Details

Time bar (total: 31.3s)

sample338.0ms

Algorithm
intervals
Results
164.0ms1342×body80nan
65.0ms411×body80valid

simplify194.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05417
117417
271017
3494017
4500217

prune7.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.7b

Counts
2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

5.1b
(* (* (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))))
10.4b
(pow (/ d h) (/ 1.0 2.0))
11.0b
(pow (/ d l) (/ 1.0 2.0))
14.1b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite47.0ms

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:
13.0ms
(* (* (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))))
5.0ms
(pow (/ d h) (/ 1.0 2.0))
5.0ms
(pow (/ d l) (/ 1.0 2.0))
15.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.6s

Counts
4 → 12
Calls
4 calls:
655.0ms
(* (* (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))))
76.0ms
(pow (/ d h) (/ 1.0 2.0))
75.0ms
(pow (/ d l) (/ 1.0 2.0))
817.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify44.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
012282042
150011847

prune1.7s

Filtered
188 candidates to 109 candidates (42.0%)
Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New16721188
Fresh000
Picked101
Done000
Total16821189

Merged error: 11.4b

Counts
189 → 21

localize42.0ms

Local error

Found 4 expressions with local error:

2.0b
(pow (/ d (cbrt h)) (/ 1.0 2.0))
5.1b
(* (* (* (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))))
11.0b
(pow (/ d l) (/ 1.0 2.0))
14.1b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
809×add-exp-log
563×prod-exp
282×pow-exp
184×div-exp
95×pow-to-exp
54×times-frac
46×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
35×unpow-prod-down
34×add-cbrt-cube
32×rec-exp 1-exp
26×pow-unpow
16×associate-*r* cbrt-unprod
10×pow1
9×cbrt-prod
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 → 318
Calls
4 calls:
7.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
29.0ms
(* (* (* (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))))
5.0ms
(pow (/ d l) (/ 1.0 2.0))
12.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.1s

Counts
4 → 12
Calls
4 calls:
213.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
974.0ms
(* (* (* (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))))
79.0ms
(pow (/ d l) (/ 1.0 2.0))
836.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify87.0ms

Algorithm
egg-herbie
Counts
330 → 330
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
019266096
150025691

prune2.3s

Filtered
330 candidates to 120 candidates (63.6%)
Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New3219330
Fresh51520
Picked101
Done000
Total32724351

Merged error: 10.7b

Counts
351 → 24

localize57.0ms

Local error

Found 4 expressions with local error:

2.0b
(pow (/ d (cbrt h)) (/ 1.0 2.0))
2.9b
(pow (/ (cbrt d) l) (/ 1.0 2.0))
5.1b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
14.1b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite505.0ms

Algorithm
rewrite-expression-head
Rules
6364×add-exp-log
4945×prod-exp
2616×pow-exp
1623×div-exp
790×pow-to-exp
528×1-exp
232×rec-exp
63×times-frac
52×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
44×unpow-prod-down
43×add-cbrt-cube
26×pow-unpow
23×cbrt-unprod
18×cbrt-prod
16×associate-*r*
13×pow1
5×cbrt-undiv div-inv
4×pow-prod-down add-log-exp
3×associate-*r/ associate-*l/
2×distribute-rgt-in sub-neg pow-pow distribute-lft-in associate-*l* *-commutative sqr-pow
1×frac-times flip3-- flip--
Counts
4 → 1255
Calls
4 calls:
7.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
7.0ms
(pow (/ (cbrt d) l) (/ 1.0 2.0))
70.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 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))))
12.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.9s

Counts
4 → 12
Calls
4 calls:
212.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
184.0ms
(pow (/ (cbrt d) l) (/ 1.0 2.0))
681.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 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))))
818.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify351.0ms

Algorithm
egg-herbie
Counts
1267 → 1267
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
0500139767

prune3.8s

Filtered
1267 candidates to 154 candidates (87.8%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New126161267
Fresh91423
Picked101
Done000
Total1271201291

Merged error: 8.3b

Counts
1291 → 20

localize58.0ms

Local error

Found 4 expressions with local error:

2.9b
(pow (/ (cbrt d) l) (/ 1.0 2.0))
5.1b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ 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))))
5.2b
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.9b
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

rewrite298.0ms

Algorithm
rewrite-expression-head
Rules
6335×add-exp-log
4937×prod-exp
2609×pow-exp
1607×div-exp
788×pow-to-exp
528×1-exp
232×rec-exp
48×add-cbrt-cube
28×add-sqr-sqrt *-un-lft-identity times-frac
26×add-cube-cbrt
25×cbrt-unprod
22×unpow-prod-down
13×pow-unpow
12×pow1
9×cbrt-prod
8×associate-*r*
6×cbrt-undiv
4×pow-prod-down add-log-exp
3×div-inv
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/ associate-*l* *-commutative
1×flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 1208
Calls
4 calls:
6.0ms
(pow (/ (cbrt d) l) (/ 1.0 2.0))
72.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 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))))
7.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
10.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

series2.6s

Counts
4 → 12
Calls
4 calls:
189.0ms
(pow (/ (cbrt d) l) (/ 1.0 2.0))
687.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 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))))
844.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
831.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

simplify348.0ms

Algorithm
egg-herbie
Counts
1220 → 1220
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
0490137937
1500137901

prune1.4s

Filtered
1220 candidates to 98 candidates (92.0%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New121551220
Fresh41519
Picked101
Done000
Total1220201240

Merged error: 8.3b

Counts
1240 → 20

regimes1.8s

Accuracy

18.7% (4.7b remaining)

Error of 14.3b against oracle of 9.7b and baseline of 15.4b

bsearch4.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0106163
1106163

end0.0ms

sample9.7s

Algorithm
intervals
Results
4.9s38918×body80nan
2.0s12782×body80valid

Profiling

Loading profile data...