Details

Time bar (total: 38.1s)

sample9.3s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 6.829834%

Guaranteed chance to sample good point: 0.157222%

Results
43.0ms405×body80nan
24.0ms256×body80valid
4.0ms42×body80invalid

simplify120.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04914
115314
265214
3362414
4500214

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 34.5b

Counts
2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

6.4b
(/ (* l l) Om)
7.1b
(* n (pow (/ l Om) 2.0))
9.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.3b
(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
26×add-exp-log
24×add-sqr-sqrt
23×pow1
20×associate-*r/ associate-*r* add-cbrt-cube
16×add-cube-cbrt *-un-lft-identity
15×unpow-prod-down
13×times-frac
12×pow-prod-down
11×prod-exp
10×flip3-- flip--
8×frac-sub cbrt-unprod
6×sqrt-div
4×distribute-rgt-in sub-neg distribute-lft-in sqrt-pow1 associate-*l* associate--l+ add-log-exp unswap-sqr
3×div-exp associate-/r*
2×cbrt-undiv pow-exp *-commutative div-inv sqr-pow
1×pow-to-exp frac-2neg pow1/2 clear-num sqrt-prod associate-/l*
Counts
4 → 112
Calls
4 calls:
5.0ms
(/ (* l l) Om)
9.0ms
(* n (pow (/ l Om) 2.0))
13.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
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:
3.0ms
(/ (* l l) Om)
44.0ms
(* n (pow (/ l Om) 2.0))
377.0ms
(* (* (* 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*)))))

simplify132.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010261598
149371447
250011447

prune586.0ms

Filtered
88 candidates to 124 candidates (-40.9%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New11014124
Fresh000
Picked101
Done000
Total11114125

Merged error: 23.7b

Counts
125 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

5.1b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.1b
(* n (pow (/ l Om) 2.0))
9.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.3b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite50.0ms

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:
13.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.0ms
(* n (pow (/ l Om) 2.0))
12.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
11.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series2.6s

Counts
4 → 12
Calls
4 calls:
134.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
46.0ms
(* n (pow (/ l Om) 2.0))
377.0ms
(* (* (* 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*)))))

simplify44.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
010711765
150011602

prune315.0ms

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

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New1256131
Fresh4913
Picked101
Done000
Total13015145

Merged error: 22.8b

Counts
145 → 15

localize22.0ms

Local error

Found 4 expressions with local error:

9.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
9.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.3b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
20.3b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
42×pow1
40×associate-*r/
24×pow-prod-down
22×add-exp-log add-cbrt-cube
20×flip3-- flip--
16×frac-sub
12×sqrt-div prod-exp cbrt-unprod
8×distribute-rgt-in sub-neg distribute-lft-in sqrt-pow1 associate--l+
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*r*
4×add-log-exp
2×pow1/2 associate-*l* sqrt-prod *-commutative
Counts
4 → 108
Calls
4 calls:
13.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
13.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
12.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
11.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series4.9s

Counts
4 → 12
Calls
4 calls:
378.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
383.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
2.1s
(sqrt (* (* (* 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*)))))

simplify110.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07322568
135812320
250012320

prune460.0ms

Filtered
80 candidates to 120 candidates (-50.0%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New1200120
Fresh01414
Picked011
Done000
Total12015135

Merged error: 22.8b

Counts
135 → 15

localize24.0ms

Local error

Found 4 expressions with local error:

5.1b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
6.4b
(/ (* l l) Om)
9.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
20.3b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
96×add-exp-log
64×prod-exp
27×add-cbrt-cube
25×pow1
22×associate-*r/
18×pow-exp
13×pow-prod-down cbrt-unprod
11×flip3-- div-exp flip--
10×add-sqr-sqrt *-un-lft-identity
9×pow-to-exp
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 associate-/r*
2×cbrt-undiv associate-*l* *-commutative
1×frac-2neg pow1/2 clear-num sqrt-prod div-inv associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 120
Calls
4 calls:
17.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
5.0ms
(/ (* l l) Om)
13.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
11.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series2.6s

Counts
4 → 12
Calls
4 calls:
134.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
3.0ms
(/ (* l l) Om)
384.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
2.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify48.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
011092295
150011937

prune229.0ms

Filtered
76 candidates to 132 candidates (-73.7%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New1293132
Fresh21113
Picked101
Done011
Total13215147

Merged error: 22.3b

Counts
147 → 15

regimes1.3s

Accuracy

36% (6.7b remaining)

Error of 28.0b against oracle of 21.4b and baseline of 31.8b

bsearch4.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05286
15286

end0.0ms

sample12.6s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 6.829834%

Guaranteed chance to sample good point: 0.157222%

Results
1.3s13182×body80nan
788.0ms8000×body80valid
124.0ms1190×body80invalid

Profiling

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