Details

Time bar (total: 1.0m)

sample353.0ms

Algorithm
intervals
Results
117.0ms521×body80nan
46.0ms299×body80valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 2 (113.0ms)

IterNodesCost
02128
17328
269427
done500027

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize51.0ms

Local error

Found 4 expressions with local error:

7.3b
(/ (* l l) Om)
7.7b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.4b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite515.0ms

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 log1p-expm1-u add-log-exp
3×times-frac div-exp associate-/r*
2×cbrt-undiv associate-*l* pow-exp *-commutative
1×pow-to-exp frac-2neg pow1/2 clear-num sqrt-prod div-inv associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 141
Calls
4 calls:
15.0ms
(/ (* l l) Om)
68.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
234.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
188.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.5s

Counts
4 → 12
Calls
4 calls:
22.0ms
(/ (* l l) Om)
617.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
2.0s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify2.4s

Counts
153 → 153
Iterations

Useful iterations: done (2.4s)

IterNodesCost
04114799
137814354
done50004292

prune969.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 26.8b

localize50.0ms

Local error

Found 4 expressions with local error:

5.7b
(* n (pow (/ l Om) 2.0))
7.7b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.4b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite457.0ms

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:
38.0ms
(* n (pow (/ l Om) 2.0))
67.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
189.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
155.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series11.0s

Counts
4 → 12
Calls
4 calls:
258.0ms
(* n (pow (/ l Om) 2.0))
559.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
2.1s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
8.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify1.6s

Counts
169 → 169
Iterations

Useful iterations: done (1.5s)

IterNodesCost
04435038
done50014568

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 25.7b

localize53.0ms

Local error

Found 4 expressions with local error:

7.7b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
8.0b
(* n (pow (/ l Om) (/ 2.0 2)))
12.4b
(* (* (* 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*))))
20.8b
(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*)))))

rewrite819.0ms

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:
254.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
53.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
273.0ms
(* (* (* 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*))))
231.0ms
(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*)))))

series10.7s

Counts
4 → 12
Calls
4 calls:
625.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
290.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
2.1s
(* (* (* 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*))))
7.7s
(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*)))))

simplify1.2s

Counts
186 → 186
Iterations

Useful iterations: done (1.2s)

IterNodesCost
04797307
done50005807

prune1.4s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 24.5b

localize60.0ms

Local error

Found 4 expressions with local error:

14.3b
(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
14.3b
(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
14.3b
(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
20.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* (cbrt (* n (pow (/ l Om) (/ 2.0 2)))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite870.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1
10×associate-*r/
6×sqrt-div pow-prod-down
5×flip3-- flip--
4×add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity sqrt-pow1 frac-sub add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-prod pow1/3
1×pow1/2 sqrt-prod
Counts
4 → 54
Calls
4 calls:
8.0ms
(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
9.0ms
(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
13.0ms
(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
838.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* (cbrt (* n (pow (/ l Om) (/ 2.0 2)))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series8.3s

Counts
4 → 12
Calls
4 calls:
247.0ms
(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
241.0ms
(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
247.0ms
(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
7.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* (cbrt (* n (pow (/ l Om) (/ 2.0 2)))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify738.0ms

Counts
66 → 66
Iterations

Useful iterations: done (736.0ms)

IterNodesCost
01862430
111722244
done50001589

prune391.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 23.4b

regimes720.0ms

Accuracy

-15% (12.5b remaining)

Error of 33.0b against oracle of 20.5b and baseline of 31.4b

bsearch322.0ms

Steps
ItersRangePoint
7
-4.3001252255487655e-17
-2.4032652355907974e-19
-3.2513477547904614e-17
9
-3.5168607798453615e+179
-9.114963810516401e+173
-5.211532218213158e+175

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
046223
160223
done60223

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.9s14816×body80nan
1.4s9208×body80valid