Details

Time bar (total: 51.5s)

sample526.0ms

Algorithm
intervals
Results
300.0ms1352×body80nan
86.0ms421×body80valid

simplify3.3s

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: 23.8b

localize31.0ms

Local error

Found 4 expressions with local error:

5.8b
(/ (* M D) (* 2.0 d))
9.7b
(pow (/ d h) (/ 1.0 2.0))
10.1b
(pow (/ d l) (/ 1.0 2.0))
11.2b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
167×add-exp-log
78×prod-exp
51×div-exp
46×times-frac
39×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
37×add-cbrt-cube
26×unpow-prod-down pow-unpow
24×pow-exp
14×cbrt-unprod
13×associate-*r*
9×cbrt-undiv
8×pow1
6×pow-to-exp div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l/
2×pow-pow sqr-pow
1×frac-times frac-2neg associate-*r/ associate-*l* pow-prod-down clear-num associate-/r* *-commutative associate-/l*
Counts
4 → 167
Calls
4 calls:
13.0ms
(/ (* M D) (* 2.0 d))
15.0ms
(pow (/ d h) (/ 1.0 2.0))
8.0ms
(pow (/ d l) (/ 1.0 2.0))
84.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.3s

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ (* M D) (* 2.0 d))
76.0ms
(pow (/ d h) (/ 1.0 2.0))
96.0ms
(pow (/ d l) (/ 1.0 2.0))
1.0s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.9s

Counts
179 → 179
Iterations

Useful iterations: 2 (868.0ms)

IterNodesCost
03922931
19532662
234662380
done50002380

prune1.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.5b

localize92.0ms

Local error

Found 4 expressions with local error:

5.7b
(* (* (* (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))))
5.8b
(/ (* M D) (* 2.0 d))
10.1b
(pow (/ d l) (/ 1.0 2.0))
11.2b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite673.0ms

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:
483.0ms
(* (* (* (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))))
27.0ms
(/ (* M D) (* 2.0 d))
16.0ms
(pow (/ d l) (/ 1.0 2.0))
123.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.6s

Counts
4 → 12
Calls
4 calls:
1.4s
(* (* (* (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))))
40.0ms
(/ (* M D) (* 2.0 d))
110.0ms
(pow (/ d l) (/ 1.0 2.0))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify937.0ms

Counts
318 → 318
Iterations

Useful iterations: done (918.0ms)

IterNodesCost
063012762
1141111384
done500110169

prune1.2s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 8.3b

localize75.0ms

Local error

Found 4 expressions with local error:

2.6b
(pow (/ d (cbrt h)) (/ 1.0 2.0))
5.7b
(* (* (* (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))))
5.8b
(/ (* M D) (* 2.0 d))
11.2b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite1.2s

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:
10.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
735.0ms
(* (* (* (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))))
15.0ms
(/ (* M D) (* 2.0 d))
54.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.7s

Counts
4 → 12
Calls
4 calls:
262.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
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))))
41.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify2.4s

Counts
1551 → 1551
Iterations

Useful iterations: done (2.3s)

IterNodesCost
0182298103
1279779686
done500073388

prune1.5s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 7.9b

localize67.0ms

Local error

Found 4 expressions with local error:

4.1b
(/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l)))
4.7b
(* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
5.7b
(* (* (* (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)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
5.8b
(/ (* M D) (* 2.0 d))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
8503×add-exp-log
6534×prod-exp
3464×pow-exp
2065×div-exp
974×pow-to-exp
592×rec-exp 1-exp
95×add-cbrt-cube
52×cbrt-unprod
35×cbrt-undiv
29×add-sqr-sqrt
25×associate-*r*
23×times-frac
21×add-cube-cbrt *-un-lft-identity
11×pow1
10×cbrt-prod
6×associate-*l* 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/ unswap-sqr
2×sub-neg frac-2neg associate-*l/ clear-num associate-/r* *-commutative associate-/l*
1×frac-times flip3-- flip-- associate-/l/
Counts
4 → 1598
Calls
4 calls:
39.0ms
(/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l)))
114.0ms
(* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
773.0ms
(* (* (* (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)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
28.0ms
(/ (* M D) (* 2.0 d))

series3.5s

Counts
4 → 12
Calls
4 calls:
824.0ms
(/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l)))
1.2s
(* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
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)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
52.0ms
(/ (* M D) (* 2.0 d))

simplify2.7s

Counts
1610 → 1610
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01823111287
1283292462
done500185618

prune1.9s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 7.7b

regimes1.5s

Accuracy

4% (5.6b remaining)

Error of 16.0b against oracle of 10.4b and baseline of 16.2b

bsearch616.0ms

Steps
ItersRangePoint
9
-1.3664137271603664e-146
-2.8881051568685524e-152
-5.294735836166802e-147

simplify18.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
054147
170147
done70147

end0.0ms

sample18.0s

Algorithm
intervals
Results
10.5s38881×body80nan
3.8s12926×body80valid