
181.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
29.0ms
(/ (* M D) (* 2.0 d))
924.0ms
(* (* (* (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))))
763.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.2s

Counts
1255 → 1255
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0151984720
1249970393
done500062024

prune1.1s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 9.1b

localize62.0ms

Local error

Found 4 expressions with local error:

5.2b
(/ (* M D) (* 2.0 d))
5.8b
(* (* (* (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)))
6.8b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
7.7b
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
6964×add-exp-log
5245×prod-exp
2612×pow-exp
1626×div-exp
788×pow-to-exp
232×rec-exp 1-exp
57×add-cbrt-cube
42×prod-diff
36×add-sqr-sqrt *-un-lft-identity
34×add-cube-cbrt
27×cbrt-unprod
23×distribute-rgt-in distribute-lft-in
22×times-frac
11×pow1
10×cbrt-undiv
8×associate-*r* div-inv
4×expm1-log1p-u pow-prod-down associate-*l/ associate-/r* log1p-expm1-u add-log-exp
2×sub-neg frac-2neg associate-*r/ associate-*l* clear-num *-commutative associate-/l*
1×flip3-- flip-- associate-/l/ distribute-lft-out-- difference-of-squares
Counts
4 → 1242
Calls
4 calls:
12.0ms
(/ (* M D) (* 2.0 d))
493.0ms
(* (* (* (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)))
47.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
257.0ms
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)

series2.5s

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (* M D) (* 2.0 d))
910.0ms
(* (* (* (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)))
766.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
757.0ms
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)

simplify1.2s

Counts
1254 → 1254
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0149391106
1245375741
done500166662

prune776.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 8.7b

regimes1.6s

Accuracy

13.8% (4.7b remaining)

Error of 14.9b against oracle of 10.2b and baseline of 15.7b

bsearch295.0ms

Steps
ItersRangePoint
9
-4.209419363785588e-21
-5.74722603920921e-26
-4.824389863243857e-22

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
048136
161136
done61136

end0.0ms

sample7.8s

Algorithm
intervals
Results
3.7s38290×body80nan
1.7s12854×body80valid