Details

Time bar (total: 59.2s)

sample542.0ms

Algorithm
intervals
Results
122.0ms476×body80nan
118.0ms293×body80valid

simplify2.1s

Counts
1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize52.0ms

Local error

Found 4 expressions with local error:

7.3b
(* n (pow (/ l Om) 2.0))
8.1b
(/ (* l l) Om)
10.9b
(* (* (* 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*)))))

rewrite414.0ms

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:
32.0ms
(* n (pow (/ l Om) 2.0))
10.0ms
(/ (* l l) Om)
192.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
166.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.5s

Counts
4 → 12
Calls
4 calls:
238.0ms
(* n (pow (/ l Om) 2.0))
20.0ms
(/ (* l l) Om)
2.0s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.3s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify2.3s

Counts
124 → 124

prune866.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 20.9b

localize55.0ms

Local error

Found 4 expressions with local error:

6.1b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.3b
(* n (pow (/ l Om) 2.0))
10.9b
(* (* (* 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*)))))

rewrite429.0ms

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:
70.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
35.0ms
(* n (pow (/ l Om) 2.0))
195.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
123.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.2s

Counts
4 → 12
Calls
4 calls:
588.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
259.0ms
(* n (pow (/ l Om) 2.0))
2.0s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify578.0ms

Counts
131 → 131

prune850.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 19.5b

localize30.0ms

Local error

Found 4 expressions with local error:

4.9b
(* n (pow (/ l Om) (/ 2.0 2)))
6.1b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.9b
(* (* (* 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*)))))

rewrite734.0ms

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:
38.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
193.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
286.0ms
(* (* (* 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*))))
210.0ms
(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*)))))

series8.8s

Counts
4 → 12
Calls
4 calls:
181.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
449.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.6s
(* (* (* 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*))))
6.6s
(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*)))))

simplify474.0ms

Counts
148 → 148

prune609.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.4b

localize40.0ms

Local error

Found 4 expressions with local error:

6.0b
(* (* (* 2.0 n) (- t (- (* 2.0 (/ l (/ Om l))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U)
6.1b
(* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))
7.3b
(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
18.5b
(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (/ l (/ Om l))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U) 1))

rewrite249.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
25×associate-*r*
23×add-exp-log
19×*-un-lft-identity
17×add-cube-cbrt add-cbrt-cube
16×unpow-prod-down
15×pow1
11×prod-exp
10×times-frac associate-*l*
8×cbrt-unprod
7×pow-prod-down
5×sqrt-prod unswap-sqr
4×associate-*r/ add-log-exp sqr-pow
3×*-commutative
2×distribute-rgt-in sub-neg rem-sqrt-square flip3-- distribute-lft-in associate-*l/ pow-exp flip--
1×distribute-lft-neg-out distribute-lft-neg-in pow-to-exp neg-mul-1 distribute-rgt-neg-in sqrt-pow1 pow1/2 div-exp div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 106
Calls
4 calls:
176.0ms
(* (* (* 2.0 n) (- t (- (* 2.0 (/ l (/ Om l))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U)
31.0ms
(* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))
27.0ms
(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
11.0ms
(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (/ l (/ Om l))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U) 1))

series12.2s

Counts
4 → 12
Calls
4 calls:
1.3s
(* (* (* 2.0 n) (- t (- (* 2.0 (/ l (/ Om l))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U)
308.0ms
(* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))
148.0ms
(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
10.4s
(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (/ l (/ Om l))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U) 1))

simplify1.3s

Counts
118 → 118

prune474.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.9b

regimes627.0ms

Accuracy

8.1% (11.6b remaining)

Error of 30.2b against oracle of 18.6b and baseline of 31.2b

bsearch673.0ms

Steps
ItersRangePoint
7
1.288531225676383e+262
3.6137232352492556e+263
1.976343330438959e+262
10
960649127616.5507
5.170311694882416e+21
4.361934755255584e+20
6
1.4341566573600888e-226
1.1818197341596392e-225
5.824775899044275e-226
8
-5.704069418746261e-199
-1.2080201743982823e-201
-6.212072691974284e-200
9
-2.3988152764038513e+205
-2.292627744121757e+200
-2.2140464730475112e+201

simplify729.0ms

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.5s14796×body80nan
1.5s9256×body80valid