Details

Time bar (total: 23.1s)

sample228.0ms

Algorithm
intervals
Results
116.0ms1070×body80nan
53.0ms374×body80valid

simplify207.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 25.2b

Counts
2 → 1

localize33.0ms

Local error

Found 4 expressions with local error:

4.7b
(* (* (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))))
11.1b
(pow (/ d h) (/ 1.0 2.0))
13.1b
(pow (/ d l) (/ 1.0 2.0))
13.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite46.0ms

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

series1.7s

Counts
4 → 12
Calls
4 calls:
823.0ms
(* (* (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))))
68.0ms
(pow (/ d h) (/ 1.0 2.0))
67.0ms
(pow (/ d l) (/ 1.0 2.0))
758.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify50.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012282042
150011847

prune682.0ms

Filtered
188 candidates to 109 candidates (58.0%)
Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New16721188
Fresh000
Picked101
Done000
Total16821189

Merged error: 10.0b

Counts
189 → 21

localize44.0ms

Local error

Found 4 expressions with local error:

4.5b
(/ (* M D) (* 2.0 d))
4.7b
(* (* (* (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))))
13.1b
(pow (/ d l) (/ 1.0 2.0))
13.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite79.0ms

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×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 → 292
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
26.0ms
(* (* (* (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))
13.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.7s

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (* M D) (* 2.0 d))
869.0ms
(* (* (* (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))))
67.0ms
(pow (/ d l) (/ 1.0 2.0))
748.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify84.0ms

Algorithm
egg-herbie
Counts
304 → 304
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
018025799
150015527

prune729.0ms

Filtered
304 candidates to 95 candidates (31.3%)
Pruning

28 alts after pruning (28 fresh and 0 done)

PrunedKeptTotal
New29113304
Fresh51520
Picked101
Done000
Total29728325

Merged error: 8.5b

Counts
325 → 28

localize53.0ms

Local error

Found 4 expressions with local error:

3.2b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
4.5b
(/ (* M D) (* 2.0 d))
4.7b
(* (* (* (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))))
13.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite364.0ms

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
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 → 1525
Calls
4 calls:
7.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
6.0ms
(/ (* M D) (* 2.0 d))
95.0ms
(* (* (* (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))))
12.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.9s

Counts
4 → 12
Calls
4 calls:
183.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
28.0ms
(/ (* M D) (* 2.0 d))
882.0ms
(* (* (* (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))))
759.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify441.0ms

Algorithm
egg-herbie
Counts
1537 → 1537
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
0500150973

prune1.2s

Filtered
1537 candidates to 131 candidates (8.5%)
Pruning

28 alts after pruning (28 fresh and 0 done)

PrunedKeptTotal
New153161537
Fresh52227
Picked101
Done000
Total1537281565

Merged error: 6.6b

Counts
1565 → 28

localize59.0ms

Local error

Found 4 expressions with local error:

4.5b
(/ (* M D) (* 2.0 d))
4.7b
(* (* (* (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 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
7.8b
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
8.5b
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

rewrite355.0ms

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
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 → 1478
Calls
4 calls:
14.0ms
(/ (* M D) (* 2.0 d))
89.0ms
(* (* (* (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))))
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))

series2.5s

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (* M D) (* 2.0 d))
902.0ms
(* (* (* (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))))
783.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
741.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

simplify621.0ms

Algorithm
egg-herbie
Counts
1490 → 1490
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0500150608

prune701.0ms

Filtered
1490 candidates to 96 candidates (6.4%)
Pruning

30 alts after pruning (30 fresh and 0 done)

PrunedKeptTotal
New148641490
Fresh12627
Picked101
Done000
Total1488301518

Merged error: 5.4b

Counts
1518 → 30

regimes1.6s

Accuracy

35.9% (5.6b remaining)

Error of 14.6b against oracle of 9.0b and baseline of 17.8b

bsearch5.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
084173
184173

end0.0ms

sample7.7s

Algorithm
intervals
Results
4.2s38791×body80nan
1.8s12843×body80valid