Details

Time bar (total: 16.7s)

sample134.0ms

Algorithm
intervals
Results
52.0ms502×body80nan
27.0ms291×body80valid

simplify119.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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: 33.3b

Counts
2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

6.4b
(* n (pow (/ l Om) 2.0))
8.2b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
9.9b
(/ (* l l) Om)
19.7b
(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
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))
12.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
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*)))))

series2.6s

Counts
4 → 12
Calls
4 calls:
44.0ms
(* n (pow (/ l Om) 2.0))
375.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
3.0ms
(/ (* l l) Om)
2.1s
(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
124 → 124
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
010261598
149371447
250011447

prune363.0ms

Filtered
124 candidates to 88 candidates (29.0%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New11014124
Fresh000
Picked101
Done000
Total11114125

Merged error: 22.0b

Counts
125 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

6.4b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.4b
(* n (pow (/ l Om) 2.0))
8.2b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.7b
(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:
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*))))
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:
132.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
43.0ms
(* n (pow (/ l Om) 2.0))
369.0ms
(* (* (* 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*)))))

simplify44.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010711769
150011602

prune309.0ms

Filtered
131 candidates to 86 candidates (34.4%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1292131
Fresh31013
Picked101
Done000
Total13312145

Merged error: 20.3b

Counts
145 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

6.4b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.4b
(* n (pow (/ l Om) 2.0))
7.5b
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
19.7b
(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:
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 (/ 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:
134.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
46.0ms
(* n (pow (/ l Om) 2.0))
369.0ms
(* (* 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*))))))

simplify44.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011361922
150011732

prune325.0ms

Filtered
141 candidates to 85 candidates (39.7%)
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New1347141
Fresh3811
Picked011
Done000
Total13716153

Merged error: 16.4b

Counts
153 → 16

localize26.0ms

Local error

Found 4 expressions with local error:

15.4b
(cbrt (/ l Om))
15.4b
(cbrt (/ l Om))
15.4b
(cbrt (/ l Om))
19.7b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*))))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×times-frac
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
17×pow1
16×associate-*r/
8×pow-prod-down
6×sqrt-div
5×flip3-- sqrt-pow1 flip--
4×add-exp-log frac-sub add-cbrt-cube add-log-exp
3×cbrt-div pow1/3 div-inv
1×pow1/2 sqrt-prod
Counts
4 → 86
Calls
4 calls:
2.0ms
(cbrt (/ l Om))
2.0ms
(cbrt (/ l Om))
2.0ms
(cbrt (/ l Om))
12.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*))))))

series2.1s

Counts
4 → 12
Calls
4 calls:
13.0ms
(cbrt (/ l Om))
13.0ms
(cbrt (/ l Om))
13.0ms
(cbrt (/ l Om))
2.0s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*))))))

simplify67.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
06291155
125151107
250011095

prune227.0ms

Filtered
98 candidates to 83 candidates (15.3%)
Pruning

16 alts after pruning (14 fresh and 2 done)

PrunedKeptTotal
New98098
Fresh01414
Picked011
Done011
Total9816114

Merged error: 16.4b

Counts
114 → 16

regimes1.1s

Accuracy

7.2% (11.2b remaining)

Error of 29.5b against oracle of 18.3b and baseline of 30.4b

bsearch70.0ms

Steps
ItersRangePoint
7
-7.281250730627748e-292
-4.0542112299476386e-293
-4.7526331389498764e-293

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04737
14737

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.4s14996×body80nan
874.0ms9192×body80valid

Profiling

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