Details

Time bar (total: 43.9s)

sample342.0ms

Algorithm
intervals
Results
32.0ms464×body80nan
19.0ms286×body80valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
02128
14928
215127
360327
4316227
done500027

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.0b

localize22.0ms

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*)))))

rewrite120.0ms

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:
14.0ms
(* n (pow (/ l Om) 2.0))
3.0ms
(/ (* l l) Om)
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*)))))

series6.1s

Counts
4 → 12
Calls
4 calls:
138.0ms
(* 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*))))
4.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify426.0ms

Counts
144 → 144
Iterations

Useful iterations: done (420.0ms)

IterNodesCost
03893995
110903803
done50003705

prune637.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 24.0b

localize23.0ms

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*)))))

rewrite138.0ms

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:
24.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
14.0ms
(* 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*))))
40.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.5s

Counts
4 → 12
Calls
4 calls:
363.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
146.0ms
(* n (pow (/ l Om) 2.0))
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*)))))

simplify458.0ms

Counts
169 → 169
Iterations

Useful iterations: done (452.0ms)

IterNodesCost
04425038
112444647
done50004531

prune727.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 23.7b

localize24.0ms

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*)))))

rewrite217.0ms

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:
82.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
14.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
64.0ms
(* (* (* 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*))))
49.0ms
(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*)))))

series6.3s

Counts
4 → 12
Calls
4 calls:
355.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
154.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
1.3s
(* (* (* 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*))))
4.6s
(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*)))))

simplify464.0ms

Counts
186 → 186
Iterations

Useful iterations: done (457.0ms)

IterNodesCost
04787307
113705730
done50005624

prune646.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 23.7b

localize30.0ms

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*)))))

rewrite525.0ms

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:
31.0ms
(* (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ l (cbrt Om)) (/ 2.0 2)))
306.0ms
(* (* (* (* 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*))
86.0ms
(* (* (* 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*))))
66.0ms
(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*)))))

series12.6s

Counts
4 → 12
Calls
4 calls:
344.0ms
(* (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ l (cbrt Om)) (/ 2.0 2)))
849.0ms
(* (* (* (* 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*))
2.4s
(* (* (* 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*))))
9.0s
(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*)))))

simplify1.2s

Counts
371 → 371
Iterations

Useful iterations: done (1.1s)

IterNodesCost
073417193
1218715696
done500115553

prune860.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 23.3b

regimes578.0ms

Accuracy

-10.5% (10.9b remaining)

Error of 32.3b against oracle of 21.4b and baseline of 31.3b

bsearch652.0ms

Steps
ItersRangePoint
9
4.804100632602528e-67
2.7611622660763156e-60
5.912036692986568e-67
8
1.5334997071314855e-133
2.5003733336451863e-129
2.1783139283433974e-130
9
2.1272389128491144e-249
1.478630379486068e-241
1.2760462906237903e-247
10
-2.477443934184605e-149
-2.070907975864449e-166
-2.5000808834023845e-158

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
050278
167222
done67222

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.0s14778×body80nan
636.0ms9169×body80valid