Details

Time bar (total: 57.4s)

sample149.0ms

Algorithm
intervals
Results
44.0ms481×body80nan
35.0ms298×body80valid

simplify3.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02128
14928
215228
362728
4297828
done500028

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize33.0ms

Local error

Found 4 expressions with local error:

6.9b
(* n (pow (/ l Om) 2.0))
8.0b
(/ (* l l) Om)
10.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite363.0ms

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:
30.0ms
(* n (pow (/ l Om) 2.0))
10.0ms
(/ (* l l) Om)
174.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
141.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series8.5s

Counts
4 → 12
Calls
4 calls:
219.0ms
(* n (pow (/ l Om) 2.0))
20.0ms
(/ (* l l) Om)
1.6s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
6.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify2.4s

Counts
124 → 124
Iterations

Useful iterations: 2 (858.0ms)

IterNodesCost
03443129
19462953
238472649
done50002649

prune675.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 24.4b

localize18.0ms

Local error

Found 4 expressions with local error:

6.4b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.9b
(* n (pow (/ l Om) 2.0))
10.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite379.0ms

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:
49.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
35.0ms
(* n (pow (/ l Om) 2.0))
172.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
115.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.3s

Counts
4 → 12
Calls
4 calls:
610.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
220.0ms
(* n (pow (/ l Om) 2.0))
2.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify3.1s

Counts
131 → 131
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
03493452
19733239
240912945
done50012945

prune697.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.9b

localize44.0ms

Local error

Found 4 expressions with local error:

13.7b
(cbrt (/ l Om))
13.7b
(cbrt (/ l Om))
13.7b
(cbrt (/ l Om))
19.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×times-frac
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
14×pow1
10×associate-*r/
6×sqrt-div pow-prod-down
5×flip3-- flip--
4×add-exp-log sqrt-pow1 frac-sub add-cbrt-cube add-log-exp
3×cbrt-div pow1/3 div-inv
1×pow1/2 sqrt-prod
Counts
4 → 85
Calls
4 calls:
2.0ms
(cbrt (/ l Om))
2.0ms
(cbrt (/ l Om))
2.0ms
(cbrt (/ l Om))
198.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

series7.6s

Counts
4 → 12
Calls
4 calls:
105.0ms
(cbrt (/ l Om))
99.0ms
(cbrt (/ l Om))
109.0ms
(cbrt (/ l Om))
7.3s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

simplify1.4s

Counts
97 → 97
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02282019
15901867
223721798
done50001775

prune819.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.7b

localize28.0ms

Local error

Found 4 expressions with local error:

19.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (cbrt (* (* n (pow (/ l Om) 2.0)) (- U U*))) (cbrt (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (cbrt (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))
27.0b
(cbrt (* (* n (pow (/ l Om) 2.0)) (- U U*)))
27.0b
(cbrt (* (* n (pow (/ l Om) 2.0)) (- U U*)))
27.0b
(cbrt (* (* n (pow (/ l Om) 2.0)) (- U U*)))

rewrite684.0ms

Algorithm
rewrite-expression-head
Rules
184×associate-*r/
114×cbrt-div
84×flip3-- flip--
56×frac-times
54×sqrt-div
52×frac-sub
28×associate-*l/
14×pow1
6×pow-prod-down
4×add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity sqrt-pow1 add-cbrt-cube add-log-exp
3×cbrt-prod pow1/3
1×pow1/2 sqrt-prod
Counts
4 → 100
Calls
4 calls:
536.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (cbrt (* (* n (pow (/ l Om) 2.0)) (- U U*))) (cbrt (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (cbrt (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))
35.0ms
(cbrt (* (* n (pow (/ l Om) 2.0)) (- U U*)))
38.0ms
(cbrt (* (* n (pow (/ l Om) 2.0)) (- U U*)))
61.0ms
(cbrt (* (* n (pow (/ l Om) 2.0)) (- U U*)))

series9.3s

Counts
4 → 12
Calls
4 calls:
7.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (cbrt (* (* n (pow (/ l Om) 2.0)) (- U U*))) (cbrt (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (cbrt (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))
524.0ms
(cbrt (* (* n (pow (/ l Om) 2.0)) (- U U*)))
484.0ms
(cbrt (* (* n (pow (/ l Om) 2.0)) (- U U*)))
504.0ms
(cbrt (* (* n (pow (/ l Om) 2.0)) (- U U*)))

simplify1.9s

Counts
112 → 112
Iterations

Useful iterations: done (1.9s)

IterNodesCost
05149591
112428837
237838055
done50007997

prune737.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 21.7b

regimes726.0ms

Accuracy

15.5% (8.3b remaining)

Error of 30.1b against oracle of 21.8b and baseline of 31.6b

bsearch205.0ms

Steps
ItersRangePoint
10
5.9142685482905006e+106
1.1318126295060305e+120
4.212962541612979e+117

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03474
14574
done4574

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.4s14744×body80nan
874.0ms9169×body80valid