Details

Time bar (total: 40.1s)

sample334.0ms

Algorithm
intervals
Results
33.0ms475×body80nan
20.0ms297×body80valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02128
14928
214928
356928
4282328
done500128

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize21.0ms

Local error

Found 4 expressions with local error:

6.1b
(* n (pow (/ l Om) 2.0))
8.9b
(/ (* l l) Om)
9.5b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
24×add-sqr-sqrt
23×pow1
20×associate-*r/ associate-*r* add-cbrt-cube
16×add-cube-cbrt *-un-lft-identity
15×unpow-prod-down
13×times-frac
12×pow-prod-down
11×prod-exp
10×flip3-- flip--
8×frac-sub cbrt-unprod
6×sqrt-div
4×distribute-rgt-in sub-neg distribute-lft-in sqrt-pow1 associate-*l* associate--l+ add-log-exp unswap-sqr
3×div-exp associate-/r*
2×cbrt-undiv pow-exp *-commutative div-inv sqr-pow
1×pow-to-exp frac-2neg pow1/2 clear-num sqrt-prod associate-/l*
Counts
4 → 112
Calls
4 calls:
15.0ms
(* n (pow (/ l Om) 2.0))
3.0ms
(/ (* l l) Om)
47.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
38.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.2s

Counts
4 → 12
Calls
4 calls:
139.0ms
(* n (pow (/ l Om) 2.0))
19.0ms
(/ (* l l) Om)
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify1.4s

Counts
124 → 124
Iterations

Useful iterations: 2 (554.0ms)

IterNodesCost
03443129
19582953
239392649
done50002649

prune569.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 22.0b

localize19.0ms

Local error

Found 4 expressions with local error:

5.7b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.1b
(* n (pow (/ l Om) 2.0))
9.5b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite127.0ms

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:
23.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
17.0ms
(* n (pow (/ l Om) 2.0))
47.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
34.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.6s

Counts
4 → 12
Calls
4 calls:
346.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
137.0ms
(* n (pow (/ l Om) 2.0))
1.4s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify1.5s

Counts
131 → 131
Iterations

Useful iterations: 2 (614.0ms)

IterNodesCost
03493452
19873239
241882945
done50002945

prune538.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 20.7b

localize21.0ms

Local error

Found 4 expressions with local error:

5.4b
(* n (pow (/ l Om) (/ 2.0 2)))
5.7b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
9.5b
(* (* (* 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*))))
20.2b
(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*)))))

rewrite207.0ms

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:
15.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
84.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
59.0ms
(* (* (* 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*))))
42.0ms
(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*)))))

series6.5s

Counts
4 → 12
Calls
4 calls:
160.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
358.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.3s
(* (* (* 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*))))
4.7s
(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*)))))

simplify1.6s

Counts
148 → 148
Iterations

Useful iterations: 2 (700.0ms)

IterNodesCost
03855057
111144054
246013650
done50003650

prune566.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 20.0b

localize20.0ms

Local error

Found 4 expressions with local error:

4.0b
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
5.4b
(* n (pow (/ l Om) (/ 2.0 2)))
9.5b
(* (* (* 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*)))))
20.2b
(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*))))))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
30×unpow-prod-down associate-*r/
29×add-exp-log
25×*-un-lft-identity associate-*r*
23×pow1 add-cube-cbrt
21×associate-*l*
20×times-frac
17×add-cbrt-cube
14×prod-exp
12×pow-prod-down
11×flip3-- flip--
8×frac-sub cbrt-unprod unswap-sqr
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
4×sqrt-pow1 pow-exp associate--l+ add-log-exp sqr-pow
3×*-commutative
2×pow-to-exp div-exp div-inv
1×pow1/2 sqrt-prod distribute-lft-out-- difference-of-squares
Counts
4 → 136
Calls
4 calls:
23.0ms
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
15.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
57.0ms
(* (* (* 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*)))))
41.0ms
(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*))))))

series6.5s

Counts
4 → 12
Calls
4 calls:
319.0ms
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
158.0ms
(* 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*)))))
4.7s
(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*))))))

simplify1.5s

Counts
148 → 148
Iterations

Useful iterations: 2 (649.0ms)

IterNodesCost
03974455
110804209
244123507
done50003507

prune597.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 19.6b

regimes772.0ms

Accuracy

16.5% (8.5b remaining)

Error of 28.9b against oracle of 20.4b and baseline of 30.6b

bsearch349.0ms

Steps
ItersRangePoint
8
6.666268870843101e+37
2.980559139220902e+41
2.856592318713015e+41
7
-1.1470207047355208e+50
-5.137084903285435e+48
-4.482863757784701e+49
9
-1.4524365819500653e+216
-8.163952542228318e+208
-7.718602062440974e+211

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
049131
165129
done65129

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.1s15049×body80nan
643.0ms9215×body80valid