Details

Time bar (total: 1.2m)

sample343.0ms

Algorithm
intervals
Results
100.0ms484×body80nan
73.0ms281×body80valid

simplify3.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
02128
14928
215228
362728
4297828
done500028

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize27.0ms

Local error

Found 4 expressions with local error:

6.0b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.3b
(/ (* l l) Om)
12.2b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.4b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite440.0ms

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:
65.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
13.0ms
(/ (* l l) Om)
167.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
189.0ms
(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:
633.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
44.0ms
(/ (* l l) Om)
2.0s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify3.0s

Counts
115 → 115
Iterations

Useful iterations: 2 (975.0ms)

IterNodesCost
03183217
19193026
240512706
done50012706

prune818.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 23.5b

localize42.0ms

Local error

Found 4 expressions with local error:

4.0b
(* n (pow (/ l Om) 2.0))
6.0b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.2b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.4b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite501.0ms

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:
30.0ms
(* n (pow (/ l Om) 2.0))
89.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
256.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
120.0ms
(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:
219.0ms
(* n (pow (/ l Om) 2.0))
561.0ms
(* (* 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*))))
7.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify2.8s

Counts
131 → 131
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
03493452
19733239
240882945
done50012945

prune750.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 21.9b

localize41.0ms

Local error

Found 4 expressions with local error:

5.8b
(* n (pow (/ l Om) (/ 2.0 2)))
6.0b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
12.2b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
20.4b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite796.0ms

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)))
225.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
323.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
202.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series10.3s

Counts
4 → 12
Calls
4 calls:
287.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
605.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.9s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
7.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify2.9s

Counts
148 → 148
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
03855057
110664054
244913650
done50003650

prune887.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 21.1b

localize65.0ms

Local error

Found 4 expressions with local error:

4.0b
(- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
6.0b
(* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
12.2b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
20.4b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
239×add-exp-log
187×prod-exp
38×pow-exp
32×add-cbrt-cube
26×associate-*r/
25×pow1 cbrt-unprod
19×pow-to-exp div-exp
16×flip3-- flip--
13×pow-prod-down
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 associate--r+
3×diff-log
2×associate-*l* *-commutative
1×associate--l- pow1/2 sqrt-prod distribute-lft-out-- difference-of-squares
Counts
4 → 150
Calls
4 calls:
167.0ms
(- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
923.0ms
(* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
557.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
400.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series11.6s

Counts
4 → 12
Calls
4 calls:
1.2s
(- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
607.0ms
(* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
2.2s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt 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 (/ l Om)))) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify3.3s

Counts
162 → 162
Iterations

Useful iterations: 2 (1.5s)

IterNodesCost
03877967
110837361
249475142
done50015142

prune767.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 20.6b

regimes907.0ms

Accuracy

20.5% (8.3b remaining)

Error of 29.1b against oracle of 20.8b and baseline of 31.3b

bsearch200.0ms

Steps
ItersRangePoint
8
2.5965101593636474e-46
7.511447638869724e-43
6.289693439117107e-43
2
-4.75157920309255e+15
-4110355191848148.5
-4433626581462758.0

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
041112
156112
done56112

end0.0ms

sample5.1s

Algorithm
intervals
Results
1.8s15019×body80nan
1.8s9134×body80valid