Details

Time bar (total: 34.2s)

sample7.3s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 3.287618%

Guaranteed chance to sample good point: 20.190824%

Results
42.0ms452×body80nan
31.0ms302×body80valid

simplify115.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04914
115314
265214
3362414
4500214

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.8b

Counts
2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

6.4b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.2b
(/ (* l l) Om)
11.1b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.6b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
25×pow1
23×add-cbrt-cube
22×associate-*r/
16×prod-exp
13×pow-prod-down
11×flip3-- flip--
10×add-sqr-sqrt *-un-lft-identity cbrt-unprod
8×add-cube-cbrt associate-*r* frac-sub
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
4×sqrt-pow1 associate--l+ add-log-exp
3×times-frac div-exp associate-/r*
2×cbrt-undiv associate-*l* pow-exp *-commutative
1×pow-to-exp frac-2neg pow1/2 clear-num sqrt-prod div-inv associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 103
Calls
4 calls:
13.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.0ms
(/ (* l l) Om)
11.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series2.5s

Counts
4 → 12
Calls
4 calls:
133.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.0ms
(/ (* l l) Om)
370.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
2.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify121.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
010041621
148961448
250011448

prune270.0ms

Filtered
75 candidates to 115 candidates (-53.3%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New10510115
Fresh000
Picked101
Done000
Total10610116

Merged error: 22.4b

Counts
116 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

4.0b
(* n (pow (/ l Om) 2.0))
6.4b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
11.1b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.6b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
35×add-exp-log
25×pow1 add-sqr-sqrt associate-*r*
22×associate-*r/
20×add-cbrt-cube
19×prod-exp
17×*-un-lft-identity
15×add-cube-cbrt unpow-prod-down
13×pow-prod-down
11×flip3-- flip--
10×times-frac cbrt-unprod
8×frac-sub
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
5×associate-*l*
4×sqrt-pow1 pow-exp associate--l+ add-log-exp unswap-sqr
3×*-commutative
2×pow-to-exp div-exp sqr-pow
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 119
Calls
4 calls:
10.0ms
(* n (pow (/ l Om) 2.0))
10.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
11.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series2.6s

Counts
4 → 12
Calls
4 calls:
43.0ms
(* n (pow (/ l Om) 2.0))
132.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
361.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
2.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify43.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010711765
150011602

prune278.0ms

Filtered
86 candidates to 131 candidates (-52.3%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1274131
Fresh459
Picked011
Done000
Total13110141

Merged error: 21.9b

Counts
141 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

6.0b
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.4b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.2b
(/ (* l l) Om)
18.6b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
35×add-exp-log
34×associate-*r/
31×pow1
26×add-cbrt-cube
18×distribute-rgt-in distribute-lft-in prod-exp
17×pow-prod-down
12×cbrt-unprod
11×flip3-- flip--
10×sub-neg
9×add-sqr-sqrt *-un-lft-identity
8×associate--l+ frac-sub
7×add-cube-cbrt
6×sqrt-div associate-*r*
5×sqrt-pow1
4×add-log-exp
3×times-frac div-exp associate-/r*
2×cbrt-undiv associate-*l* pow-exp *-commutative
1×pow-to-exp frac-2neg pow1/2 clear-num sqrt-prod div-inv associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 113
Calls
4 calls:
12.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
11.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.0ms
(/ (* l l) Om)
11.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series2.5s

Counts
4 → 12
Calls
4 calls:
373.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
133.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.0ms
(/ (* l l) Om)
2.0s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify122.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010691778
147511578
250011578

prune269.0ms

Filtered
71 candidates to 125 candidates (-76.1%)
Pruning

17 alts after pruning (15 fresh and 2 done)

PrunedKeptTotal
New1187125
Fresh088
Picked011
Done011
Total11817135

Merged error: 18.1b

Counts
135 → 17

localize27.0ms

Local error

Found 4 expressions with local error:

18.6b
(sqrt (* (* (cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) (cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))) (cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))
19.6b
(cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
19.6b
(cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
19.6b
(cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
1548×associate-*r/
900×cbrt-div
750×flip3-- flip--
600×frac-sub
540×frac-times
342×sqrt-div
90×associate-*l/
24×pow1
15×sqrt-pow1
12×pow1/3
9×pow-prod-up
6×pow-plus
5×pow-prod-down
4×add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×cbrt-prod pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 411
Calls
4 calls:
40.0ms
(sqrt (* (* (cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) (cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))) (cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))
10.0ms
(cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
10.0ms
(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) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series3.0s

Counts
4 → 12
Calls
4 calls:
1.6s
(sqrt (* (* (cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) (cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))) (cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))
472.0ms
(cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
470.0ms
(cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
472.0ms
(cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify465.0ms

Algorithm
egg-herbie
Counts
423 → 423
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
0244546115
1453445984
2500245978

prune2.0s

Filtered
148 candidates to 423 candidates (-185.8%)
Pruning

17 alts after pruning (15 fresh and 2 done)

PrunedKeptTotal
New4221423
Fresh01414
Picked101
Done022
Total42317440

Merged error: 18.1b

Counts
440 → 17

regimes1.3s

Accuracy

-2.9% (12.9b remaining)

Error of 33.1b against oracle of 20.2b and baseline of 32.7b

bsearch334.0ms

Steps
ItersRangePoint
8
4.194173936172518e+133
7.0312455499524275e+137
8.396131385583266e+135
7
-2.1485268644800448e-149
-4.174285045592783e-151
-4.599605135016806e-150
7
-1.1864262264546433e+97
-3.886569557871528e+95
-6.170507470734155e+96
8
-2.0085241743029418e+139
-1.2077412954389315e+136
-1.166278901215385e+139

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
010178
110178

end0.0ms

sample10.6s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 3.287618%

Guaranteed chance to sample good point: 20.190824%

Results
1.4s13923×body80nan
903.0ms9178×body80valid

Profiling

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