Details

Time bar (total: 59.7s)

sample306.0ms

Algorithm
intervals
Results
107.0ms521×body80nan
45.0ms299×body80valid

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
02128
14928
215228
362728
4297828
done500028

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize63.0ms

Local error

Found 4 expressions with local error:

7.3b
(/ (* l l) Om)
7.7b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.4b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite436.0ms

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:
21.0ms
(/ (* l l) Om)
65.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
220.0ms
(* (* (* 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*)))))

series10.0s

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ (* l l) Om)
552.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
2.0s
(* (* (* 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*)))))

simplify2.7s

Counts
115 → 115
Iterations

Useful iterations: 2 (874.0ms)

IterNodesCost
03183217
19183026
240432706
done50002706

prune697.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 26.9b

localize59.0ms

Local error

Found 4 expressions with local error:

5.7b
(* n (pow (/ l Om) 2.0))
7.7b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.4b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite521.0ms

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:
34.0ms
(* n (pow (/ l Om) 2.0))
80.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
235.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
167.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.4s

Counts
4 → 12
Calls
4 calls:
281.0ms
(* n (pow (/ l Om) 2.0))
538.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
2.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.3s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify2.7s

Counts
131 → 131
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
03503452
19733239
240782945
done50002945

prune745.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 25.8b

localize62.0ms

Local error

Found 4 expressions with local error:

7.7b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
8.0b
(* n (pow (/ l Om) (/ 2.0 2)))
12.4b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
20.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite800.0ms

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:
234.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
33.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
323.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
203.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series9.8s

Counts
4 → 12
Calls
4 calls:
436.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
216.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
1.9s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
7.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify1.9s

Counts
148 → 148
Iterations

Useful iterations: 2 (769.0ms)

IterNodesCost
03865057
110664054
244663650
done50003650

prune588.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 25.7b

localize33.0ms

Local error

Found 4 expressions with local error:

5.7b
(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
6.3b
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))
7.7b
(* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))
20.8b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))))))

rewrite445.0ms

Algorithm
rewrite-expression-head
Rules
38×add-exp-log
31×pow1
24×add-sqr-sqrt associate-*r/
23×add-cbrt-cube
21×prod-exp
19×associate-*r*
17×pow-prod-down
16×distribute-rgt-in *-un-lft-identity distribute-lft-in
15×unpow-prod-down
14×add-cube-cbrt
12×cbrt-unprod
11×flip3-- flip--
10×times-frac associate-*l/
9×associate-*l*
8×sub-neg associate--l+ frac-sub
6×sqrt-div
5×sqrt-pow1
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 → 125
Calls
4 calls:
29.0ms
(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
211.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))
52.0ms
(* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))
147.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))))))

series7.2s

Counts
4 → 12
Calls
4 calls:
160.0ms
(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
1.4s
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))
333.0ms
(* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))
5.3s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))))))

simplify1.4s

Counts
137 → 137
Iterations

Useful iterations: done (1.4s)

IterNodesCost
03594263
110054004
238093582
done50013570

prune474.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 22.4b

regimes621.0ms

Accuracy

25.7% (9.3b remaining)

Error of 27.8b against oracle of 18.5b and baseline of 31.0b

bsearch167.0ms

Steps
ItersRangePoint
10
-5.10070569146941e-304
1.0382457741670337e-301
3.2675070946382715e-308

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03879
15079
done5079

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.6s9208×body80valid
1.5s14816×body80nan