Details

Time bar (total: 42.0s)

sample483.0ms

Algorithm
intervals
Results
226.0ms422×body80nan
103.0ms294×body80valid

simplify1.7s

Counts
1 → 1
Iterations
IterNodes
done2001
42001
3693
2157
150
021

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.7b

localize49.0ms

Local error

Found 4 expressions with local error:

6.6b
(* (* n (pow (/ l Om) 2)) (- U U*))
8.9b
(/ (* l l) Om)
13.2b
(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
17.5b
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite380.0ms

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 insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* times-frac div-exp
2×cbrt-undiv associate-*l* pow-exp *-commutative
1×pow-to-exp clear-num frac-2neg pow1/2 sqrt-prod div-inv associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 145
Calls
4 calls:
36.0ms
(* (* n (pow (/ l Om) 2)) (- U U*))
16.0ms
(/ (* l l) Om)
164.0ms
(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
159.0ms
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

series2.6s

Counts
4 → 12
Calls
4 calls:
183.0ms
(* (* n (pow (/ l Om) 2)) (- U U*))
34.0ms
(/ (* l l) Om)
597.0ms
(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
1.8s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

simplify1.3s

Counts
157 → 157
Iterations
IterNodes
done2002
22002
11165
0376

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 22.0b

localize81.0ms

Local error

Found 4 expressions with local error:

6.6b
(* n (pow (/ l Om) 2))
6.6b
(* (* n (pow (/ l Om) 2)) (- U U*))
13.2b
(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
17.5b
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite370.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
35×add-exp-log
33×*-un-lft-identity
31×add-cube-cbrt
30×prod-diff
26×associate-*r*
25×pow1
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* unswap-sqr
4×expm1-log1p-u sqrt-pow1 pow-exp insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×pow-to-exp div-exp unpow2 sqr-pow
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 163
Calls
4 calls:
28.0ms
(* n (pow (/ l Om) 2))
56.0ms
(* (* n (pow (/ l Om) 2)) (- U U*))
173.0ms
(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
108.0ms
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

series2.6s

Counts
4 → 12
Calls
4 calls:
92.0ms
(* n (pow (/ l Om) 2))
166.0ms
(* (* n (pow (/ l Om) 2)) (- U U*))
589.0ms
(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
1.8s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

simplify1.7s

Counts
175 → 175
Iterations
IterNodes
done2002
22002
11216
0406

prune1.5s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 21.1b

localize66.0ms

Local error

Found 4 expressions with local error:

4.7b
(* n (/ l Om))
6.6b
(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
13.2b
(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
17.5b
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

rewrite583.0ms

Algorithm
rewrite-expression-head
Rules
104×associate-*r/
47×add-cbrt-cube add-exp-log
45×frac-times
44×flip3-- frac-sub flip--
37×add-sqr-sqrt
34×pow1
32×*-un-lft-identity
30×prod-diff associate-*l/ add-cube-cbrt
25×prod-exp cbrt-unprod
24×sqrt-div
21×distribute-rgt-in distribute-lft-in associate-*r*
19×pow-prod-down
10×times-frac associate--l+
6×cbrt-undiv sub-neg div-exp
5×associate-*l*
4×expm1-log1p-u sqrt-pow1 insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×unswap-sqr
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 210
Calls
4 calls:
17.0ms
(* n (/ l Om))
152.0ms
(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
233.0ms
(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
172.0ms
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

series2.6s

Counts
4 → 12
Calls
4 calls:
29.0ms
(* n (/ l Om))
177.0ms
(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
640.0ms
(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
1.8s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

simplify1.9s

Counts
222 → 222
Iterations
IterNodes
done2000
22000
11637
0530

prune2.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 19.2b

localize61.0ms

Local error

Found 4 expressions with local error:

5.5b
(/ (* (* (* n l) (/ l Om)) (- U U*)) Om)
6.7b
(* (* (* n l) (/ l Om)) (- U U*))
13.2b
(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (/ (* (* (* n l) (/ l Om)) (- U U*)) Om)))
17.5b
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (/ (* (* (* n l) (/ l Om)) (- U U*)) Om))))

rewrite492.0ms

Algorithm
rewrite-expression-head
Rules
66×prod-diff
56×add-cbrt-cube add-exp-log
52×add-sqr-sqrt *-un-lft-identity
48×add-cube-cbrt
39×distribute-rgt-in distribute-lft-in
32×pow1
28×prod-exp cbrt-unprod
21×times-frac
18×pow-prod-down associate-*r/
10×cbrt-undiv div-exp associate-*r* associate--l+
8×flip3-- flip--
7×div-inv
6×sub-neg
5×associate-/l/
4×expm1-log1p-u frac-times sqrt-pow1 sqrt-div frac-sub insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r*
2×associate-*l* associate-*l/ *-commutative distribute-lft-out-- difference-of-squares
1×clear-num frac-2neg pow1/2 sqrt-prod associate-/l*
Counts
4 → 200
Calls
4 calls:
117.0ms
(/ (* (* (* n l) (/ l Om)) (- U U*)) Om)
103.0ms
(* (* (* n l) (/ l Om)) (- U U*))
147.0ms
(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (/ (* (* (* n l) (/ l Om)) (- U U*)) Om)))
117.0ms
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (/ (* (* (* n l) (/ l Om)) (- U U*)) Om))))

series2.9s

Counts
4 → 12
Calls
4 calls:
185.0ms
(/ (* (* (* n l) (/ l Om)) (- U U*)) Om)
165.0ms
(* (* (* n l) (/ l Om)) (- U U*))
624.0ms
(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (/ (* (* (* n l) (/ l Om)) (- U U*)) Om)))
1.9s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (/ (* (* (* n l) (/ l Om)) (- U U*)) Om))))

simplify1.9s

Counts
212 → 212
Iterations
IterNodes
done2001
22001
11513
0479

prune2.0s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 18.7b

regimes2.1s

Accuracy

19.4% (9.2b remaining)

Error of 28.6b against oracle of 19.4b and baseline of 30.8b

bsearch1.6s

Steps
ItersRangePoint
11
5.066505836662404e+85
9.270364086845479e+107
3.2878796761193827e+96
8
5.332643125243965e-209
3.9061345690755997e-206
3.336337607476201e-207
10
-3.635463953268134e-283
-2.6761002384274148e-295
-3.1769776407334526e-289
7
-7.023611533287395e+72
-2.996488415338156e+70
-4.4451804611309516e+70

simplify38.0ms

Iterations
IterNodes
done81
181
061

end0.0ms

sample9.3s

Algorithm
intervals
Results
4.8s14844×body80nan
2.8s9206×body80valid