Details

Time bar (total: 36.3s)

sample359.0ms

Algorithm
intervals
Results
40.0ms554×body80nan
19.0ms281×body80valid

simplify130.0ms

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: 35.5b

localize23.0ms

Local error

Found 4 expressions with local error:

6.1b
(* n (pow (/ l Om) 2.0))
9.4b
(/ (* l l) Om)
10.4b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.7b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
26×add-exp-log
23×pow1
20×add-cube-cbrt *-un-lft-identity associate-*r/ associate-*r* add-cbrt-cube
15×unpow-prod-down
13×times-frac
12×prod-diff pow-prod-down
11×prod-exp
10×distribute-rgt-in flip3-- distribute-lft-in associate--l+ flip--
frac-sub cbrt-unprod
sqrt-div
expm1-log1p-u sub-neg sqrt-pow1 associate-*l* log1p-expm1-u add-log-exp unswap-sqr
div-exp associate-/r*
cbrt-undiv pow-exp *-commutative div-inv sqr-pow
pow-to-exp frac-2neg pow1/2 clear-num sqrt-prod associate-/l*
Counts
4 → 132
Calls
4 calls:
15.0ms
(* n (pow (/ l Om) 2.0))
4.0ms
(/ (* l l) Om)
59.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
45.0ms
(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:
140.0ms
(* n (pow (/ l Om) 2.0))
25.0ms
(/ (* 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*)))))

simplify47.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
010791948
150011746

prune613.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 24.1b

localize20.0ms

Local error

Found 4 expressions with local error:

5.8b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.1b
(* n (pow (/ l Om) 2.0))
10.4b
(* (* (* 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*)))))

rewrite150.0ms

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
frac-sub
sub-neg sqrt-div
associate-*l*
expm1-log1p-u sqrt-pow1 pow-exp log1p-expm1-u add-log-exp unswap-sqr
*-commutative
pow-to-exp div-exp sqr-pow
pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 157
Calls
4 calls:
28.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
15.0ms
(* n (pow (/ l Om) 2.0))
53.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
47.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.5s

Counts
4 → 12
Calls
4 calls:
359.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
138.0ms
(* 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*))))
4.7s
(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
169 → 169
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012272461
150022136

prune584.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 22.2b

localize21.0ms

Local error

Found 4 expressions with local error:

5.0b
(* n (pow (/ l Om) (/ 2.0 2)))
5.8b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.4b
(* (* (* 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*))))
19.7b
(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*)))))

rewrite234.0ms

Algorithm
rewrite-expression-head
Rules
99×add-exp-log
67×prod-exp
41×add-sqr-sqrt
33×*-un-lft-identity
31×add-cube-cbrt
30×prod-diff
25×pow1 associate-*r*
24×add-cbrt-cube
22×associate-*r/
21×distribute-rgt-in distribute-lft-in
20×pow-exp
15×unpow-prod-down
13×pow-prod-down cbrt-unprod
11×flip3-- flip--
10×pow-to-exp times-frac div-exp associate--l+
frac-sub
sub-neg sqrt-div
associate-*l*
expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp unswap-sqr
*-commutative
sqr-pow
pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 174
Calls
4 calls:
17.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
88.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
69.0ms
(* (* (* 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*))))
52.0ms
(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*)))))

series6.5s

Counts
4 → 12
Calls
4 calls:
161.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
359.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.3s
(* (* (* 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*))))
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*)))))

simplify58.0ms

Algorithm
egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013533511
150012841

prune649.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 22.2b

localize28.0ms

Local error

Found 4 expressions with local error:

5.0b
(* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0))
5.8b
(* (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.4b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
19.7b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite386.0ms

Algorithm
rewrite-expression-head
Rules
509×add-exp-log
387×prod-exp
180×pow-exp
85×div-exp
65×pow-to-exp
39×add-sqr-sqrt *-un-lft-identity
37×add-cube-cbrt associate-*r*
34×unpow-prod-down
32×add-cbrt-cube
30×rec-exp 1-exp prod-diff
25×pow1
22×associate-*r/
21×distribute-rgt-in distribute-lft-in times-frac
19×cbrt-unprod
13×pow-prod-down
11×flip3-- flip--
10×associate--l+
frac-sub
sub-neg sqrt-div
expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp sqr-pow
associate-*l* *-commutative
pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 282
Calls
4 calls:
27.0ms
(* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0))
201.0ms
(* (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (pow (/ l Om) (/ 2.0 2))) (- U U*))
77.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
61.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series9.4s

Counts
4 → 12
Calls
4 calls:
173.0ms
(* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0))
514.0ms
(* (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.9s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
6.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify78.0ms

Algorithm
egg-herbie
Counts
294 → 294
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
018524897
150024417

prune875.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.2b

regimes397.0ms

Accuracy

17.2% (8.6b remaining)

Error of 30.5b against oracle of 21.9b and baseline of 32.3b

bsearch326.0ms

Steps
ItersRangePoint
6
4.9269745033409015e+61
3.770559472124491e+62
1.9059710833939732e+62
10
6.062267330111416e-234
3.7991955889564722e-224
1.0445431991481594e-227
6
1.935864971986492e-290
1.0652670669251518e-289
3.992601817896191e-290

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
05568
15834
26134
36134

end0.0ms

sample2.5s

Algorithm
intervals
Results
994.0ms15130×body80nan
603.0ms9216×body80valid