Details

Time bar (total: 22.8s)

sample7.9s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0.402832%

Guaranteed chance to sample good point: 14.229685%

Results
20.0ms256×body80valid
7.0ms86×body80nan
3.0ms40×body80invalid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21789
34469
415309
550019

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 16.1b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

2.4b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.2b
(/ (* M D) (* 2.0 d))
4.3b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
10.8b
(* (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:
5.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.0ms
(/ (* M D) (* 2.0 d))
2.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
12.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series524.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
6.0ms
(/ (* M D) (* 2.0 d))
142.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
205.0ms
(* (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
250021043

prune271.0ms

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: 7.7b

Counts
126 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

3.0b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
4.2b
(/ (* M D) (* 2.0 d))
4.3b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.7b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

rewrite29.0ms

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:
6.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
8.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

series567.0ms

Counts
4 → 12
Calls
4 calls:
208.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.0ms
(/ (* M D) (* 2.0 d))
144.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
209.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

simplify68.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
0693924
12737841
25002839

prune225.0ms

Filtered
69 candidates to 108 candidates (-56.5%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1062108
Fresh178
Picked101
Done000
Total1089117

Merged error: 7.5b

Counts
117 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

4.2b
(/ (* M D) (* 2.0 d))
4.3b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
5.4b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.7b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
361×add-exp-log
180×prod-exp
125×div-exp
80×pow-exp
27×add-cbrt-cube
18×add-sqr-sqrt
16×pow-to-exp
12×*-un-lft-identity
10×add-cube-cbrt
9×associate-*l*
8×cbrt-unprod
7×cbrt-undiv
6×unpow-prod-down
5×pow1 times-frac sqrt-prod
4×associate-/r* add-log-exp
3×associate-*r* div-inv unswap-sqr
2×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 → 146
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
16.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

series564.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
145.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
199.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
214.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

simplify91.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
011132041
136511655
250021649

prune269.0ms

Filtered
71 candidates to 158 candidates (-122.5%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1562158
Fresh268
Picked101
Done000
Total1598167

Merged error: 7.3b

Counts
167 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

4.2b
(/ (* M D) (* 2.0 d))
4.3b
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l))) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (cbrt l)))))
4.5b
(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
5.4b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
86×add-exp-log
30×div-exp prod-exp
21×add-cbrt-cube
18×add-sqr-sqrt
16×unpow-prod-down
15×pow-exp
13×times-frac
12×add-cube-cbrt *-un-lft-identity
10×associate-/l*
9×associate-*l*
6×cbrt-undiv cbrt-unprod
5×pow1 div-inv
4×add-log-exp sqr-pow
3×pow-to-exp associate-*r* sqrt-prod unswap-sqr
2×frac-2neg sqrt-div clear-num associate-/r*
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip--
Counts
4 → 112
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
2.0ms
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l))) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (cbrt l)))))
9.0ms
(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series493.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
152.0ms
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l))) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (cbrt l)))))
136.0ms
(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
200.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify82.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
08871570
133971460
250021454

prune276.0ms

Filtered
82 candidates to 124 candidates (-51.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1240124
Fresh077
Picked011
Done000
Total1248132

Merged error: 7.3b

Counts
132 → 8

regimes1.9s

Accuracy

0% (1.2b remaining)

Error of 8.6b against oracle of 7.4b and baseline of 8.6b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02821
12821

end0.0ms

sample9.4s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0.402832%

Guaranteed chance to sample good point: 14.229685%

Results
651.0ms8000×body80valid
249.0ms3009×body80nan
119.0ms1347×body80invalid

Profiling

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