Details

Time bar (total: 36.4s)

sample332.0ms

Algorithm
intervals
Results
87.0ms541×body80nan
84.0ms282×body80valid

simplify1.1s

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.1b

localize49.0ms

Local error

Found 4 expressions with local error:

6.6b
(* n (pow (/ l Om) 2))
6.8b
(* (* n (pow (/ l Om) 2)) (- U U*))
10.2b
(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
19.0b
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite382.0ms

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:
26.0ms
(* n (pow (/ l Om) 2))
49.0ms
(* (* n (pow (/ l Om) 2)) (- U U*))
135.0ms
(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
164.0ms
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

series2.6s

Counts
4 → 12
Calls
4 calls:
71.0ms
(* n (pow (/ l Om) 2))
161.0ms
(* (* n (pow (/ l Om) 2)) (- U U*))
549.0ms
(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
1.9s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

simplify1.4s

Counts
175 → 175
Iterations
IterNodes
done2002
22002
11216
0407

prune1.5s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 25.0b

localize68.0ms

Local error

Found 4 expressions with local error:

6.8b
(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
8.6b
(* n (/ l Om))
10.2b
(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
19.0b
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

rewrite457.0ms

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:
99.0ms
(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
18.0ms
(* n (/ l Om))
185.0ms
(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
150.0ms
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

series2.6s

Counts
4 → 12
Calls
4 calls:
179.0ms
(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
36.0ms
(* n (/ l Om))
655.0ms
(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

simplify1.7s

Counts
222 → 222
Iterations
IterNodes
done2000
22000
11640
0530

prune2.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 19.9b

localize69.0ms

Local error

Found 4 expressions with local error:

8.2b
(* (/ l Om) (- U U*))
8.6b
(* n (/ l Om))
10.2b
(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (/ l Om)) (* (/ l Om) (- U U*)))))
19.0b
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (/ l Om)) (* (/ l Om) (- U U*))))))

rewrite346.0ms

Algorithm
rewrite-expression-head
Rules
111×associate-*r/
49×add-sqr-sqrt
44×frac-sub
42×flip3-- flip--
39×*-un-lft-identity
38×frac-times
37×add-cube-cbrt
30×prod-diff
27×pow1
24×sqrt-div
23×add-cbrt-cube add-exp-log
21×distribute-rgt-in distribute-lft-in associate-*r*
20×times-frac
17×associate-*l*
14×pow-prod-down
13×associate-*l/
10×prod-exp associate--l+ cbrt-unprod
6×sub-neg
4×expm1-log1p-u sqrt-pow1 insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×*-commutative
2×cbrt-undiv div-exp div-inv
1×pow1/2 sqrt-prod distribute-lft-out-- difference-of-squares
Counts
4 → 206
Calls
4 calls:
23.0ms
(* (/ l Om) (- U U*))
16.0ms
(* n (/ l Om))
164.0ms
(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (/ l Om)) (* (/ l Om) (- U U*)))))
138.0ms
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (/ l Om)) (* (/ l Om) (- U U*))))))

series2.2s

Counts
4 → 12
Calls
4 calls:
102.0ms
(* (/ l Om) (- U U*))
34.0ms
(* n (/ l Om))
550.0ms
(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (/ l Om)) (* (/ l Om) (- U U*)))))
1.5s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (/ l Om)) (* (/ l Om) (- U U*))))))

simplify1.6s

Counts
218 → 218
Iterations
IterNodes
done2000
22000
11596
0526

prune2.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 19.6b

localize61.0ms

Local error

Found 4 expressions with local error:

5.7b
(/ (* l l) Om)
8.2b
(* (/ l Om) (- U U*))
8.6b
(* n (/ l Om))
19.0b
(sqrt (* (* 2 n) (* U (- (- t (* 2 (/ (* l l) Om))) (* (* n (/ l Om)) (* (/ l Om) (- U U*)))))))

rewrite329.0ms

Algorithm
rewrite-expression-head
Rules
81×associate-*r/
46×add-sqr-sqrt
36×*-un-lft-identity
34×add-cube-cbrt
24×sqrt-div
23×times-frac
22×flip3-- frac-sub flip--
21×pow1
20×frac-times
19×add-cbrt-cube add-exp-log
18×associate-*r* prod-diff
16×associate-*l*
11×distribute-rgt-in distribute-lft-in
10×pow-prod-down
7×associate-*l/
5×sqrt-pow1 prod-exp cbrt-unprod
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×associate-/r* div-inv
2×sub-neg *-commutative
1×clear-num frac-2neg pow1/2 sqrt-prod associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 163
Calls
4 calls:
18.0ms
(/ (* l l) Om)
42.0ms
(* (/ l Om) (- U U*))
18.0ms
(* n (/ l Om))
245.0ms
(sqrt (* (* 2 n) (* U (- (- t (* 2 (/ (* l l) Om))) (* (* n (/ l Om)) (* (/ l Om) (- U U*)))))))

series1.5s

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (* l l) Om)
72.0ms
(* (/ l Om) (- U U*))
30.0ms
(* n (/ l Om))
1.4s
(sqrt (* (* 2 n) (* U (- (- t (* 2 (/ (* l l) Om))) (* (* n (/ l Om)) (* (/ l Om) (- U U*)))))))

simplify1.5s

Counts
175 → 175
Iterations
IterNodes
done2002
22002
11452
0473

prune1.6s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 15.6b

regimes1.7s

Accuracy

12.8% (10.1b remaining)

Error of 27.4b against oracle of 17.3b and baseline of 28.9b

bsearch1.1s

Steps
ItersRangePoint
8
1.0908995732703803e+50
2.87158603664453e+52
2.4979801865310678e+51
8
1.5371246682122835e-254
7.884749728391912e-252
7.547628596937392e-254
6
7.749155804819553e-258
7.366069440523844e-257
7.197261728987005e-257
9
-7.38712241445897e-307
9.193220719009415e-305
1.340924181894456e-308
8
-3.0941532946919524e-208
-3.7253137004505654e-211
-6.580462540237744e-211

simplify50.0ms

Iterations
IterNodes
done81
181
063

end0.0ms

sample7.9s

Algorithm
intervals
Results
4.0s15008×body80nan
2.7s9207×body80valid