Details

Time bar (total: 39.9s)

sample350.0ms

Algorithm
intervals
Results
38.0ms556×body80nan
22.0ms295×body80valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02128
14928
214928
356928
4282328
done500128

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize28.0ms

Local error

Found 4 expressions with local error:

7.1b
(/ (* l l) Om)
8.1b
(* n (pow (/ l Om) 2.0))
10.8b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.5b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite110.0ms

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:
4.0ms
(/ (* l l) Om)
15.0ms
(* n (pow (/ l Om) 2.0))
52.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
33.0ms
(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:
19.0ms
(/ (* l l) Om)
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*)))))

simplify1.3s

Counts
124 → 124
Iterations

Useful iterations: 2 (554.0ms)

IterNodesCost
03443129
19592953
239502649
done50012649

prune543.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 23.3b

localize19.0ms

Local error

Found 4 expressions with local error:

6.5b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.1b
(* n (pow (/ l Om) 2.0))
10.8b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.5b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* 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*))
15.0ms
(* n (pow (/ l Om) 2.0))
51.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
30.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.7s

Counts
4 → 12
Calls
4 calls:
359.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
139.0ms
(* n (pow (/ l Om) 2.0))
1.4s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify1.4s

Counts
131 → 131
Iterations

Useful iterations: 2 (621.0ms)

IterNodesCost
03503452
19873239
241672945
done50002945

prune515.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.2b

localize26.0ms

Local error

Found 4 expressions with local error:

4.4b
(* n (pow (/ l Om) (/ 2.0 2)))
6.5b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.8b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
18.5b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite210.0ms

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:
17.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
84.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
62.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
40.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series6.5s

Counts
4 → 12
Calls
4 calls:
165.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
368.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify1.5s

Counts
148 → 148
Iterations

Useful iterations: 2 (693.0ms)

IterNodesCost
03865057
111144054
245883650
done50003650

prune554.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.7b

localize26.0ms

Local error

Found 4 expressions with local error:

4.4b
(* n (pow (/ l Om) (/ 2.0 2)))
7.5b
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
10.8b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
18.5b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
30×unpow-prod-down associate-*r/
29×add-exp-log
25×*-un-lft-identity associate-*r*
23×pow1 add-cube-cbrt
21×associate-*l*
20×times-frac
17×add-cbrt-cube
14×prod-exp
12×pow-prod-down
11×flip3-- flip--
8×frac-sub cbrt-unprod unswap-sqr
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
4×sqrt-pow1 pow-exp associate--l+ add-log-exp sqr-pow
3×*-commutative
2×pow-to-exp div-exp div-inv
1×pow1/2 sqrt-prod distribute-lft-out-- difference-of-squares
Counts
4 → 136
Calls
4 calls:
15.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
22.0ms
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
59.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
36.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

series6.5s

Counts
4 → 12
Calls
4 calls:
160.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
324.0ms
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* 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 (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

simplify1.5s

Counts
148 → 148
Iterations

Useful iterations: 2 (653.0ms)

IterNodesCost
03984455
110794209
243893507
done50003507

prune616.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 20.7b

regimes517.0ms

Accuracy

-1.9% (9.8b remaining)

Error of 31.2b against oracle of 21.4b and baseline of 31.0b

bsearch421.0ms

Steps
ItersRangePoint
10
5.761168895017816e+38
6.252508614851994e+54
5.849773459839704e+38
8
5.196301700147731e-22
1.1700142316632325e-17
1.1504183261425661e-17
6
-2.466953028791217e-290
-2.983722748916224e-291
-6.0596639631783474e-291
6
-3.258792823672545e-139
-7.7838102355166905e-140
-2.0815983574246957e-139

simplify11.0ms

Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
052191
171154
done71154

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.0s15073×body80nan
640.0ms9245×body80valid