Details

Time bar (total: 1.3m)

sample181.0ms

Algorithm
intervals
Results
68.0ms478×body80nan
55.0ms300×body80valid

simplify3.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
021737
149737
2148737
3599737
42710737
done5006737

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize46.0ms

Local error

Found 4 expressions with local error:

8.1b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.5b
(/ (* l l) Om)
11.8b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.4b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite309.0ms

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×associate-*r* frac-sub add-cube-cbrt
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
4×sqrt-pow1 associate--l+ add-log-exp
3×associate-/r* times-frac div-exp
2×cbrt-undiv associate-*l* pow-exp *-commutative
1×pow-to-exp clear-num frac-2neg pow1/2 sqrt-prod div-inv associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 103
Calls
4 calls:
50.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
15.0ms
(/ (* l l) Om)
166.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
74.0ms
(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:
529.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
28.0ms
(/ (* l l) Om)
1.9s
(* (* (* 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*)))))

simplify3.9s

Counts
115 → 115
Iterations

Useful iterations: done (3.9s)

IterNodesCost
031875102
198867294
2431766374
done500565954

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 24.8b

localize58.0ms

Local error

Found 4 expressions with local error:

6.0b
(* n (pow (/ l Om) 2.0))
8.1b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
11.8b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.4b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite683.0ms

Algorithm
rewrite-expression-head
Rules
35×add-exp-log
25×add-sqr-sqrt pow1 associate-*r*
22×associate-*r/
20×add-cbrt-cube
19×prod-exp
17×*-un-lft-identity
15×unpow-prod-down add-cube-cbrt
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:
20.0ms
(* n (pow (/ l Om) 2.0))
57.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
139.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
460.0ms
(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:
231.0ms
(* n (pow (/ l Om) 2.0))
552.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.8s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify4.3s

Counts
131 → 131
Iterations

Useful iterations: done (4.3s)

IterNodesCost
034985114
1101477074
2396976714
done500275974

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 22.9b

localize54.0ms

Local error

Found 4 expressions with local error:

4.0b
(* (pow (/ l Om) 2.0) (- U U*))
6.5b
(* n (* (pow (/ l Om) 2.0) (- U U*)))
11.8b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))
18.4b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))

rewrite353.0ms

Algorithm
rewrite-expression-head
Rules
35×add-exp-log
34×associate-*r/
25×add-sqr-sqrt pow1
21×associate-*l*
20×add-cbrt-cube
19×prod-exp
17×*-un-lft-identity
15×unpow-prod-down add-cube-cbrt
14×distribute-rgt-in distribute-lft-in
13×pow-prod-down
12×flip3-- flip--
10×sub-neg times-frac cbrt-unprod
9×associate-*r*
8×frac-sub
6×sqrt-div
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 → 129
Calls
4 calls:
48.0ms
(* (pow (/ l Om) 2.0) (- U U*))
68.0ms
(* n (* (pow (/ l Om) 2.0) (- U U*)))
141.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))
90.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))

series9.8s

Counts
4 → 12
Calls
4 calls:
473.0ms
(* (pow (/ l Om) 2.0) (- U U*))
516.0ms
(* 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*)))))
6.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))

simplify4.5s

Counts
141 → 141
Iterations

Useful iterations: done (4.5s)

IterNodesCost
035695293
1101686806
2424786246
done500185506

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 22.2b

localize106.0ms

Local error

Found 4 expressions with local error:

4.0b
(* (pow (/ l Om) 2.0) (- U U*))
4.1b
(* (* (cbrt n) (cbrt n)) (* (cbrt n) (* (pow (/ l Om) 2.0) (- U U*))))
11.8b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* (pow (/ l Om) 2.0) (- U U*))))))
18.4b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* (pow (/ l Om) 2.0) (- U U*)))))))

rewrite588.0ms

Algorithm
rewrite-expression-head
Rules
69×add-exp-log
46×prod-exp
44×associate-*r/
35×pow1
30×distribute-rgt-in distribute-lft-in
26×add-cbrt-cube
24×add-sqr-sqrt
22×cbrt-unprod
20×pow-prod-down
19×associate-*l*
16×*-un-lft-identity
15×unpow-prod-down
14×sub-neg add-cube-cbrt
12×flip3-- flip--
10×times-frac
9×associate-*r*
8×frac-sub
6×sqrt-div pow-exp
4×sqrt-pow1 associate--l+ add-log-exp unswap-sqr
3×pow-to-exp div-exp *-commutative
2×sqr-pow
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 149
Calls
4 calls:
54.0ms
(* (pow (/ l Om) 2.0) (- U U*))
150.0ms
(* (* (cbrt n) (cbrt n)) (* (cbrt n) (* (pow (/ l Om) 2.0) (- U U*))))
232.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* (pow (/ l Om) 2.0) (- U U*))))))
145.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* (pow (/ l Om) 2.0) (- U U*)))))))

series10.5s

Counts
4 → 12
Calls
4 calls:
515.0ms
(* (pow (/ l Om) 2.0) (- U U*))
535.0ms
(* (* (cbrt n) (cbrt n)) (* (cbrt n) (* (pow (/ l Om) 2.0) (- U U*))))
2.1s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* (pow (/ l Om) 2.0) (- U U*))))))
7.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* (pow (/ l Om) 2.0) (- U U*)))))))

simplify5.1s

Counts
161 → 161
Iterations

Useful iterations: done (5.1s)

IterNodesCost
0398124762
11172115385
24845113958
done5003113555

prune1.4s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 22.2b

regimes1.4s

Accuracy

10.1% (10.3b remaining)

Error of 32.0b against oracle of 21.8b and baseline of 33.2b

bsearch198.0ms

Steps
ItersRangePoint
9
1.0581550330740528e-262
1.9737143529480668e-255
9.479964460137454e-259

simplify11.0ms

Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
0311188
1411188
done411188

end0.0ms

sample6.5s

Algorithm
intervals
Results
3.6s15130×body80nan
1.6s9159×body80valid