Details

Time bar (total: 18.9s)

analyze1.9s

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%81.1%18.9%7
0%68.6%31.4%8
0%59.2%40.8%9
0%59.2%40.8%10
0%59.2%40.8%11
0.4%49.5%50.1%12
0.8%44.4%54.8%13
1.4%39.9%58.7%14

sample139.0ms

Algorithm
intervals
Results
46.0ms256×body80valid
32.0ms220×body80nan
31.0ms151×body80invalid

simplify49.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
0504535

prune21.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.7b

Counts
2 → 2

localize30.0ms

Local error

Found 4 expressions with local error:

8.6b
(* (* (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))))
11.7b
(pow (/ d h) (/ 1.0 2.0))
12.7b
(pow (/ d l) (/ 1.0 2.0))
13.4b
(* (* (/ 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×sub-neg pow-pow associate-*l* pow-prod-down *-commutative sqr-pow
1×distribute-rgt-in frac-times flip3-- distribute-lft-in flip--
Counts
4 → 174
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))
12.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series524.0ms

Counts
4 → 12
Calls
4 calls:
273.0ms
(* (* (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))))
12.0ms
(pow (/ d h) (/ 1.0 2.0))
12.0ms
(pow (/ d l) (/ 1.0 2.0))
227.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify49.0ms

Algorithm
egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
051733758

prune591.0ms

Filtered
113 candidates to 186 candidates (-64.6%)
Pruning

23 alts after pruning (23 fresh and 0 done)

PrunedKeptTotal
New16323186
Fresh101
Picked101
Done000
Total16523188

Merged error: 14.3b

Counts
188 → 23

localize42.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (* M D) (* 2.0 d))
8.6b
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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))))
12.7b
(pow (/ d l) (/ 1.0 2.0))
13.4b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite71.0ms

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×sub-neg associate-*l* pow-prod-down *-commutative
1×distribute-rgt-in frac-times flip3-- pow-pow frac-2neg distribute-lft-in clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 258
Calls
4 calls:
5.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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))))
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))

series517.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
269.0ms
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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))))
14.0ms
(pow (/ d l) (/ 1.0 2.0))
228.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify81.0ms

Algorithm
egg-herbie
Counts
270 → 270
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
050677741

prune510.0ms

Filtered
92 candidates to 270 candidates (-193.5%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New2646270
Fresh22022
Picked101
Done000
Total26726293

Merged error: 13.9b

Counts
293 → 26

localize54.0ms

Local error

Found 4 expressions with local error:

13.1b
(cbrt (/ d l))
13.1b
(cbrt (/ d l))
13.1b
(cbrt (/ d l))
13.4b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
149×add-exp-log
74×prod-exp
45×div-exp
39×cbrt-prod
36×times-frac
32×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
25×add-cbrt-cube
20×pow-exp
13×associate-*r*
10×cbrt-unprod
6×pow1
5×cbrt-undiv
4×pow-to-exp div-inv add-log-exp
3×cbrt-div pow1/3 associate-*l/
1×frac-times associate-*r/ associate-*l* pow-prod-down *-commutative
Counts
4 → 128
Calls
4 calls:
2.0ms
(cbrt (/ d l))
2.0ms
(cbrt (/ d l))
2.0ms
(cbrt (/ d l))
12.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series268.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(cbrt (/ d l))
12.0ms
(cbrt (/ d l))
12.0ms
(cbrt (/ d l))
229.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify67.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049731885
149731885

prune546.0ms

Filtered
97 candidates to 140 candidates (-44.3%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New1355140
Fresh42125
Picked101
Done000
Total14026166

Merged error: 13.6b

Counts
166 → 26

localize56.0ms

Local error

Found 4 expressions with local error:

8.6b
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (* (cbrt (/ d l)) (cbrt (/ d l))) (/ 1.0 2.0)) (pow (cbrt (/ d l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (* (pow (* D (/ M (* 2.0 d))) 2.0) h)) (/ 1 l))))
13.1b
(cbrt (/ d l))
13.1b
(cbrt (/ d l))
13.1b
(cbrt (/ d l))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
2097×add-exp-log
1762×prod-exp
732×pow-exp
346×pow-to-exp
299×div-exp
39×cbrt-prod
27×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
22×add-cbrt-cube
13×cbrt-unprod
9×pow1
4×add-log-exp
3×cbrt-div pow1/3 associate-*r* pow-prod-down div-inv
2×sub-neg associate-*r/
1×distribute-rgt-in flip3-- distribute-lft-in associate-*l* *-commutative flip--
Counts
4 → 467
Calls
4 calls:
45.0ms
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (* (cbrt (/ d l)) (cbrt (/ d l))) (/ 1.0 2.0)) (pow (cbrt (/ d l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (* (pow (* D (/ M (* 2.0 d))) 2.0) h)) (/ 1 l))))
2.0ms
(cbrt (/ d l))
2.0ms
(cbrt (/ d l))
2.0ms
(cbrt (/ d l))

series314.0ms

Counts
4 → 12
Calls
4 calls:
277.0ms
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (* (cbrt (/ d l)) (cbrt (/ d l))) (/ 1.0 2.0)) (pow (cbrt (/ d l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (* (pow (* D (/ M (* 2.0 d))) 2.0) h)) (/ 1 l))))
12.0ms
(cbrt (/ d l))
12.0ms
(cbrt (/ d l))
12.0ms
(cbrt (/ d l))

simplify225.0ms

Algorithm
egg-herbie
Counts
479 → 479
Iterations

Useful iterations: 0 (134.0ms)

IterNodesCost
0504417242

prune355.0ms

Filtered
85 candidates to 479 candidates (-463.5%)
Pruning

27 alts after pruning (27 fresh and 0 done)

PrunedKeptTotal
New4718479
Fresh61925
Picked101
Done000
Total47827505

Merged error: 13.6b

Counts
505 → 27

regimes1.8s

Accuracy

10.7% (8.8b remaining)

Error of 19.8b against oracle of 11.0b and baseline of 20.9b

bsearch4.3s

Steps
ItersRangePoint
9
66416954331.770706
7.471707473774436e+19
15621975732124.564
9
-1.309096645026212e+52
-4.656676827647432e+45
-2.142515683081868e+51

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
092191
192191

end0.0ms

analyze1.9s

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%81.1%18.9%7
0%68.6%31.4%8
0%59.2%40.8%9
0%59.2%40.8%10
0%59.2%40.8%11
0.4%49.5%50.1%12
0.8%44.4%54.8%13
1.4%39.9%58.7%14

sample4.3s

Algorithm
intervals
Results
1.4s8000×body80valid
1.2s8202×body80nan
894.0ms4733×body80invalid

Profiling

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