Details

Time bar (total: 37.4s)

sample335.0ms

Algorithm
intervals
Results
33.0ms475×body80nan
20.0ms297×body80valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
02128
14928
215127
360127
4304827
done500127

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.9b

localize29.0ms

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*)))))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
26×add-exp-log
23×pow1
20×add-cube-cbrt *-un-lft-identity associate-*r/ associate-*r* add-cbrt-cube
15×unpow-prod-down
13×times-frac
12×prod-diff pow-prod-down
11×prod-exp
10×distribute-rgt-in flip3-- distribute-lft-in associate--l+ flip--
8×frac-sub cbrt-unprod
6×sqrt-div
4×expm1-log1p-u sub-neg sqrt-pow1 associate-*l* log1p-expm1-u 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 → 132
Calls
4 calls:
15.0ms
(* n (pow (/ l Om) 2.0))
3.0ms
(/ (* l l) Om)
55.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
44.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.1s

Counts
4 → 12
Calls
4 calls:
145.0ms
(* 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*))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify1.6s

Counts
144 → 144
Iterations

Useful iterations: 2 (583.0ms)

IterNodesCost
03893995
110733803
248203329
done50003329

prune657.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 21.9b

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*)))))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
35×add-exp-log
33×*-un-lft-identity
31×add-cube-cbrt
30×prod-diff
25×pow1 associate-*r*
22×associate-*r/
21×distribute-rgt-in distribute-lft-in
20×add-cbrt-cube
19×prod-exp
15×unpow-prod-down
13×pow-prod-down
11×flip3-- flip--
10×times-frac associate--l+ cbrt-unprod
8×frac-sub
6×sub-neg sqrt-div
5×associate-*l*
4×expm1-log1p-u sqrt-pow1 pow-exp log1p-expm1-u 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 → 157
Calls
4 calls:
26.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
15.0ms
(* n (pow (/ l Om) 2.0))
53.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
41.0ms
(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:
356.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
269.0ms
(* n (pow (/ l Om) 2.0))
1.3s
(* (* (* 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*)))))

simplify422.0ms

Counts
169 → 169
Iterations

Useful iterations: done (415.0ms)

IterNodesCost
04425038
112254647
done50014519

prune644.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 20.9b

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*)))))

rewrite223.0ms

Algorithm
rewrite-expression-head
Rules
99×add-exp-log
67×prod-exp
41×add-sqr-sqrt
33×*-un-lft-identity
31×add-cube-cbrt
30×prod-diff
25×pow1 associate-*r*
24×add-cbrt-cube
22×associate-*r/
21×distribute-rgt-in distribute-lft-in
20×pow-exp
15×unpow-prod-down
13×pow-prod-down cbrt-unprod
11×flip3-- flip--
10×pow-to-exp times-frac div-exp associate--l+
8×frac-sub
6×sub-neg sqrt-div
5×associate-*l*
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u 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 → 174
Calls
4 calls:
14.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
83.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
65.0ms
(* (* (* 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*))))
52.0ms
(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:
163.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
365.0ms
(* (* (* 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*))))
4.6s
(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*)))))

simplify442.0ms

Counts
186 → 186
Iterations

Useful iterations: done (435.0ms)

IterNodesCost
04787307
113525730
done50015512

prune697.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 20.0b

localize21.0ms

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*))))))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
41×*-un-lft-identity
39×add-cube-cbrt
30×unpow-prod-down associate-*r/ prod-diff
29×add-exp-log
25×associate-*r*
23×pow1
21×distribute-rgt-in distribute-lft-in associate-*l*
20×times-frac
17×add-cbrt-cube
14×prod-exp
12×pow-prod-down
11×flip3-- flip--
10×associate--l+
8×frac-sub cbrt-unprod unswap-sqr
6×sub-neg sqrt-div
4×expm1-log1p-u sqrt-pow1 pow-exp log1p-expm1-u 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 → 174
Calls
4 calls:
25.0ms
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
14.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
60.0ms
(* (* (* 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*)))))
50.0ms
(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*))))))

series6.4s

Counts
4 → 12
Calls
4 calls:
331.0ms
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
162.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
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*)))))
4.6s
(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*))))))

simplify608.0ms

Counts
186 → 186
Iterations

Useful iterations: done (601.0ms)

IterNodesCost
04906325
112785900
done50015320

prune699.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 20.0b

regimes686.0ms

Accuracy

16.9% (8.2b remaining)

Error of 28.9b against oracle of 20.7b and baseline of 30.6b

bsearch330.0ms

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

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
050156
166154
done66154

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.0s15049×body80nan
622.0ms9215×body80valid