Details

Time bar (total: 9.3s)

sample54.0ms

Algorithm
intervals
Results
22.0ms292×body80valid
9.0ms122×body80nan

simplify56.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21789
34469
415309
550019

prune3.0ms

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: 14.9b

Counts
2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.5b
(/ (* M D) (* 2.0 d))
4.7b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
12.0b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite28.0ms

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

series1.5s

Counts
4 → 12
Calls
4 calls:
414.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
28.0ms
(/ (* M D) (* 2.0 d))
370.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
685.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify76.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
06091075
12742997
25003994

prune363.0ms

Filtered
125 candidates to 81 candidates (64.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1178125
Fresh000
Picked101
Done000
Total1188126

Merged error: 8.4b

Counts
126 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

4.2b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.3b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
4.5b
(/ (* M D) (* 2.0 d))
4.7b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))

rewrite27.0ms

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

series1.8s

Counts
4 → 12
Calls
4 calls:
690.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
732.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
34.0ms
(/ (* M D) (* 2.0 d))
370.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))

simplify65.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
0560829
12559746
25001744

prune299.0ms

Filtered
108 candidates to 70 candidates (64.8%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1062108
Fresh077
Picked011
Done000
Total10610116

Merged error: 7.7b

Counts
116 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

4.7b
(sqrt (- 1.0 (/ (* (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)))
16.5b
(cbrt (/ (* M D) (* 2.0 d)))
16.5b
(cbrt (/ (* M D) (* 2.0 d)))
16.5b
(cbrt (/ (* M D) (* 2.0 d)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
11×add-sqr-sqrt
10×*-un-lft-identity
8×add-cube-cbrt
5×pow1 sqrt-prod
4×add-exp-log add-cbrt-cube add-log-exp
3×cbrt-div times-frac pow1/3 div-inv
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 59
Calls
4 calls:
4.0ms
(sqrt (- 1.0 (/ (* (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)))
5.0ms
(cbrt (/ (* M D) (* 2.0 d)))

series804.0ms

Counts
4 → 12
Calls
4 calls:
483.0ms
(sqrt (- 1.0 (/ (* (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)))
103.0ms
(cbrt (/ (* M D) (* 2.0 d)))
111.0ms
(cbrt (/ (* M D) (* 2.0 d)))
106.0ms
(cbrt (/ (* M D) (* 2.0 d)))

simplify75.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (65.0ms)

IterNodesCost
0204881
1512835
22164820
35002818

prune328.0ms

Filtered
71 candidates to 58 candidates (81.7%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New70171
Fresh178
Picked101
Done011
Total72981

Merged error: 7.7b

Counts
81 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

6.9b
(cbrt (pow (sqrt (- 1.0 (/ (* (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))) 3))
16.5b
(cbrt (/ (* M D) (* 2.0 d)))
16.5b
(cbrt (/ (* M D) (* 2.0 d)))
16.5b
(cbrt (/ (* M D) (* 2.0 d)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
37×cbrt-prod
16×add-sqr-sqrt *-un-lft-identity
12×add-cube-cbrt
10×sqrt-prod
8×unpow-prod-down cube-prod
5×cbrt-div
4×pow1 add-exp-log pow1/3 add-cbrt-cube add-log-exp
3×times-frac div-inv
2×cube-div sqrt-div distribute-lft-out-- difference-of-squares
1×cube-mult flip3-- unpow3 flip-- rem-cbrt-cube sqr-pow
Counts
4 → 75
Calls
4 calls:
11.0ms
(cbrt (pow (sqrt (- 1.0 (/ (* (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))) 3))
4.0ms
(cbrt (/ (* M D) (* 2.0 d)))
4.0ms
(cbrt (/ (* M D) (* 2.0 d)))
5.0ms
(cbrt (/ (* M D) (* 2.0 d)))

series816.0ms

Counts
4 → 12
Calls
4 calls:
493.0ms
(cbrt (pow (sqrt (- 1.0 (/ (* (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))) 3))
106.0ms
(cbrt (/ (* M D) (* 2.0 d)))
108.0ms
(cbrt (/ (* M D) (* 2.0 d)))
109.0ms
(cbrt (/ (* M D) (* 2.0 d)))

simplify106.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
03121449
19101418
235181403
350011403

prune335.0ms

Filtered
87 candidates to 58 candidates (66.7%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New87087
Fresh077
Picked011
Done011
Total87996

Merged error: 7.7b

Counts
96 → 9

regimes1.0s

Accuracy

63% (1.3b remaining)

Error of 8.4b against oracle of 7.1b and baseline of 10.5b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05043
15043

end0.0ms

sample1.4s

Algorithm
intervals
Results
710.0ms9255×body80valid
251.0ms3195×body80nan

Profiling

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