Details

Time bar (total: 32.3s)

sample342.0ms

Algorithm
intervals
Results
32.0ms451×body80nan
19.0ms275×body80valid

simplify128.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04914
115514
268414
3389814
4500114

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize29.0ms

Local error

Found 4 expressions with local error:

7.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.5b
(/ (* l l) Om)
10.9b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
15.9b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite134.0ms

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:
25.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.0ms
(/ (* l l) Om)
55.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
44.0ms
(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:
360.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
24.0ms
(/ (* 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*)))))

simplify54.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011762335
150012011

prune560.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 18.3b

localize24.0ms

Local error

Found 4 expressions with local error:

6.0b
(* n (pow (/ l Om) 2.0))
7.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.5b
(/ (* l l) Om)
15.9b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
31×add-exp-log
30×*-un-lft-identity
28×add-cube-cbrt
22×associate-*r*
19×pow1
18×associate-*r/ prod-diff
16×add-cbrt-cube
15×unpow-prod-down
14×prod-exp
13×times-frac
11×distribute-rgt-in distribute-lft-in
9×pow-prod-down
6×flip3-- sqrt-div flip--
5×sqrt-pow1 cbrt-unprod
4×expm1-log1p-u div-exp associate-*l* pow-exp frac-sub log1p-expm1-u add-log-exp unswap-sqr
3×associate-/r*
2×cbrt-undiv pow-to-exp sub-neg *-commutative div-inv sqr-pow
1×frac-2neg pow1/2 clear-num sqrt-prod associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 132
Calls
4 calls:
15.0ms
(* n (pow (/ l Om) 2.0))
27.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.0ms
(/ (* l l) Om)
62.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series5.2s

Counts
4 → 12
Calls
4 calls:
139.0ms
(* n (pow (/ l Om) 2.0))
363.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
19.0ms
(/ (* l l) Om)
4.7s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify44.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010221437
150011244

prune541.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.0b

localize19.0ms

Local error

Found 4 expressions with local error:

5.4b
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.0b
(* n (pow (/ l Om) 2.0))
7.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
15.9b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite172.0ms

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:
59.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
15.0ms
(* n (pow (/ l Om) 2.0))
24.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
65.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series6.6s

Counts
4 → 12
Calls
4 calls:
1.3s
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
138.0ms
(* n (pow (/ l Om) 2.0))
353.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
4.8s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify55.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
014042974
150022579

prune622.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.8b

localize22.0ms

Local error

Found 4 expressions with local error:

5.2b
(* n (pow (/ l Om) (/ 2.0 2)))
5.4b
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
7.6b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
15.9b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

rewrite273.0ms

Algorithm
rewrite-expression-head
Rules
102×add-exp-log
69×prod-exp
51×distribute-rgt-in distribute-lft-in
44×add-sqr-sqrt
42×prod-diff
36×*-un-lft-identity
34×add-cube-cbrt associate-*r/
31×pow1
27×add-cbrt-cube
23×associate-*r*
20×pow-exp associate--l+
17×pow-prod-down
15×unpow-prod-down cbrt-unprod
11×flip3-- flip--
10×pow-to-exp sub-neg times-frac div-exp
8×frac-sub
6×sqrt-div
5×sqrt-pow1 associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×*-commutative
2×sqr-pow
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 196
Calls
4 calls:
15.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
84.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
84.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
80.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

series6.6s

Counts
4 → 12
Calls
4 calls:
170.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
1.4s
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
375.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
4.7s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

simplify71.0ms

Algorithm
egg-herbie
Counts
208 → 208
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
015304203
150023368

prune651.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.6b

regimes914.0ms

Accuracy

33.4% (8.6b remaining)

Error of 26.8b against oracle of 18.2b and baseline of 31.1b

bsearch235.0ms

Steps
ItersRangePoint
8
-1.640344397674756e-308
2.3284295378993804e-306
1.5370107522182492e-307
8
-2.715559418712464e-135
-2.0908746616514593e-138
-1.7917712095234028e-135

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06957
17357
28057
38057

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.0s14806×body80nan
633.0ms9075×body80valid