Details

Time bar (total: 57.0s)

sample442.0ms

Algorithm
intervals
Results
146.0ms298×body80valid
107.0ms475×body80nan

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02128
14928
215228
363228
4391928
done500028

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize59.0ms

Local error

Found 4 expressions with local error:

7.8b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.0b
(/ (* l l) Om)
10.3b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.7b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite406.0ms

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:
74.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
14.0ms
(/ (* l l) Om)
181.0ms
(* (* (* 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*)))))

series10.0s

Counts
4 → 12
Calls
4 calls:
537.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
35.0ms
(/ (* l l) Om)
1.8s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify620.0ms

Counts
115 → 115
Iterations

Useful iterations: done (615.0ms)

IterNodesCost
03183217
19913034
done50002742

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 22.7b

localize50.0ms

Local error

Found 4 expressions with local error:

6.0b
(* n (pow (/ l Om) 2.0))
7.8b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.3b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.7b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite403.0ms

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:
28.0ms
(* n (pow (/ l Om) 2.0))
61.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
154.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
154.0ms
(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:
191.0ms
(* n (pow (/ l Om) 2.0))
527.0ms
(* (* 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*))))
7.3s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify527.0ms

Counts
131 → 131
Iterations

Useful iterations: done (522.0ms)

IterNodesCost
03493452
110233256
done50012971

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.8b

localize56.0ms

Local error

Found 4 expressions with local error:

5.8b
(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
6.0b
(* n (pow (/ l Om) 2.0))
7.8b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
18.7b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite418.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log add-sqr-sqrt associate-*r/
25×associate-*r*
21×pow1
18×*-un-lft-identity
16×add-cube-cbrt
15×unpow-prod-down
14×prod-exp
13×add-cbrt-cube
11×flip3-- flip--
10×times-frac pow-prod-down
8×frac-sub
7×associate-*l*
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
5×sqrt-pow1 cbrt-unprod unswap-sqr
4×pow-exp associate--l+ add-log-exp
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 → 117
Calls
4 calls:
130.0ms
(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
50.0ms
(* n (pow (/ l Om) 2.0))
68.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
164.0ms
(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:
1.3s
(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
191.0ms
(* n (pow (/ l Om) 2.0))
535.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.9s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify2.3s

Counts
129 → 129
Iterations

Useful iterations: done (2.3s)

IterNodesCost
03333092
19352905
244982724
done50002716

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 18.0b

localize53.0ms

Local error

Found 4 expressions with local error:

4.8b
(* n (pow (/ l Om) (/ 2.0 2)))
5.8b
(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
7.8b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
18.7b
(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*))))))

rewrite831.0ms

Algorithm
rewrite-expression-head
Rules
92×add-exp-log
62×prod-exp
28×add-sqr-sqrt associate-*r/
25×associate-*r*
21×pow1
20×pow-exp
18×*-un-lft-identity
17×add-cbrt-cube
16×add-cube-cbrt
15×unpow-prod-down
11×flip3-- flip--
10×pow-to-exp times-frac div-exp pow-prod-down
8×frac-sub cbrt-unprod
7×associate-*l*
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
5×sqrt-pow1 unswap-sqr
4×associate--l+ add-log-exp
3×*-commutative
2×sqr-pow
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 134
Calls
4 calls:
53.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
257.0ms
(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
222.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
286.0ms
(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*))))))

series7.6s

Counts
4 → 12
Calls
4 calls:
176.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
914.0ms
(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
389.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
6.1s
(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*))))))

simplify416.0ms

Counts
146 → 146
Iterations

Useful iterations: done (411.0ms)

IterNodesCost
03694637
110463838
done50003429

prune762.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 17.7b

regimes974.0ms

Accuracy

11.5% (10.6b remaining)

Error of 29.1b against oracle of 18.6b and baseline of 30.5b

bsearch122.0ms

Steps
ItersRangePoint
7
8.638393346241565e+119
1.8600849311099558e+121
1.2577210802851978e+120

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03471
14671
done4671

end0.0ms

sample4.6s

Algorithm
intervals
Results
2.2s14815×body80nan
1.0s9208×body80valid