Details

Time bar (total: 22.4s)

sample280.0ms

Algorithm
intervals
Results
146.0ms1136×body80nan
68.0ms414×body80valid

simplify193.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05417
117417
271017
3494017
4500217

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.7b

Counts
2 → 1

localize34.0ms

Local error

Found 4 expressions with local error:

6.2b
(* (* (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))))
10.8b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
10.8b
(pow (/ d l) (/ 1.0 2.0))
14.3b
(pow (/ d h) (/ 1.0 2.0))

rewrite49.0ms

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:
14.0ms
(* (* (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))))
13.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
6.0ms
(pow (/ d l) (/ 1.0 2.0))
6.0ms
(pow (/ d h) (/ 1.0 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
611.0ms
(* (* (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))))
721.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
64.0ms
(pow (/ d l) (/ 1.0 2.0))
65.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify46.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012282042
150011847

prune637.0ms

Filtered
188 candidates to 109 candidates (58.0%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New16820188
Fresh000
Picked101
Done000
Total16920189

Merged error: 12.1b

Counts
189 → 20

localize43.0ms

Local error

Found 4 expressions with local error:

5.3b
(/ (* M D) (* 2.0 d))
6.2b
(* (* (* (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
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
10.8b
(pow (/ d l) (/ 1.0 2.0))

rewrite78.0ms

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:
6.0ms
(/ (* M D) (* 2.0 d))
30.0ms
(* (* (* (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))))
13.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
9.0ms
(pow (/ d l) (/ 1.0 2.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
629.0ms
(* (* (* (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))))
716.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
64.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify78.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
016425552
150025211

prune689.0ms

Filtered
272 candidates to 89 candidates (32.7%)
Pruning

25 alts after pruning (25 fresh and 0 done)

PrunedKeptTotal
New26210272
Fresh41519
Picked101
Done000
Total26725292

Merged error: 11.0b

Counts
292 → 25

localize59.0ms

Local error

Found 4 expressions with local error:

2.5b
(pow (/ (cbrt d) l) (/ 1.0 2.0))
5.3b
(/ (* M D) (* 2.0 d))
6.2b
(* (* (* (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)) 1) (/ 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))))
10.8b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite270.0ms

Algorithm
rewrite-expression-head
Rules
5473×add-exp-log
4081×prod-exp
1994×pow-exp
1384×div-exp
643×pow-to-exp
232×1-exp
55×add-cbrt-cube
37×times-frac
32×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
4×pow-prod-down div-inv add-log-exp
3×associate-*r/ associate-*l/
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 997
Calls
4 calls:
7.0ms
(pow (/ (cbrt d) l) (/ 1.0 2.0))
6.0ms
(/ (* M D) (* 2.0 d))
74.0ms
(* (* (* (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)) 1) (/ 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))))
13.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.8s

Counts
4 → 12
Calls
4 calls:
161.0ms
(pow (/ (cbrt d) l) (/ 1.0 2.0))
26.0ms
(/ (* M D) (* 2.0 d))
938.0ms
(* (* (* (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)) 1) (/ 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))))
713.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify315.0ms

Algorithm
egg-herbie
Counts
1009 → 1009
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
0423933870
1500233678

prune1.1s

Filtered
1009 candidates to 105 candidates (10.4%)
Pruning

28 alts after pruning (28 fresh and 0 done)

PrunedKeptTotal
New100271009
Fresh32124
Picked101
Done000
Total1006281034

Merged error: 10.0b

Counts
1034 → 28

localize56.0ms

Local error

Found 4 expressions with local error:

3.5b
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
5.3b
(/ (* M D) (* 2.0 d))
6.2b
(* (* (* (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)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) 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)

rewrite267.0ms

Algorithm
rewrite-expression-head
Rules
5444×add-exp-log
4073×prod-exp
1987×pow-exp
1368×div-exp
641×pow-to-exp
232×1-exp
60×add-cbrt-cube
29×cbrt-unprod
11×pow1
10×cbrt-undiv
8×add-sqr-sqrt *-un-lft-identity associate-*r*
6×add-cube-cbrt
4×pow-prod-down add-log-exp
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in times-frac associate-*r/ associate-*l* clear-num associate-/r* *-commutative div-inv associate-/l*
1×flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 950
Calls
4 calls:
11.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
6.0ms
(/ (* M D) (* 2.0 d))
75.0ms
(* (* (* (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)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
8.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)

series2.5s

Counts
4 → 12
Calls
4 calls:
752.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
33.0ms
(/ (* M D) (* 2.0 d))
956.0ms
(* (* (* (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)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
742.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)

simplify318.0ms

Algorithm
egg-herbie
Counts
962 → 962
Iterations

Useful iterations: 1 (45.0ms)

IterNodesCost
0390533518
1500233321

prune542.0ms

Filtered
962 candidates to 70 candidates (7.3%)
Pruning

29 alts after pruning (29 fresh and 0 done)

PrunedKeptTotal
New9593962
Fresh12627
Picked101
Done000
Total96129990

Merged error: 9.6b

Counts
990 → 29

regimes1.4s

Accuracy

13.1% (5.0b remaining)

Error of 15.8b against oracle of 10.8b and baseline of 16.5b

bsearch5.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
070170
170170

end0.0ms

sample8.7s

Algorithm
intervals
Results
4.8s38069×body80nan
2.1s12605×body80valid