Details

Time bar (total: 52.7s)

sample512.0ms

Algorithm
intervals
Results
228.0ms1103×body80nan
143.0ms408×body80valid

simplify3.9s

Counts
1 → 1
Iterations
IterNodes
done5000
43968
3655
2170
154
022

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize80.0ms

Local error

Found 4 expressions with local error:

5.5b
(/ (* M D) (* 2.0 d))
9.5b
(pow (/ d h) (/ 1.0 2.0))
12.5b
(pow (/ d l) (/ 1.0 2.0))
14.5b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
167×add-exp-log
78×prod-exp
51×div-exp
46×times-frac
39×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
37×add-cbrt-cube
26×pow-unpow unpow-prod-down
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 clear-num associate-/r* frac-2neg associate-*l* pow-prod-down associate-*r/ *-commutative associate-/l*
Counts
4 → 167
Calls
4 calls:
21.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(pow (/ d h) (/ 1.0 2.0))
13.0ms
(pow (/ d l) (/ 1.0 2.0))
83.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.3s

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ (* M D) (* 2.0 d))
98.0ms
(pow (/ d h) (/ 1.0 2.0))
84.0ms
(pow (/ d l) (/ 1.0 2.0))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify2.8s

Counts
179 → 179
Iterations
IterNodes
done5001
23993
11167
0392

prune1.7s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 13.0b

localize91.0ms

Local error

Found 4 expressions with local error:

5.0b
(* (* (* (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))))
5.5b
(/ (* M D) (* 2.0 d))
12.5b
(pow (/ d l) (/ 1.0 2.0))
14.5b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite877.0ms

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 *-un-lft-identity times-frac add-cube-cbrt
20×cbrt-unprod
16×associate-*r*
13×pow-unpow unpow-prod-down
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-*l/ associate-*r/
2×sub-neg 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 → 306
Calls
4 calls:
376.0ms
(* (* (* (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))))
11.0ms
(/ (* M D) (* 2.0 d))
8.0ms
(pow (/ d l) (/ 1.0 2.0))
456.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.5s

Counts
4 → 12
Calls
4 calls:
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))))
39.0ms
(/ (* M D) (* 2.0 d))
92.0ms
(pow (/ d l) (/ 1.0 2.0))
1.0s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify2.5s

Counts
318 → 318
Iterations
IterNodes
done5000
11739
0629

prune1.8s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 9.0b

localize122.0ms

Local error

Found 4 expressions with local error:

5.5b
(/ (* M D) (* 2.0 d))
6.6b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.7b
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
12.5b
(pow (/ d l) (/ 1.0 2.0))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
166×add-exp-log
78×prod-exp
51×div-exp
39×add-cbrt-cube
22×times-frac pow-exp
21×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
14×cbrt-unprod
13×pow-unpow unpow-prod-down
10×cbrt-undiv
7×pow1
5×pow-to-exp
4×expm1-log1p-u associate-/r* associate-*l/ log1p-expm1-u div-inv add-log-exp
3×associate-*r*
2×clear-num frac-2neg associate-/l*
1×pow-pow associate-*l* pow-prod-down *-commutative sqr-pow associate-/l/
Counts
4 → 137
Calls
4 calls:
18.0ms
(/ (* M D) (* 2.0 d))
75.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
76.0ms
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
13.0ms
(pow (/ d l) (/ 1.0 2.0))

series2.0s

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ (* M D) (* 2.0 d))
925.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
920.0ms
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
105.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify2.0s

Counts
149 → 149
Iterations
IterNodes
done5000
23646
1954
0337

prune1.4s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 7.6b

localize209.0ms

Local error

Found 4 expressions with local error:

5.0b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)))
5.5b
(/ (* M D) (* 2.0 d))
6.6b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.7b
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)

rewrite693.0ms

Algorithm
rewrite-expression-head
Rules
3528×add-exp-log
2893×prod-exp
1394×pow-exp
623×div-exp
521×pow-to-exp
136×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 associate-/r* pow-prod-down associate-*l/ log1p-expm1-u add-log-exp
2×clear-num sub-neg frac-2neg associate-*l* associate-*r/ *-commutative associate-/l*
1×flip3-- flip-- distribute-lft-out-- difference-of-squares associate-/l/
Counts
4 → 798
Calls
4 calls:
442.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)))
19.0ms
(/ (* M D) (* 2.0 d))
41.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
67.0ms
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)

series2.8s

Counts
4 → 12
Calls
4 calls:
827.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)))
30.0ms
(/ (* M D) (* 2.0 d))
962.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
991.0ms
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)

simplify2.5s

Counts
810 → 810
Iterations
IterNodes
done5002
12415
01005

prune2.2s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 6.6b

regimes2.4s

Accuracy

-3.1% (8.5b remaining)

Error of 16.4b against oracle of 7.8b and baseline of 16.1b

bsearch462.0ms

Steps
ItersRangePoint
9
2.9298098091097796e+65
4.326484123994717e+71
5.20618408237528e+70

simplify33.0ms

Iterations
IterNodes
done62
162
047

end0.0ms

sample17.5s

Algorithm
intervals
Results
9.9s38309×body80nan
3.8s12742×body80valid