Details

Time bar (total: 36.3s)

sample352.0ms

Algorithm
intervals
Results
34.0ms430×body80nan
22.0ms289×body80valid

simplify137.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04914
115314
265214
3362414
4500214

prune6.0ms

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

localize21.0ms

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*)))))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
180×add-sqr-sqrt
142×associate-*l*
114×*-un-lft-identity
82×associate-*r*
64×add-cube-cbrt
61×unswap-sqr
58×times-frac
48×sqrt-prod
32×add-exp-log
31×distribute-lft-out--
28×pow1
23×add-cbrt-cube
22×associate-*r/
21×unpow-prod-down
16×prod-exp
15×pow-prod-down associate-/l*
13×difference-of-squares
12×swap-sqr *-commutative
11×flip3-- flip--
10×cbrt-unprod
8×frac-sub
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
5×sqr-pow
4×rem-sqrt-square sqrt-pow1 associate--l+ add-log-exp
3×div-exp associate-/r*
2×cbrt-undiv pow-exp div-inv
1×pow-to-exp frac-2neg pow1/2 clear-num
Counts
4 → 283
Calls
4 calls:
8.0ms
(/ (* l l) Om)
22.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
82.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
92.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.5s

Counts
4 → 12
Calls
4 calls:
19.0ms
(/ (* l l) Om)
363.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify71.0ms

Algorithm
egg-herbie
Counts
295 → 295
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
014743542
150013397

prune953.0ms

Filtered
295 candidates to 206 candidates (30.2%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New27322295
Fresh000
Picked101
Done000
Total27422296

Merged error: 14.3b

Counts
296 → 22

localize28.0ms

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*)))))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
122×add-sqr-sqrt
114×associate-*l*
72×cbrt-prod
59×*-un-lft-identity
58×associate-*r*
52×sqrt-prod
48×unswap-sqr
33×add-cube-cbrt
19×unpow-prod-down
18×add-exp-log
16×distribute-lft-out--
12×pow1 times-frac associate-*r/
9×prod-exp *-commutative add-cbrt-cube
7×difference-of-squares
6×flip3-- sqrt-div flip--
5×rem-sqrt-square
4×pow-prod-down frac-sub add-log-exp sqr-pow
3×cbrt-unprod
2×distribute-rgt-in sub-neg distribute-lft-in sqrt-pow1 pow1/3 pow-exp
1×pow-to-exp pow1/2 div-exp div-inv
Counts
4 → 195
Calls
4 calls:
19.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.0ms
(cbrt (* (* 2.0 n) U))
7.0ms
(cbrt (* (* 2.0 n) U))
84.0ms
(sqrt (* (cbrt (* (* 2.0 n) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.6s

Counts
4 → 12
Calls
4 calls:
359.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
97.0ms
(cbrt (* (* 2.0 n) U))
97.0ms
(cbrt (* (* 2.0 n) U))
10.0s
(sqrt (* (cbrt (* (* 2.0 n) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify111.0ms

Algorithm
egg-herbie
Counts
207 → 207
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
010332486
139402436
250022430

prune898.0ms

Filtered
207 candidates to 162 candidates (21.7%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New1989207
Fresh41721
Picked101
Done000
Total20326229

Merged error: 13.6b

Counts
229 → 26

localize29.0ms

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 pow1/3 add-cbrt-cube add-log-exp
Counts
4 → 120
Calls
4 calls:
7.0ms
(cbrt (* (* 2.0 n) U))
8.0ms
(cbrt (* (* 2.0 n) U))
7.0ms
(cbrt (* (* 2.0 n) U))
8.0ms
(cbrt (* (* 2.0 n) U))

series392.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(cbrt (* (* 2.0 n) U))
97.0ms
(cbrt (* (* 2.0 n) U))
97.0ms
(cbrt (* (* 2.0 n) U))
101.0ms
(cbrt (* (* 2.0 n) U))

simplify61.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 4 (51.0ms)

IterNodesCost
0180820
1430792
2944760
31906744
45001740

prune755.0ms

Filtered
132 candidates to 104 candidates (21.2%)
Pruning

25 alts after pruning (24 fresh and 1 done)

PrunedKeptTotal
New1311132
Fresh22325
Picked011
Done000
Total13325158

Merged error: 13.6b

Counts
158 → 25

localize38.0ms

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))

rewrite118.0ms

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 frac-sub add-cbrt-cube add-log-exp
3×pow1/3
2×unpow-prod-down sqrt-pow1
1×times-frac pow1/2 pow-prod-down sqr-pow
Counts
4 → 168
Calls
4 calls:
87.0ms
(sqrt (* (cbrt (cbrt (* (* 2.0 n) U))) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
8.0ms
(cbrt (* (* 2.0 n) U))
7.0ms
(cbrt (* (* 2.0 n) U))
8.0ms
(cbrt (* (* 2.0 n) U))

series9.8s

Counts
4 → 12
Calls
4 calls:
9.5s
(sqrt (* (cbrt (cbrt (* (* 2.0 n) U))) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
102.0ms
(cbrt (* (* 2.0 n) U))
98.0ms
(cbrt (* (* 2.0 n) U))
99.0ms
(cbrt (* (* 2.0 n) U))

simplify88.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
08082433
127242397
250012387

prune1.2s

Filtered
180 candidates to 146 candidates (18.9%)
Pruning

25 alts after pruning (23 fresh and 2 done)

PrunedKeptTotal
New1791180
Fresh12223
Picked011
Done011
Total18025205

Merged error: 13.6b

Counts
205 → 25

regimes918.0ms

Accuracy

10% (12.0b remaining)

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

bsearch378.0ms

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

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
081106
181106

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.1s14745×body80nan
671.0ms9120×body80valid