Details

Time bar (total: 39.3s)

sample97.0ms

Algorithm
intervals
Results
39.0ms556×body80nan
20.0ms295×body80valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
02128
14928
215127
360327
4316227
done500027

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.8b

localize19.0ms

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*)))))

rewrite117.0ms

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:
4.0ms
(/ (* l l) Om)
16.0ms
(* n (pow (/ l Om) 2.0))
49.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
43.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.4s

Counts
4 → 12
Calls
4 calls:
24.0ms
(/ (* l l) Om)
139.0ms
(* 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*))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify407.0ms

Counts
144 → 144
Iterations

Useful iterations: done (402.0ms)

IterNodesCost
03893995
110913803
done50003705

prune712.0ms

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*)))))

rewrite154.0ms

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:
30.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
25.0ms
(* n (pow (/ l Om) 2.0))
49.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
43.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series7.0s

Counts
4 → 12
Calls
4 calls:
362.0ms
(* (* 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 (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
5.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify485.0ms

Counts
169 → 169
Iterations

Useful iterations: done (477.0ms)

IterNodesCost
04435038
112424647
done50024519

prune763.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.2b

localize27.0ms

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*)))))

rewrite220.0ms

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:
14.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
83.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
65.0ms
(* (* (* 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*))))
49.0ms
(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*)))))

series6.8s

Counts
4 → 12
Calls
4 calls:
163.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
366.0ms
(* (* (* 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*))))
4.9s
(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*)))))

simplify518.0ms

Counts
186 → 186
Iterations

Useful iterations: done (511.0ms)

IterNodesCost
04797307
113685730
done50005624

prune796.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 20.3b

localize21.0ms

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*))))))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
41×*-un-lft-identity
39×add-cube-cbrt
30×unpow-prod-down associate-*r/ prod-diff
29×add-exp-log
25×associate-*r*
23×pow1
21×distribute-rgt-in distribute-lft-in associate-*l*
20×times-frac
17×add-cbrt-cube
14×prod-exp
12×pow-prod-down
11×flip3-- flip--
10×associate--l+
8×frac-sub cbrt-unprod unswap-sqr
6×sub-neg sqrt-div
4×expm1-log1p-u sqrt-pow1 pow-exp log1p-expm1-u 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 → 174
Calls
4 calls:
15.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
24.0ms
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
82.0ms
(* (* (* 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*)))))
51.0ms
(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*))))))

series7.3s

Counts
4 → 12
Calls
4 calls:
164.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
341.0ms
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
1.4s
(* (* (* 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*)))))
5.4s
(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*))))))

simplify488.0ms

Counts
186 → 186
Iterations

Useful iterations: done (481.0ms)

IterNodesCost
04916325
112955900
done50015336

prune1.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 20.3b

regimes756.0ms

Accuracy

-1.6% (10.6b remaining)

Error of 31.2b against oracle of 20.7b and baseline of 31.0b

bsearch451.0ms

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

simplify10.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
051191
169154
done69154

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.1s15073×body80nan
711.0ms9245×body80valid