Details

Time bar (total: 22.6s)

sample267.0ms

Algorithm
intervals
Results
127.0ms1341×body80nan
53.0ms419×body80valid

simplify190.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05417
117417
271017
3494017
4500217
done500217

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.3b

localize29.0ms

Local error

Found 4 expressions with local error:

7.1b
(* (* (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))))
10.6b
(pow (/ d h) (/ 1.0 2.0))
10.8b
(pow (/ d l) (/ 1.0 2.0))
14.5b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite135.0ms

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:
59.0ms
(* (* (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))))
9.0ms
(pow (/ d h) (/ 1.0 2.0))
7.0ms
(pow (/ d l) (/ 1.0 2.0))
51.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.6s

Counts
4 → 12
Calls
4 calls:
690.0ms
(* (* (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))))
69.0ms
(pow (/ d h) (/ 1.0 2.0))
69.0ms
(pow (/ d l) (/ 1.0 2.0))
742.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify44.0ms

Counts
188 → 188
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012282042
150011847
done50011847

prune706.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.8b

localize47.0ms

Local error

Found 4 expressions with local error:

3.6b
(/ (* M D) (* 2.0 d))
7.1b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
10.8b
(pow (/ d l) (/ 1.0 2.0))
14.5b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite401.0ms

Algorithm
rewrite-expression-head
Rules
738×add-exp-log
487×prod-exp
216×pow-exp
171×div-exp
78×pow-to-exp
46×add-cbrt-cube
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 → 260
Calls
4 calls:
12.0ms
(/ (* M D) (* 2.0 d))
306.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
8.0ms
(pow (/ d l) (/ 1.0 2.0))
53.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (* M D) (* 2.0 d))
685.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
68.0ms
(pow (/ d l) (/ 1.0 2.0))
761.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify67.0ms

Counts
272 → 272
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
016425552
150025211
done50025211

prune721.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 11.6b

localize50.0ms

Local error

Found 4 expressions with local error:

3.8b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))
7.1b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))))
7.4b
(* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))
10.8b
(pow (/ d l) (/ 1.0 2.0))

rewrite625.0ms

Algorithm
rewrite-expression-head
Rules
1015×add-exp-log
676×prod-exp
246×pow-exp
223×div-exp
84×pow-to-exp
66×add-cbrt-cube
47×cbrt-unprod
37×times-frac
36×add-sqr-sqrt
34×add-cube-cbrt *-un-lft-identity
26×associate-*r*
19×unpow-prod-down
13×cbrt-undiv pow-unpow
12×pow1
11×associate-*l*
9×cbrt-prod
4×pow-prod-down div-inv add-log-exp
3×associate-*r/ associate-*l/ *-commutative unswap-sqr sqr-pow
2×distribute-rgt-in sub-neg distribute-lft-in
1×frac-times flip3-- pow-pow flip--
Counts
4 → 326
Calls
4 calls:
36.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))
308.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))))
244.0ms
(* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))
7.0ms
(pow (/ d l) (/ 1.0 2.0))

series2.0s

Counts
4 → 12
Calls
4 calls:
472.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))
716.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))))
794.0ms
(* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))
66.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify82.0ms

Counts
338 → 338
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
020487780
150017270
done50017270

prune1.0s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 9.5b

localize56.0ms

Local error

Found 4 expressions with local error:

3.6b
(/ (* M D) (* 2.0 d))
3.8b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))
7.1b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))))
7.4b
(* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
6223×add-exp-log
4506×prod-exp
2022×pow-exp
1439×div-exp
648×pow-to-exp
87×add-cbrt-cube
58×cbrt-unprod
26×associate-*r*
22×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity times-frac
17×cbrt-undiv
14×pow1
11×associate-*l*
9×cbrt-prod
6×unpow-prod-down pow-prod-down
4×add-log-exp
3×associate-*r/ associate-*l/ *-commutative div-inv unswap-sqr
2×distribute-rgt-in sub-neg distribute-lft-in sqr-pow
1×frac-times flip3-- frac-2neg clear-num associate-/r* flip-- associate-/l*
Counts
4 → 1037
Calls
4 calls:
12.0ms
(/ (* M D) (* 2.0 d))
36.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))
527.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))))
246.0ms
(* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))

series2.0s

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (* M D) (* 2.0 d))
475.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))
709.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))))
773.0ms
(* (* (/ 1.0 2.0) (* (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt h) (cbrt h)))) (/ (cbrt h) l))

simplify329.0ms

Counts
1049 → 1049
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0442343828
1500143550
done500143550

prune892.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 8.5b

regimes1.2s

Accuracy

0% (4.6b remaining)

Error of 14.1b against oracle of 9.5b and baseline of 14.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04853
14853
done4853

end0.0ms

sample7.3s

Algorithm
intervals
Results
3.5s37845×body80nan
1.6s12766×body80valid