Details

Time bar (total: 44.7s)

sample84.0ms

Algorithm
intervals
Results
33.0ms464×body80nan
18.0ms286×body80valid

simplify1.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02128
14928
214928
357128
4290228
done500128

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.7b

localize19.0ms

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*)))))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
24×add-sqr-sqrt
23×pow1
20×associate-*r/ associate-*r* add-cbrt-cube
16×add-cube-cbrt *-un-lft-identity
15×unpow-prod-down
13×times-frac
12×pow-prod-down
11×prod-exp
10×flip3-- flip--
8×frac-sub cbrt-unprod
6×sqrt-div
4×distribute-rgt-in sub-neg distribute-lft-in sqrt-pow1 associate-*l* associate--l+ 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 → 112
Calls
4 calls:
15.0ms
(* n (pow (/ l Om) 2.0))
3.0ms
(/ (* l l) Om)
50.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
32.0ms
(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:
146.0ms
(* n (pow (/ l Om) 2.0))
18.0ms
(/ (* l l) Om)
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify1.5s

Counts
124 → 124
Iterations

Useful iterations: 2 (358.0ms)

IterNodesCost
03443129
19722953
246342649
done50002649

prune541.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 23.6b

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*)))))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
35×add-exp-log
25×pow1 add-sqr-sqrt associate-*r*
22×associate-*r/
20×add-cbrt-cube
19×prod-exp
17×*-un-lft-identity
15×add-cube-cbrt unpow-prod-down
13×pow-prod-down
11×flip3-- flip--
10×times-frac cbrt-unprod
8×frac-sub
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
5×associate-*l*
4×sqrt-pow1 pow-exp associate--l+ 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 → 119
Calls
4 calls:
23.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
17.0ms
(* n (pow (/ l Om) 2.0))
47.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
34.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.7s

Counts
4 → 12
Calls
4 calls:
347.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
272.0ms
(* 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*)))))

simplify1.7s

Counts
131 → 131
Iterations

Useful iterations: 2 (350.0ms)

IterNodesCost
03493452
19963239
248512945
done50002945

prune527.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 23.3b

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*)))))

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
99×add-exp-log
67×prod-exp
25×pow1 add-sqr-sqrt associate-*r*
24×add-cbrt-cube
22×associate-*r/
20×pow-exp
17×*-un-lft-identity
15×add-cube-cbrt unpow-prod-down
13×pow-prod-down cbrt-unprod
11×flip3-- flip--
10×pow-to-exp times-frac div-exp
8×frac-sub
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
5×associate-*l*
4×sqrt-pow1 associate--l+ 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 → 136
Calls
4 calls:
85.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
15.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
61.0ms
(* (* (* 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*))))
39.0ms
(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*)))))

series6.6s

Counts
4 → 12
Calls
4 calls:
372.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
168.0ms
(* 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*))))
4.8s
(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*)))))

simplify410.0ms

Counts
148 → 148
Iterations

Useful iterations: done (404.0ms)

IterNodesCost
03855057
111224054
done50013948

prune576.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 23.3b

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*)))))

rewrite534.0ms

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
34×associate-*r*
32×add-cbrt-cube
25×pow1
22×add-sqr-sqrt unpow-prod-down *-un-lft-identity associate-*r/
20×add-cube-cbrt
19×cbrt-unprod
18×times-frac
13×pow-prod-down
11×flip3-- flip--
9×cbrt-prod
8×frac-sub
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
4×sqrt-pow1 associate--l+ add-log-exp
3×associate-*l* *-commutative
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 321
Calls
4 calls:
33.0ms
(* (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ l (cbrt Om)) (/ 2.0 2)))
322.0ms
(* (* (* (* 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*))
85.0ms
(* (* (* 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*))))
58.0ms
(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*)))))

series12.2s

Counts
4 → 12
Calls
4 calls:
308.0ms
(* (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2))) (pow (/ l (cbrt Om)) (/ 2.0 2)))
795.0ms
(* (* (* (* 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*))))
8.8s
(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*)))))

simplify906.0ms

Counts
333 → 333
Iterations

Useful iterations: done (879.0ms)

IterNodesCost
064114059
1193312740
done500112503

prune668.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 23.0b

regimes626.0ms

Accuracy

-9.7% (11.7b remaining)

Error of 32.3b against oracle of 20.7b and baseline of 31.3b

bsearch582.0ms

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

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
049272
166222
done66222

end0.0ms

sample2.4s

Algorithm
intervals
Results
949.0ms14778×body80nan
601.0ms9169×body80valid