Details

Time bar (total: 58.8s)

sample290.0ms

Algorithm
intervals
Results
132.0ms478×body80nan
45.0ms300×body80valid

simplify4.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
021737
149737
2148737
3599737
42710737
done5006737

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize84.0ms

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*)))))

rewrite314.0ms

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:
44.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
11.0ms
(/ (* l l) Om)
139.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
112.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.5s

Counts
4 → 12
Calls
4 calls:
557.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
27.0ms
(/ (* l l) Om)
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*)))))

simplify4.1s

Counts
115 → 115
Iterations

Useful iterations: done (4.1s)

IterNodesCost
031875102
198867294
2431766374
done500565954

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 24.8b

localize49.0ms

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*)))))

rewrite274.0ms

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:
33.0ms
(* n (pow (/ l Om) 2.0))
36.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
126.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
75.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series7.1s

Counts
4 → 12
Calls
4 calls:
154.0ms
(* n (pow (/ l Om) 2.0))
387.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
5.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify3.0s

Counts
131 → 131
Iterations

Useful iterations: done (3.0s)

IterNodesCost
034985114
1101477074
2396976714
done500275974

prune792.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 22.9b

localize34.0ms

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*))))))

rewrite234.0ms

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:
30.0ms
(* (pow (/ l Om) 2.0) (- U U*))
32.0ms
(* n (* (pow (/ l Om) 2.0) (- U U*)))
100.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))
67.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))

series7.2s

Counts
4 → 12
Calls
4 calls:
344.0ms
(* (pow (/ l Om) 2.0) (- U U*))
364.0ms
(* n (* (pow (/ l Om) 2.0) (- U U*)))
1.6s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))

simplify2.8s

Counts
141 → 141
Iterations

Useful iterations: done (2.8s)

IterNodesCost
035695293
1101686806
2424786246
done500185506

prune813.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 22.2b

localize57.0ms

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*)))))))

rewrite498.0ms

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:
44.0ms
(* (pow (/ l Om) 2.0) (- U U*))
153.0ms
(* (* (cbrt n) (cbrt n)) (* (cbrt n) (* (pow (/ l Om) 2.0) (- U U*))))
197.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* (pow (/ l Om) 2.0) (- U U*))))))
94.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* (pow (/ l Om) 2.0) (- U U*)))))))

series7.2s

Counts
4 → 12
Calls
4 calls:
335.0ms
(* (pow (/ l Om) 2.0) (- U U*))
397.0ms
(* (* (cbrt n) (cbrt n)) (* (cbrt n) (* (pow (/ l Om) 2.0) (- U U*))))
1.4s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* (pow (/ l Om) 2.0) (- U U*))))))
5.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* (pow (/ l Om) 2.0) (- U U*)))))))

simplify3.2s

Counts
161 → 161
Iterations

Useful iterations: done (3.2s)

IterNodesCost
0398124762
11172115385
24845113958
done5003113555

prune855.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 22.2b

regimes823.0ms

Accuracy

10.1% (10.3b remaining)

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

bsearch143.0ms

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

simplify9.0ms

Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
0311188
1411188
done411188

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.8s15130×body80nan
1.2s9159×body80valid