Details

Time bar (total: 54.3s)

sample236.0ms

Algorithm
intervals
Results
93.0ms503×body80nan
34.0ms288×body80valid

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
02128
14928
215228
363228
4391928
done500028

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize30.0ms

Local error

Found 4 expressions with local error:

6.9b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.3b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
11.1b
(/ (* l l) Om)
22.5b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite478.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
25×pow1
23×add-cbrt-cube
22×associate-*r/
16×prod-exp
13×pow-prod-down
11×flip3-- flip--
10×add-sqr-sqrt *-un-lft-identity cbrt-unprod
8×add-cube-cbrt associate-*r* frac-sub
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
4×sqrt-pow1 associate--l+ 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 → 103
Calls
4 calls:
68.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
237.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
22.0ms
(/ (* l l) Om)
142.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.7s

Counts
4 → 12
Calls
4 calls:
500.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.9s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
25.0ms
(/ (* l l) Om)
7.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify584.0ms

Counts
115 → 115
Iterations

Useful iterations: done (575.0ms)

IterNodesCost
03183217
19883034
done50012744

prune836.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 23.4b

localize36.0ms

Local error

Found 4 expressions with local error:

4.7b
(* n (pow (/ l Om) 2.0))
6.9b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.3b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
22.5b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite458.0ms

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:
47.0ms
(* n (pow (/ l Om) 2.0))
60.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
220.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
122.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.1s

Counts
4 → 12
Calls
4 calls:
198.0ms
(* n (pow (/ l Om) 2.0))
524.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.9s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify575.0ms

Counts
131 → 131
Iterations

Useful iterations: done (567.0ms)

IterNodesCost
03503452
110243247
done50012971

prune802.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 22.4b

localize34.0ms

Local error

Found 4 expressions with local error:

4.7b
(* n (pow (/ l Om) 2.0))
5.6b
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.9b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
22.5b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite454.0ms

Algorithm
rewrite-expression-head
Rules
38×add-exp-log
34×associate-*r/
31×pow1
24×add-sqr-sqrt
23×associate-*r* add-cbrt-cube
21×prod-exp
18×distribute-rgt-in distribute-lft-in
17×pow-prod-down
16×*-un-lft-identity
15×unpow-prod-down
14×add-cube-cbrt
12×cbrt-unprod
11×flip3-- flip--
10×sub-neg times-frac
8×associate--l+ frac-sub
6×sqrt-div
5×sqrt-pow1 associate-*l*
4×pow-exp 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 → 129
Calls
4 calls:
27.0ms
(* n (pow (/ l Om) 2.0))
198.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
78.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
146.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series9.5s

Counts
4 → 12
Calls
4 calls:
246.0ms
(* n (pow (/ l Om) 2.0))
1.8s
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
530.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.9s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify659.0ms

Counts
141 → 141
Iterations

Useful iterations: done (654.0ms)

IterNodesCost
03683780
110793573
done50013231

prune789.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 18.3b

localize40.0ms

Local error

Found 4 expressions with local error:

3.7b
(- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U*)))
6.9b
(* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U*))
8.3b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U*))))
22.5b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U*)))))

rewrite829.0ms

Algorithm
rewrite-expression-head
Rules
58×add-exp-log
40×prod-exp
32×pow1
26×associate-*r/
25×add-cbrt-cube
19×cbrt-unprod
18×pow-prod-down
16×flip3-- flip--
12×frac-sub
10×sub-neg
9×add-log-exp
8×distribute-rgt-in add-sqr-sqrt *-un-lft-identity distribute-lft-in associate-*r*
6×add-cube-cbrt sqrt-div associate--l+
4×sqrt-pow1 pow-exp associate--r+
3×diff-log
2×pow-to-exp div-exp associate-*l* *-commutative
1×associate--l- pow1/2 sqrt-prod distribute-lft-out-- difference-of-squares
Counts
4 → 117
Calls
4 calls:
82.0ms
(- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U*)))
288.0ms
(* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U*))
281.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U*))))
173.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U*)))))

series8.5s

Counts
4 → 12
Calls
4 calls:
782.0ms
(- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U*)))
422.0ms
(* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U*))
1.6s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U*))))
5.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U*)))))

simplify403.0ms

Counts
129 → 129
Iterations

Useful iterations: done (395.0ms)

IterNodesCost
03315268
110394976
done50013991

prune592.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 18.0b

regimes596.0ms

Accuracy

22.8% (9.6b remaining)

Error of 28.1b against oracle of 18.5b and baseline of 30.9b

bsearch150.0ms

Steps
ItersRangePoint
9
1.3470057887584473e-271
6.123564548615608e-263
2.0656859127974356e-269

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03468
14568
done4568

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.9s14686×body80nan
1.3s9214×body80valid