Details

Time bar (total: 32.2s)

sample96.0ms

Algorithm
intervals
Results
36.0ms408×body80nan
27.0ms298×body80valid

simplify120.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04914
115314
265214
3362414
4500214

prune7.0ms

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: 38.4b

Counts
2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

6.7b
(* n (pow (/ l Om) 2.0))
7.6b
(/ (* l l) Om)
12.5b
(* (* (* 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*)))))

rewrite39.0ms

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:
8.0ms
(* n (pow (/ l Om) 2.0))
5.0ms
(/ (* l l) Om)
12.0ms
(* (* (* 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*)))))

series6.0s

Counts
4 → 12
Calls
4 calls:
144.0ms
(* 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*))))
4.6s
(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 (24.0ms)

IterNodesCost
09641521
148051370
250011370

prune474.0ms

Filtered
124 candidates to 87 candidates (70.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New11311124
Fresh000
Picked101
Done000
Total11411125

Merged error: 22.9b

Counts
125 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

6.5b
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.7b
(* n (pow (/ l Om) 2.0))
7.6b
(/ (* l l) Om)
20.3b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
32×associate-*r/
29×pow1 add-exp-log
23×add-sqr-sqrt add-cbrt-cube
18×associate-*r*
16×distribute-rgt-in distribute-lft-in pow-prod-down
15×add-cube-cbrt unpow-prod-down *-un-lft-identity
13×times-frac prod-exp
10×flip3-- flip-- cbrt-unprod
8×sub-neg associate--l+ frac-sub
6×sqrt-div
5×sqrt-pow1
4×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 → 122
Calls
4 calls:
12.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
9.0ms
(* n (pow (/ l Om) 2.0))
5.0ms
(/ (* l l) Om)
10.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series6.2s

Counts
4 → 12
Calls
4 calls:
1.3s
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
147.0ms
(* n (pow (/ l Om) 2.0))
18.0ms
(/ (* l l) Om)
4.7s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify127.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010291678
147561500
250011500

prune471.0ms

Filtered
134 candidates to 84 candidates (62.7%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New1268134
Fresh3710
Picked101
Done000
Total13015145

Merged error: 19.2b

Counts
145 → 15

localize18.0ms

Local error

Found 4 expressions with local error:

5.1b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.5b
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.7b
(* n (pow (/ l Om) 2.0))
20.3b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite51.0ms

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:
10.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
8.0ms
(* n (pow (/ l Om) 2.0))
15.0ms
(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:
358.0ms
(* (* 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*)))))
143.0ms
(* n (pow (/ l Om) 2.0))
4.9s
(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
141 → 141
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010521826
150011638

prune443.0ms

Filtered
141 candidates to 84 candidates (59.6%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New1374141
Fresh21214
Picked101
Done000
Total14016156

Merged error: 18.7b

Counts
156 → 16

localize28.0ms

Local error

Found 4 expressions with local error:

5.1b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.5b
(* (* 2.0 n) (* U (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.7b
(* n (pow (/ l Om) 2.0))
20.3b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite46.0ms

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:
10.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
9.0ms
(* n (pow (/ l Om) 2.0))
10.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series6.5s

Counts
4 → 12
Calls
4 calls:
362.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.3s
(* (* 2.0 n) (* U (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
142.0ms
(* n (pow (/ l Om) 2.0))
4.6s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify48.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
010582336
150012088

prune465.0ms

Filtered
141 candidates to 85 candidates (60.3%)
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New1401141
Fresh11415
Picked011
Done000
Total14116157

Merged error: 18.7b

Counts
157 → 16

regimes644.0ms

Accuracy

15.1% (11.1b remaining)

Error of 30.2b against oracle of 19.1b and baseline of 32.2b

bsearch383.0ms

Steps
ItersRangePoint
8
2.1471300630732583e+116
1.5673321611050321e+119
2.294579162631725e+116
7
2.656363560440644e-70
2.504395569177456e-68
5.587018487448942e-70
9
1.969868899164438e-288
2.7176143769836795e-281
2.0842190509153543e-288

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06663
16663

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.4s14863×body80nan
844.0ms9225×body80valid

Profiling

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