Details

Time bar (total: 44.0s)

sample86.0ms

Algorithm
intervals
Results
30.0ms430×body80nan
23.0ms289×body80valid

simplify123.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04914
115514
268414
3389814
4500114

prune4.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 35.5b

Counts
2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

6.5b
(/ (* l l) Om)
8.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.1b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.4b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite708.0ms

Algorithm
rewrite-expression-head
Rules
3806×add-sqr-sqrt
1452×prod-diff
1226×*-un-lft-identity
1070×associate-*l*
1062×times-frac
1049×unswap-sqr
958×associate-*r*
776×add-cube-cbrt
732×distribute-rgt-in distribute-lft-in
653×difference-of-squares
429×unpow-prod-down
382×associate--l+
231×distribute-lft-out--
178×*-commutative
160×swap-sqr
77×sqr-pow
48×sqrt-prod
32×add-exp-log div-inv
28×pow1
23×add-cbrt-cube
22×associate-*r/
16×prod-exp
15×pow-prod-down associate-/l*
11×flip3-- flip--
10×cbrt-unprod
8×frac-sub
6×sub-neg sqrt-div
4×expm1-log1p-u rem-sqrt-square sqrt-pow1 log1p-expm1-u add-log-exp
3×div-exp associate-/r*
2×cbrt-undiv pow-exp
1×pow-to-exp frac-2neg pow1/2 clear-num
Counts
4 → 1743
Calls
4 calls:
8.0ms
(/ (* l l) Om)
20.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
152.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
287.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.8s

Counts
4 → 12
Calls
4 calls:
21.0ms
(/ (* l l) Om)
391.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.4s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify661.0ms

Algorithm
egg-herbie
Counts
1755 → 1755
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
0500173925

prune5.8s

Filtered
1755 candidates to 944 candidates (46.2%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New1733221755
Fresh000
Picked101
Done000
Total1734221756

Merged error: 14.3b

Counts
1756 → 22

localize22.0ms

Local error

Found 4 expressions with local error:

8.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
11.4b
(cbrt (* (* 2.0 n) U))
11.4b
(cbrt (* (* 2.0 n) U))
12.2b
(sqrt (* (cbrt (* (* 2.0 n) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite356.0ms

Algorithm
rewrite-expression-head
Rules
134×add-sqr-sqrt
114×associate-*l*
72×cbrt-prod
71×*-un-lft-identity
58×associate-*r*
52×sqrt-prod
48×unswap-sqr
45×add-cube-cbrt
19×unpow-prod-down
18×add-exp-log prod-diff
16×distribute-lft-out--
12×pow1 times-frac associate-*r/
11×distribute-rgt-in distribute-lft-in
9×prod-exp *-commutative add-cbrt-cube
7×difference-of-squares
6×flip3-- sqrt-div flip--
5×rem-sqrt-square
4×expm1-log1p-u pow-prod-down frac-sub log1p-expm1-u add-log-exp sqr-pow
3×cbrt-unprod
2×sub-neg sqrt-pow1 pow1/3 pow-exp
1×pow-to-exp pow1/2 div-exp div-inv
Counts
4 → 221
Calls
4 calls:
21.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.0ms
(cbrt (* (* 2.0 n) U))
8.0ms
(cbrt (* (* 2.0 n) U))
304.0ms
(sqrt (* (cbrt (* (* 2.0 n) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series11.0s

Counts
4 → 12
Calls
4 calls:
373.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
101.0ms
(cbrt (* (* 2.0 n) U))
101.0ms
(cbrt (* (* 2.0 n) U))
10.4s
(sqrt (* (cbrt (* (* 2.0 n) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify139.0ms

Algorithm
egg-herbie
Counts
233 → 233
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011742906
146352730
250012730

prune981.0ms

Filtered
233 candidates to 175 candidates (24.9%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New2249233
Fresh41721
Picked101
Done000
Total22926255

Merged error: 13.6b

Counts
255 → 26

localize36.0ms

Local error

Found 4 expressions with local error:

11.4b
(cbrt (* (* 2.0 n) U))
11.4b
(cbrt (* (* 2.0 n) U))
11.4b
(cbrt (* (* 2.0 n) U))
11.4b
(cbrt (* (* 2.0 n) U))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
88×cbrt-prod
60×associate-*l*
52×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity associate-*r*
16×unswap-sqr
8×*-commutative
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp
Counts
4 → 128
Calls
4 calls:
7.0ms
(cbrt (* (* 2.0 n) U))
8.0ms
(cbrt (* (* 2.0 n) U))
8.0ms
(cbrt (* (* 2.0 n) U))
8.0ms
(cbrt (* (* 2.0 n) U))

series409.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(cbrt (* (* 2.0 n) U))
107.0ms
(cbrt (* (* 2.0 n) U))
100.0ms
(cbrt (* (* 2.0 n) U))
102.0ms
(cbrt (* (* 2.0 n) U))

simplify69.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 4 (57.0ms)

IterNodesCost
0182852
1438824
2961792
31957776
45001772

prune818.0ms

Filtered
140 candidates to 112 candidates (20.0%)
Pruning

25 alts after pruning (24 fresh and 1 done)

PrunedKeptTotal
New1391140
Fresh22325
Picked011
Done000
Total14125166

Merged error: 13.6b

Counts
166 → 25

localize39.0ms

Local error

Found 4 expressions with local error:

10.8b
(sqrt (* (cbrt (cbrt (* (* 2.0 n) U))) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
11.4b
(cbrt (* (* 2.0 n) U))
11.4b
(cbrt (* (* 2.0 n) U))
11.4b
(cbrt (* (* 2.0 n) U))

rewrite326.0ms

Algorithm
rewrite-expression-head
Rules
127×cbrt-prod
104×add-sqr-sqrt
100×associate-*l*
56×sqrt-prod
52×*-un-lft-identity
42×associate-*r*
41×unswap-sqr
28×add-cube-cbrt
15×distribute-lft-out--
10×associate-*r/
9×*-commutative
7×pow1
6×rem-sqrt-square sqrt-div difference-of-squares
5×flip3-- flip--
4×add-exp-log expm1-log1p-u frac-sub add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
2×unpow-prod-down sqrt-pow1
1×times-frac pow1/2 pow-prod-down sqr-pow
Counts
4 → 176
Calls
4 calls:
290.0ms
(sqrt (* (cbrt (cbrt (* (* 2.0 n) U))) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
12.0ms
(cbrt (* (* 2.0 n) U))
8.0ms
(cbrt (* (* 2.0 n) U))
8.0ms
(cbrt (* (* 2.0 n) U))

series10.2s

Counts
4 → 12
Calls
4 calls:
9.9s
(sqrt (* (cbrt (cbrt (* (* 2.0 n) U))) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
101.0ms
(cbrt (* (* 2.0 n) U))
108.0ms
(cbrt (* (* 2.0 n) U))
103.0ms
(cbrt (* (* 2.0 n) U))

simplify100.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
08252491
128342455
250012445

prune1.3s

Filtered
188 candidates to 154 candidates (18.1%)
Pruning

25 alts after pruning (23 fresh and 2 done)

PrunedKeptTotal
New1871188
Fresh12223
Picked011
Done011
Total18825213

Merged error: 13.6b

Counts
213 → 25

regimes1.0s

Accuracy

10% (12.0b remaining)

Error of 27.4b against oracle of 15.4b and baseline of 28.7b

bsearch415.0ms

Steps
ItersRangePoint
8
2.6913061862570087e+262
1.152299597490014e+265
2.718121113023407e+262
5
8.871289280256932e-113
2.3029284345587177e-112
1.258070492458926e-112
9
1.7219891066244823e-300
4.033023019392756e-292
4.437888771927319e-300

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
081106
181106

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.1s14745×body80nan
670.0ms9120×body80valid