Details

Time bar (total: 21.2s)

sample6.8s

Algorithm
intervals
sampling

Space saved by range analysis: 0.901177%

Space saved by search: 0.292611%

Guaranteed chance to sample good point: 0%

Results
20.0ms256×body80valid
7.0ms92×body80nan
4.0ms47×body80invalid

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21789
34469
415309
550019

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 11.3b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.2b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.9b
(/ (* M D) (* 2.0 d))
7.7b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite29.0ms

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))
11.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series553.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
151.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms
(/ (* M D) (* 2.0 d))
215.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify74.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
07381124
129591046
250011043

prune272.0ms

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

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New11312125
Fresh000
Picked101
Done000
Total11412126

Merged error: 5.3b

Counts
126 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

3.1b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.2b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.2b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.9b
(/ (* M D) (* 2.0 d))

rewrite28.0ms

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:
7.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.0ms
(/ (* M D) (* 2.0 d))

series581.0ms

Counts
4 → 12
Calls
4 calls:
214.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
153.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
209.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.0ms
(/ (* M D) (* 2.0 d))

simplify67.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
0693924
12737841
25002839

prune220.0ms

Filtered
68 candidates to 108 candidates (-58.8%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1062108
Fresh3811
Picked011
Done000
Total10911120

Merged error: 5.3b

Counts
120 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

2.8b
(* (/ M 2.0) (/ D d))
3.1b
(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)
4.2b
(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
5.2b
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)

rewrite32.0ms

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:
10.0ms
(* (/ M 2.0) (/ D d))
6.0ms
(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)
4.0ms
(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
6.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)

series579.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(* (/ M 2.0) (/ D d))
214.0ms
(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)
151.0ms
(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
208.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)

simplify76.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
08321043
13170960
25001958

prune250.0ms

Filtered
88 candidates to 132 candidates (-50.0%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1311132
Fresh279
Picked011
Done011
Total13310143

Merged error: 5.3b

Counts
143 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

2.8b
(* (/ M 2.0) (/ D d))
3.1b
(/ (* (* (pow (* (/ M 2.0) (/ D d)) 2.0) (* (cbrt h) (cbrt h))) (cbrt h)) l)
3.7b
(* (pow (* (/ M 2.0) (/ D d)) 2.0) (* (cbrt h) (cbrt h)))
4.2b
(sqrt (- 1.0 (/ (* (* (pow (* (/ M 2.0) (/ D d)) 2.0) (* (cbrt h) (cbrt h))) (cbrt h)) l)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
147×add-exp-log
77×prod-exp
38×add-sqr-sqrt
36×div-exp
28×add-cbrt-cube
25×times-frac
24×*-un-lft-identity
22×add-cube-cbrt
20×pow-exp
18×associate-*l*
14×associate-*r*
13×cbrt-unprod
8×cbrt-undiv
7×pow1
6×unswap-sqr
5×sqrt-prod
4×pow-to-exp add-log-exp
3×associate-/r* div-inv
2×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 → 136
Calls
4 calls:
10.0ms
(* (/ M 2.0) (/ D d))
15.0ms
(/ (* (* (pow (* (/ M 2.0) (/ D d)) 2.0) (* (cbrt h) (cbrt h))) (cbrt h)) l)
10.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) (* (cbrt h) (cbrt h)))
4.0ms
(sqrt (- 1.0 (/ (* (* (pow (* (/ M 2.0) (/ D d)) 2.0) (* (cbrt h) (cbrt h))) (cbrt h)) l)))

series521.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(* (/ M 2.0) (/ D d))
219.0ms
(/ (* (* (pow (* (/ M 2.0) (/ D d)) 2.0) (* (cbrt h) (cbrt h))) (cbrt h)) l)
141.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) (* (cbrt h) (cbrt h)))
155.0ms
(sqrt (- 1.0 (/ (* (* (pow (* (/ M 2.0) (/ D d)) 2.0) (* (cbrt h) (cbrt h))) (cbrt h)) l)))

simplify90.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
010181614
137961442
250021424

prune212.0ms

Filtered
89 candidates to 148 candidates (-66.3%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1480148
Fresh077
Picked011
Done022
Total14810158

Merged error: 5.3b

Counts
158 → 10

regimes2.4s

Accuracy

36.9% (1.9b remaining)

Error of 9.6b against oracle of 7.8b and baseline of 10.7b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04533
14533

end0.0ms

sample8.2s

Algorithm
intervals
sampling

Space saved by range analysis: 0.901177%

Space saved by search: 0.292611%

Guaranteed chance to sample good point: 0%

Results
632.0ms8000×body80valid
239.0ms2890×body80nan
102.0ms1264×body80invalid

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