Details

Time bar (total: 9.5s)

sample44.0ms

Algorithm
intervals
Results
17.0ms304×body80valid
6.0ms100×body80nan

simplify54.0ms

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: 15.1b

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)))))
3.2b
(/ (* M D) (* 2.0 d))
5.4b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
8.8b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite35.0ms

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))
3.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
16.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
424.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
27.0ms
(/ (* M D) (* 2.0 d))
376.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
693.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify76.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
06091075
12742997
25002994

prune423.0ms

Filtered
125 candidates to 81 candidates (64.8%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New11411125
Fresh000
Picked101
Done000
Total11511126

Merged error: 8.3b

Counts
126 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

3.2b
(/ (* M D) (* 2.0 d))
3.5b
(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l)))
5.1b
(* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
5.4b
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
210×add-exp-log
85×div-exp
79×prod-exp
57×times-frac
55×add-sqr-sqrt
33×add-cbrt-cube
30×pow-exp
25×add-cube-cbrt *-un-lft-identity
22×associate-*r*
18×unpow-prod-down
13×cbrt-undiv cbrt-prod associate-*l* cbrt-unprod
12×unswap-sqr
10×associate-/l*
7×pow1 div-inv
6×pow-to-exp sqr-pow
4×add-log-exp
3×sqrt-prod
2×frac-2neg sqrt-div clear-num associate-/r*
1×frac-times rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 176
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
11.0ms
(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l)))
27.0ms
(* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
3.0ms
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))

series1.7s

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ (* M D) (* 2.0 d))
484.0ms
(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l)))
745.0ms
(* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
425.0ms
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))

simplify119.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
010432333
149132148
250012148

prune691.0ms

Filtered
188 candidates to 122 candidates (64.9%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1826188
Fresh7310
Picked101
Done000
Total1909199

Merged error: 8.2b

Counts
199 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

5.4b
(sqrt (- 1.0 (* (/ (pow (* (cbrt (/ (* M D) (* 2.0 d))) (cbrt (/ (* M D) (* 2.0 d)))) 2.0) (cbrt l)) (* (/ (pow (cbrt (/ (* M D) (* 2.0 d))) 2.0) (cbrt l)) (/ h (cbrt l))))))
19.8b
(cbrt (/ (* M D) (* 2.0 d)))
19.8b
(cbrt (/ (* M D) (* 2.0 d)))
19.8b
(cbrt (/ (* M D) (* 2.0 d)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
9×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×cbrt-div times-frac pow1/3 sqrt-prod div-inv
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 57
Calls
4 calls:
3.0ms
(sqrt (- 1.0 (* (/ (pow (* (cbrt (/ (* M D) (* 2.0 d))) (cbrt (/ (* M D) (* 2.0 d)))) 2.0) (cbrt l)) (* (/ (pow (cbrt (/ (* M D) (* 2.0 d))) 2.0) (cbrt l)) (/ h (cbrt l))))))
5.0ms
(cbrt (/ (* M D) (* 2.0 d)))
5.0ms
(cbrt (/ (* M D) (* 2.0 d)))
5.0ms
(cbrt (/ (* M D) (* 2.0 d)))

series850.0ms

Counts
4 → 12
Calls
4 calls:
536.0ms
(sqrt (- 1.0 (* (/ (pow (* (cbrt (/ (* M D) (* 2.0 d))) (cbrt (/ (* M D) (* 2.0 d)))) 2.0) (cbrt l)) (* (/ (pow (cbrt (/ (* M D) (* 2.0 d))) 2.0) (cbrt l)) (/ h (cbrt l))))))
105.0ms
(cbrt (/ (* M D) (* 2.0 d)))
105.0ms
(cbrt (/ (* M D) (* 2.0 d)))
105.0ms
(cbrt (/ (* M D) (* 2.0 d)))

simplify41.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0284947
11179896
25001881

prune445.0ms

Filtered
69 candidates to 60 candidates (87.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New67269
Fresh178
Picked101
Done000
Total69978

Merged error: 8.2b

Counts
78 → 9

localize32.0ms

Local error

Found 4 expressions with local error:

19.8b
(cbrt (/ (* M D) (* 2.0 d)))
19.8b
(cbrt (/ (* M D) (* 2.0 d)))
19.8b
(cbrt (/ (* M D) (* 2.0 d)))
19.8b
(cbrt (/ (* M D) (* 2.0 d)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
20×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log cbrt-div times-frac pow1/3 add-cbrt-cube div-inv add-log-exp
Counts
4 → 56
Calls
4 calls:
5.0ms
(cbrt (/ (* M D) (* 2.0 d)))
5.0ms
(cbrt (/ (* M D) (* 2.0 d)))
5.0ms
(cbrt (/ (* M D) (* 2.0 d)))
5.0ms
(cbrt (/ (* M D) (* 2.0 d)))

series430.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(cbrt (/ (* M D) (* 2.0 d)))
111.0ms
(cbrt (/ (* M D) (* 2.0 d)))
107.0ms
(cbrt (/ (* M D) (* 2.0 d)))
105.0ms
(cbrt (/ (* M D) (* 2.0 d)))

simplify59.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 4 (52.0ms)

IterNodesCost
0111504
1247468
2749448
32647448
45001444

prune534.0ms

Filtered
68 candidates to 56 candidates (82.4%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New68068
Fresh088
Picked011
Done000
Total68977

Merged error: 8.2b

Counts
77 → 9

regimes950.0ms

Accuracy

26.3% (1.7b remaining)

Error of 9.2b against oracle of 7.6b and baseline of 9.9b

bsearch81.0ms

Steps
ItersRangePoint
0
-4.2396509163715e-312
-3.9462700761057e-312
-4.0929604962411e-312
9
-2.773802206185027e+287
-8.747789836165673e+279
-2.7367844680296198e+287

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03720
13720

end0.0ms

sample1.2s

Algorithm
intervals
Results
568.0ms9373×body80valid
196.0ms3145×body80nan