Details

Time bar (total: 31.5s)

sample380.0ms

Algorithm
intervals
Results
54.0ms473×body80nan
29.0ms294×body80valid

simplify132.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04914
115514
268414
3389814
4500114

prune6.0ms

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: 36.0b

Counts
2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

5.7b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.2b
(/ (* l l) Om)
9.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
30×prod-diff
26×add-sqr-sqrt *-un-lft-identity
25×pow1
24×add-cube-cbrt
23×add-cbrt-cube
22×associate-*r/
21×distribute-rgt-in distribute-lft-in
16×prod-exp
13×pow-prod-down
11×flip3-- flip--
10×associate--l+ cbrt-unprod
8×associate-*r* frac-sub
6×sub-neg sqrt-div
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u 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 → 141
Calls
4 calls:
14.0ms
(* (* n (pow (/ l Om) 2.0)) (- 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)) (- U U*))))
15.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.3s

Counts
4 → 12
Calls
4 calls:
359.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
19.0ms
(/ (* 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*)))))

simplify51.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011762335
150012011

prune520.0ms

Filtered
153 candidates to 92 candidates (60.1%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New14211153
Fresh000
Picked101
Done000
Total14311154

Merged error: 21.8b

Counts
154 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

4.8b
(* n (pow (/ l Om) 2.0))
5.7b
(* (* 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*))))
20.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
35×add-exp-log
33×*-un-lft-identity
31×add-cube-cbrt
30×prod-diff
25×pow1 associate-*r*
22×associate-*r/
21×distribute-rgt-in distribute-lft-in
20×add-cbrt-cube
19×prod-exp
15×unpow-prod-down
13×pow-prod-down
11×flip3-- flip--
10×times-frac associate--l+ cbrt-unprod
8×frac-sub
6×sub-neg sqrt-div
5×associate-*l*
4×expm1-log1p-u sqrt-pow1 pow-exp log1p-expm1-u 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 → 157
Calls
4 calls:
9.0ms
(* n (pow (/ l Om) 2.0))
12.0ms
(* (* 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*))))
17.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.4s

Counts
4 → 12
Calls
4 calls:
137.0ms
(* n (pow (/ l Om) 2.0))
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*))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify58.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012292461
150012136

prune520.0ms

Filtered
169 candidates to 103 candidates (60.9%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1654169
Fresh1910
Picked101
Done000
Total16713180

Merged error: 20.1b

Counts
180 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

13.5b
(cbrt (/ l Om))
13.5b
(cbrt (/ l Om))
13.5b
(cbrt (/ l Om))
20.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×times-frac
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
14×pow1
10×associate-*r/
6×sqrt-div pow-prod-down
5×flip3-- flip--
4×add-exp-log expm1-log1p-u sqrt-pow1 frac-sub add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 div-inv
1×pow1/2 sqrt-prod
Counts
4 → 93
Calls
4 calls:
2.0ms
(cbrt (/ l Om))
2.0ms
(cbrt (/ l Om))
2.0ms
(cbrt (/ l Om))
19.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

series4.9s

Counts
4 → 12
Calls
4 calls:
64.0ms
(cbrt (/ l Om))
63.0ms
(cbrt (/ l Om))
63.0ms
(cbrt (/ l Om))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

simplify74.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06091159
125641115
250011109

prune556.0ms

Filtered
105 candidates to 91 candidates (86.7%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1041105
Fresh01212
Picked011
Done000
Total10414118

Merged error: 20.1b

Counts
118 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

4.8b
(* n (pow (/ l Om) 2.0))
5.7b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.7b
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
20.8b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
51×distribute-rgt-in distribute-lft-in
44×add-sqr-sqrt
42×prod-diff
38×add-exp-log
36×*-un-lft-identity
34×add-cube-cbrt associate-*r/
31×pow1
23×associate-*r* add-cbrt-cube
21×prod-exp
20×associate--l+
17×pow-prod-down
15×unpow-prod-down
12×cbrt-unprod
11×flip3-- flip--
10×sub-neg times-frac
8×frac-sub
6×sqrt-div
5×sqrt-pow1 associate-*l*
4×expm1-log1p-u pow-exp log1p-expm1-u 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 → 179
Calls
4 calls:
12.0ms
(* n (pow (/ l Om) 2.0))
12.0ms
(* (* 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*)))))
16.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series6.4s

Counts
4 → 12
Calls
4 calls:
140.0ms
(* n (pow (/ l Om) 2.0))
366.0ms
(* (* 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*)))))
4.6s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify61.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
014062974
150012579

prune494.0ms

Filtered
191 candidates to 103 candidates (53.9%)
Pruning

19 alts after pruning (17 fresh and 2 done)

PrunedKeptTotal
New1847191
Fresh21012
Picked011
Done011
Total18619205

Merged error: 15.4b

Counts
205 → 19

regimes1.0s

Accuracy

27.5% (9.4b remaining)

Error of 27.6b against oracle of 18.2b and baseline of 31.1b

bsearch123.0ms

Steps
ItersRangePoint
8
-1.86472712042006e-306
2.3570956754570394e-308
-6.920675890966e-311

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04737
14737

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.4s14901×body80nan
848.0ms9198×body80valid