Details

Time bar (total: 1.1m)

sample169.0ms

Algorithm
intervals
Results
55.0ms299×body80valid
52.0ms521×body80nan

simplify2.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02128
14928
215228
362728
4297828
done500028

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize38.0ms

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*)))))

rewrite381.0ms

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:
15.0ms
(/ (* l l) Om)
64.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
168.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
130.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series8.3s

Counts
4 → 12
Calls
4 calls:
21.0ms
(/ (* l l) Om)
491.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.7s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
6.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify2.6s

Counts
115 → 115
Iterations

Useful iterations: 2 (934.0ms)

IterNodesCost
03183217
19183026
240432706
done50002706

prune707.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 26.9b

localize34.0ms

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*)))))

rewrite772.0ms

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:
36.0ms
(* n (pow (/ l Om) 2.0))
86.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
509.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
128.0ms
(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:
263.0ms
(* n (pow (/ l Om) 2.0))
508.0ms
(* (* 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*))))
7.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify3.1s

Counts
131 → 131
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
03493452
19733239
240882945
done50012945

prune790.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 25.7b

localize58.0ms

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*)))))

rewrite848.0ms

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:
243.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
41.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
322.0ms
(* (* (* 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*))))
231.0ms
(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*)))))

series10.5s

Counts
4 → 12
Calls
4 calls:
594.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
196.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
2.0s
(* (* (* 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*))))
7.7s
(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*)))))

simplify3.0s

Counts
148 → 148
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
03855057
110664054
244933650
done50003650

prune827.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 25.2b

localize39.0ms

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*))))))

rewrite527.0ms

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:
53.0ms
(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
256.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*)))))
65.0ms
(* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*))
143.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*))))))

series9.5s

Counts
4 → 12
Calls
4 calls:
213.0ms
(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
1.9s
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*)))))
415.0ms
(* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*))
6.9s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*))))))

simplify2.9s

Counts
141 → 141
Iterations

Useful iterations: done (2.8s)

IterNodesCost
03704416
110474153
241103731
done50003719

prune875.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.4b

regimes768.0ms

Accuracy

25.8% (9.3b remaining)

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

bsearch265.0ms

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

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03779
15079
done5079

end0.0ms

sample7.2s

Algorithm
intervals
Results
3.1s14816×body80nan
2.0s9208×body80valid