Details

Time bar (total: 48.2s)

sample513.0ms

Algorithm
intervals
Results
281.0ms1251×body80nan
95.0ms407×body80valid

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02235
15435
217435
372035
done500035

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.6b

localize69.0ms

Local error

Found 4 expressions with local error:

6.5b
(* (* (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))))
11.5b
(pow (/ d l) (/ 1.0 2.0))
11.8b
(pow (/ d h) (/ 1.0 2.0))
14.4b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite195.0ms

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:
68.0ms
(* (* (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))))
8.0ms
(pow (/ d l) (/ 1.0 2.0))
8.0ms
(pow (/ d h) (/ 1.0 2.0))
92.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.2s

Counts
4 → 12
Calls
4 calls:
964.0ms
(* (* (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))))
83.0ms
(pow (/ d l) (/ 1.0 2.0))
78.0ms
(pow (/ d h) (/ 1.0 2.0))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify665.0ms

Counts
202 → 202
Iterations

Useful iterations: done (648.0ms)

IterNodesCost
04635058
114764743
done50014206

prune1.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 12.2b

localize77.0ms

Local error

Found 4 expressions with local error:

6.1b
(/ (* M D) (* 2.0 d))
6.5b
(* (* (* (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))))
11.5b
(pow (/ d l) (/ 1.0 2.0))
14.4b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite567.0ms

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:
22.0ms
(/ (* M D) (* 2.0 d))
374.0ms
(* (* (* (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))))
15.0ms
(pow (/ d l) (/ 1.0 2.0))
105.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.5s

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ (* 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))))
84.0ms
(pow (/ d l) (/ 1.0 2.0))
1.0s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.1s

Counts
318 → 318
Iterations

Useful iterations: done (1.1s)

IterNodesCost
063012762
1203911647
done500010207

prune1.8s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 11.3b

localize142.0ms

Local error

Found 4 expressions with local error:

2.6b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
6.1b
(/ (* M D) (* 2.0 d))
6.5b
(* (* (* (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))))
14.4b
(* (* (/ 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
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 → 1539
Calls
4 calls:
21.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
27.0ms
(/ (* M D) (* 2.0 d))
733.0ms
(* (* (* (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))))
107.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.7s

Counts
4 → 12
Calls
4 calls:
241.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
49.0ms
(/ (* 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)) (/ h l))))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.6s

Counts
1551 → 1551
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0182298103
done500183065

prune2.2s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 9.5b

localize121.0ms

Local error

Found 4 expressions with local error:

6.0b
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
6.1b
(/ (* M D) (* 2.0 d))
6.5b
(* (* (* (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 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
6.9b
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
8092×add-exp-log
6361×prod-exp
3419×pow-exp
1884×div-exp
965×pow-to-exp
592×rec-exp 1-exp
60×add-cbrt-cube
30×prod-diff
29×cbrt-unprod
24×add-sqr-sqrt *-un-lft-identity
22×add-cube-cbrt
17×distribute-rgt-in distribute-lft-in
11×pow1
10×cbrt-undiv
8×times-frac associate-*r* div-inv
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp
2×sub-neg frac-2neg associate-*r/ associate-*l* clear-num associate-/r* *-commutative associate-/l*
1×flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 1516
Calls
4 calls:
61.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
15.0ms
(/ (* M D) (* 2.0 d))
789.0ms
(* (* (* (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 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
42.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)

series3.4s

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

simplify1.8s

Counts
1528 → 1528
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01747101978
done500185985

prune1.7s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 9.4b

regimes2.5s

Accuracy

23.1% (4.9b remaining)

Error of 14.5b against oracle of 9.6b and baseline of 15.9b

bsearch6.0ms

simplify18.0ms

Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
063273
185213
done85213

end0.0ms

sample17.5s

Algorithm
intervals
Results
9.2s38082×body80nan
4.5s12768×body80valid