Details

Time bar (total: 32.0s)

sample117.0ms

Algorithm
intervals
Results
51.0ms517×body80nan
27.0ms304×body80valid

simplify126.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04914
115314
265214
3362414
4500214

prune4.0ms

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: 29.8b

Counts
2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

6.3b
(* n (pow (/ l Om) 2.0))
7.1b
(/ (* l l) Om)
9.2b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
16.1b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite44.0ms

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:
9.0ms
(* n (pow (/ l Om) 2.0))
5.0ms
(/ (* l l) Om)
16.0ms
(* (* (* 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*)))))

series6.1s

Counts
4 → 12
Calls
4 calls:
134.0ms
(* n (pow (/ l Om) 2.0))
18.0ms
(/ (* l l) Om)
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*)))))

simplify128.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09641525
147931370
250011370

prune515.0ms

Filtered
124 candidates to 87 candidates (70.2%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New11113124
Fresh000
Picked101
Done000
Total11213125

Merged error: 19.0b

Counts
125 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

5.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.3b
(* n (pow (/ l Om) 2.0))
9.2b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
16.1b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite45.0ms

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)) (- U U*))
8.0ms
(* n (pow (/ l Om) 2.0))
12.0ms
(* (* (* 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*)))))

series6.4s

Counts
4 → 12
Calls
4 calls:
355.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
148.0ms
(* n (pow (/ l Om) 2.0))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify50.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
09871664
150011508

prune468.0ms

Filtered
131 candidates to 86 candidates (65.6%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1274131
Fresh3912
Picked101
Done000
Total13113144

Merged error: 17.5b

Counts
144 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

5.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.3b
(* n (pow (/ l Om) 2.0))
9.2b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
16.1b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite52.0ms

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:
15.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
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*)))))

series6.7s

Counts
4 → 12
Calls
4 calls:
345.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
138.0ms
(* n (pow (/ l Om) 2.0))
1.5s
(* (* (* 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*)))))

simplify51.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
09871664
150011508

prune437.0ms

Filtered
131 candidates to 86 candidates (65.6%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1310131
Fresh01212
Picked011
Done000
Total13113144

Merged error: 17.5b

Counts
144 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

5.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.3b
(* n (pow (/ l Om) 2.0))
7.9b
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
16.1b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
38×add-exp-log
34×associate-*r/
31×pow1
24×add-sqr-sqrt
23×associate-*r* add-cbrt-cube
21×prod-exp
18×distribute-rgt-in distribute-lft-in
17×pow-prod-down
16×*-un-lft-identity
15×unpow-prod-down
14×add-cube-cbrt
12×cbrt-unprod
11×flip3-- flip--
10×sub-neg times-frac
8×associate--l+ frac-sub
6×sqrt-div
5×sqrt-pow1 associate-*l*
4×pow-exp 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 → 129
Calls
4 calls:
11.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.0ms
(* n (pow (/ l Om) 2.0))
13.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
11.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series6.3s

Counts
4 → 12
Calls
4 calls:
348.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
142.0ms
(* n (pow (/ l Om) 2.0))
1.3s
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.5s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify51.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010521821
150011638

prune410.0ms

Filtered
141 candidates to 85 candidates (60.3%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1365141
Fresh4711
Picked101
Done011
Total14113154

Merged error: 13.6b

Counts
154 → 13

regimes770.0ms

Accuracy

29.8% (9.2b remaining)

Error of 27.8b against oracle of 18.6b and baseline of 31.7b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05770
15770

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.4s15111×body80nan
848.0ms9192×body80valid

Profiling

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