Details

Time bar (total: 43.3s)

sample85.0ms

Algorithm
intervals
Results
31.0ms464×body80nan
19.0ms286×body80valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
02128
14928
215127
360127
4304827
done500127

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.0b

localize24.0ms

Local error

Found 4 expressions with local error:

6.4b
(* n (pow (/ l Om) 2.0))
7.3b
(/ (* l l) Om)
10.5b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.5b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite119.0ms

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--
8×frac-sub cbrt-unprod
6×sqrt-div
4×expm1-log1p-u sub-neg sqrt-pow1 associate-*l* log1p-expm1-u 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 → 132
Calls
4 calls:
15.0ms
(* n (pow (/ l Om) 2.0))
4.0ms
(/ (* l l) Om)
54.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
42.0ms
(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:
138.0ms
(* n (pow (/ l Om) 2.0))
18.0ms
(/ (* l l) Om)
1.5s
(* (* (* 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*)))))

simplify1.5s

Counts
144 → 144
Iterations

Useful iterations: 2 (681.0ms)

IterNodesCost
03893995
110733803
244973329
done50003329

prune614.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 24.0b

localize18.0ms

Local error

Found 4 expressions with local error:

4.4b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.4b
(* n (pow (/ l Om) 2.0))
10.5b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.5b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite143.0ms

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:
27.0ms
(* (* 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 (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
42.0ms
(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*))
163.0ms
(* n (pow (/ l Om) 2.0))
1.2s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify771.0ms

Counts
169 → 169
Iterations

Useful iterations: done (765.0ms)

IterNodesCost
04425038
112254647
done50004151

prune589.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 23.7b

localize20.0ms

Local error

Found 4 expressions with local error:

4.4b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
5.9b
(* n (pow (/ l Om) (/ 2.0 2)))
10.5b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
21.5b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite230.0ms

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+
8×frac-sub
6×sub-neg sqrt-div
5×associate-*l*
4×expm1-log1p-u sqrt-pow1 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 → 174
Calls
4 calls:
88.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
15.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
65.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
54.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series6.7s

Counts
4 → 12
Calls
4 calls:
375.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
162.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
1.4s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify477.0ms

Counts
186 → 186
Iterations

Useful iterations: done (467.0ms)

IterNodesCost
04787307
113525730
done50015512

prune833.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 23.7b

localize34.0ms

Local error

Found 4 expressions with local error:

4.0b
(* (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ l (cbrt Om)) (/ 2.0 2)))
4.4b
(* (* (* (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.5b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
21.5b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite556.0ms

Algorithm
rewrite-expression-head
Rules
1007×add-exp-log
775×prod-exp
322×pow-exp
171×div-exp
111×pow-to-exp
40×rec-exp 1-exp
38×add-sqr-sqrt *-un-lft-identity
36×add-cube-cbrt
34×associate-*r*
32×add-cbrt-cube
30×prod-diff
25×pow1
22×unpow-prod-down associate-*r/
21×distribute-rgt-in distribute-lft-in
19×cbrt-unprod
18×times-frac
13×pow-prod-down
11×flip3-- flip--
10×associate--l+
9×cbrt-prod
8×frac-sub
6×sub-neg sqrt-div
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp
3×associate-*l* *-commutative
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 359
Calls
4 calls:
33.0ms
(* (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ l (cbrt Om)) (/ 2.0 2)))
325.0ms
(* (* (* (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
92.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
67.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series11.7s

Counts
4 → 12
Calls
4 calls:
297.0ms
(* (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ l (cbrt Om)) (/ 2.0 2)))
751.0ms
(* (* (* (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
2.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
8.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify568.0ms

Counts
371 → 371
Iterations

Useful iterations: done (535.0ms)

IterNodesCost
073417193
1216415684
done500015459

prune814.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 23.3b

regimes499.0ms

Accuracy

-0.9% (9.5b remaining)

Error of 30.9b against oracle of 21.4b and baseline of 30.8b

bsearch565.0ms

Steps
ItersRangePoint
9
4.804100632602528e-67
2.7611622660763156e-60
4.869273342036883e-67
8
1.5334997071314855e-133
2.5003733336451863e-129
2.4609494505594687e-129
7
-3.8858002769966305e+157
-2.392683991111876e+156
-2.635288091030918e+156

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
058183
179181
done79181

end0.0ms

sample2.5s

Algorithm
intervals
Results
970.0ms14778×body80nan
604.0ms9169×body80valid