Details

Time bar (total: 47.4s)

sample572.0ms

Algorithm
intervals
Results
357.0ms521×body80nan
45.0ms299×body80valid

simplify3.2s

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: 36.8b

localize52.0ms

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*)))))

rewrite467.0ms

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:
16.0ms
(/ (* l l) Om)
49.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
241.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
155.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.9s

Counts
4 → 12
Calls
4 calls:
24.0ms
(/ (* l l) Om)
555.0ms
(* (* 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*)))))

simplify2.9s

Counts
115 → 115
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
03183217
19183026
240432706
done50002706

prune670.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 26.9b

localize22.0ms

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 (/ 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*)))))

rewrite480.0ms

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:
35.0ms
(* n (pow (/ l Om) 2.0))
58.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
249.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
126.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series7.8s

Counts
4 → 12
Calls
4 calls:
153.0ms
(* n (pow (/ l Om) 2.0))
414.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.4s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
5.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify1.8s

Counts
131 → 131
Iterations

Useful iterations: 2 (710.0ms)

IterNodesCost
03493452
19733239
240882945
done50012945

prune472.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 25.7b

localize24.0ms

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 (/ l Om)))) (* (* (* 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 (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite465.0ms

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:
140.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
25.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
174.0ms
(* (* (* 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*))))
119.0ms
(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*)))))

series6.8s

Counts
4 → 12
Calls
4 calls:
360.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
163.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
1.2s
(* (* (* 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*))))
5.1s
(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*)))))

simplify1.8s

Counts
148 → 148
Iterations

Useful iterations: 2 (723.0ms)

IterNodesCost
03855057
110664054
244933650
done50003650

prune501.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 25.2b

localize27.0ms

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

rewrite344.0ms

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:
26.0ms
(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
153.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*)))))
46.0ms
(* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*))
112.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*))))))

series6.5s

Counts
4 → 12
Calls
4 calls:
147.0ms
(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
1.3s
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*)))))
360.0ms
(* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*))
4.7s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*))))))

simplify1.6s

Counts
141 → 141
Iterations

Useful iterations: done (1.6s)

IterNodesCost
03704416
110474153
241103731
done50003719

prune441.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.4b

regimes475.0ms

bsearch2.0ms