Details

Time bar (total: 11.6s)

analyze2.2s

Algorithm
search

sample49.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
7.0ms91×body80nan
4.0ms49×body80invalid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21789
34469
415309
550019

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 15.6b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

3.2b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.3b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.4b
(/ (* M D) (* 2.0 d))
11.8b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
35×add-sqr-sqrt
27×prod-exp
23×add-cbrt-cube
19×div-exp associate-*r*
17×add-cube-cbrt *-un-lft-identity
14×times-frac
12×associate-*l*
10×pow-exp
8×unswap-sqr
7×pow1 unpow-prod-down sqrt-prod cbrt-unprod
5×cbrt-undiv
4×sqrt-div add-log-exp
3×associate-*r/ div-inv sqr-pow
2×pow-to-exp flip3-- *-commutative flip--
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down clear-num associate-/r* associate-/l*
Counts
4 → 113
Calls
4 calls:
6.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
2.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series537.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
147.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms
(/ (* M D) (* 2.0 d))
209.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify72.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
07381124
129591046
250011043

prune248.0ms

Filtered
81 candidates to 125 candidates (-54.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1169125
Fresh000
Picked101
Done000
Total1179126

Merged error: 7.1b

Counts
126 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

3.3b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.0b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.4b
(/ (* M D) (* 2.0 d))
5.5b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
26×prod-exp
23×add-cbrt-cube
20×div-exp
18×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt pow-exp
9×associate-*l*
6×cbrt-undiv unpow-prod-down cbrt-unprod
5×pow1 times-frac sqrt-prod
4×associate-/r* add-log-exp
3×associate-*r* div-inv unswap-sqr
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/l* sqr-pow
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 96
Calls
4 calls:
4.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
6.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.0ms
(/ (* M D) (* 2.0 d))
7.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

series565.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
201.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.0ms
(/ (* M D) (* 2.0 d))
209.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

simplify67.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
0693924
12737841
25002839

prune217.0ms

Filtered
70 candidates to 108 candidates (-54.3%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1053108
Fresh178
Picked101
Done000
Total10710117

Merged error: 7.0b

Counts
117 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

5.5b
(/ (* (pow (* (cbrt (/ (* M D) (* 2.0 d))) (cbrt (/ (* M D) (* 2.0 d)))) 2.0) (* (pow (cbrt (/ (* M D) (* 2.0 d))) 2.0) h)) l)
18.0b
(cbrt (/ (* M D) (* 2.0 d)))
18.0b
(cbrt (/ (* M D) (* 2.0 d)))
18.0b
(cbrt (/ (* M D) (* 2.0 d)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
62×add-exp-log
32×prod-exp
17×div-exp
15×cbrt-prod
13×add-cbrt-cube
12×pow-exp
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
8×pow-to-exp
6×times-frac
4×pow1 div-inv add-log-exp
3×cbrt-undiv cbrt-div pow1/3 associate-/r* cbrt-unprod
1×frac-2neg clear-num associate-/l*
Counts
4 → 79
Calls
4 calls:
10.0ms
(/ (* (pow (* (cbrt (/ (* M D) (* 2.0 d))) (cbrt (/ (* M D) (* 2.0 d)))) 2.0) (* (pow (cbrt (/ (* M D) (* 2.0 d))) 2.0) h)) l)
4.0ms
(cbrt (/ (* M D) (* 2.0 d)))
4.0ms
(cbrt (/ (* M D) (* 2.0 d)))
4.0ms
(cbrt (/ (* M D) (* 2.0 d)))

series302.0ms

Counts
4 → 12
Calls
4 calls:
234.0ms
(/ (* (pow (* (cbrt (/ (* M D) (* 2.0 d))) (cbrt (/ (* M D) (* 2.0 d)))) 2.0) (* (pow (cbrt (/ (* M D) (* 2.0 d))) 2.0) h)) l)
22.0ms
(cbrt (/ (* M D) (* 2.0 d)))
24.0ms
(cbrt (/ (* M D) (* 2.0 d)))
22.0ms
(cbrt (/ (* M D) (* 2.0 d)))

simplify54.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
05371297
118831109
250011076

prune258.0ms

Filtered
64 candidates to 91 candidates (-42.2%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New91091
Fresh099
Picked011
Done000
Total9110101

Merged error: 7.0b

Counts
101 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

3.3b
(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
4.7b
(* (/ M 2.0) (/ D d))
5.0b
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
5.5b
(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
41×add-sqr-sqrt
26×prod-exp
25×*-un-lft-identity times-frac
23×add-cube-cbrt add-cbrt-cube
20×div-exp
18×associate-*l*
16×associate-*r*
10×pow-exp
7×pow1
6×cbrt-undiv cbrt-unprod unswap-sqr
5×sqrt-prod
4×add-log-exp
3×associate-/r* div-inv
2×pow-to-exp sqrt-div *-commutative sqr-pow
1×frac-times unpow-prod-down rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ clear-num flip-- associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 120
Calls
4 calls:
6.0ms
(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
10.0ms
(* (/ M 2.0) (/ D d))
5.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
6.0ms
(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)

series553.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
6.0ms
(* (/ M 2.0) (/ D d))
197.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
209.0ms
(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)

simplify69.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
08321044
13170960
25001958

prune196.0ms

Filtered
89 candidates to 132 candidates (-48.3%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1311132
Fresh088
Picked101
Done011
Total13210142

Merged error: 6.8b

Counts
142 → 10

regimes2.5s

Accuracy

45.3% (1.2b remaining)

Error of 8.4b against oracle of 7.2b and baseline of 9.4b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04836
14836

end0.0ms

analyze2.2s

Algorithm
search

sample1.4s

Algorithm
intervals
Results
612.0ms8000×body80valid
238.0ms3030×body80nan
104.0ms1341×body80invalid

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