Details

Time bar (total: 34.7s)

sample419.0ms

Algorithm
intervals
Results
39.0ms303×body80valid
27.0ms436×body80nan

simplify122.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04914
115314
265214
3362414
4500214
done500214

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize23.0ms

Local error

Found 4 expressions with local error:

5.5b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
6.0b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.0b
(/ (* l l) Om)
19.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite268.0ms

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:
121.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
44.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.0ms
(/ (* l l) Om)
88.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.5s

Counts
4 → 12
Calls
4 calls:
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
372.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
19.0ms
(/ (* l l) Om)
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify126.0ms

Counts
115 → 115
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
09371544
147641385
250011385
done50011385

prune434.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.4b

localize23.0ms

Local error

Found 4 expressions with local error:

5.3b
(* n (pow (/ l Om) 2.0))
5.5b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
6.0b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
19.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite271.0ms

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))
121.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
46.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
76.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.6s

Counts
4 → 12
Calls
4 calls:
144.0ms
(* n (pow (/ l Om) 2.0))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
368.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify38.0ms

Counts
131 → 131
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09871668
150011508
done50011508

prune495.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 18.6b

localize19.0ms

Local error

Found 4 expressions with local error:

5.3b
(* n (pow (/ l Om) 2.0))
5.5b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
6.0b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
19.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite272.0ms

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))
120.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
44.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
79.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.7s

Counts
4 → 12
Calls
4 calls:
148.0ms
(* 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*))))
362.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify39.0ms

Counts
131 → 131
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09871664
150011508
done50011508

prune476.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 18.6b

localize23.0ms

Local error

Found 4 expressions with local error:

4.3b
(* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*))))
5.3b
(* n (pow (/ l Om) 2.0))
5.5b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*)))) (cbrt (- U U*)))))
19.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*)))) (cbrt (- U U*))))))

rewrite594.0ms

Algorithm
rewrite-expression-head
Rules
246×associate-*r/
228×cbrt-div
168×flip3-- flip--
116×frac-times
104×frac-sub
58×associate-*l/
54×add-exp-log sqrt-div
33×prod-exp
28×pow1
23×add-cbrt-cube
22×add-sqr-sqrt
21×associate-*r*
15×unpow-prod-down pow-prod-down cbrt-unprod
14×add-cube-cbrt *-un-lft-identity
10×times-frac
6×pow-exp
5×associate-*l*
4×distribute-rgt-in sub-neg distribute-lft-in sqrt-pow1 associate--l+ add-log-exp unswap-sqr
3×pow-to-exp div-exp *-commutative
2×sqr-pow
1×pow1/2 sqrt-prod div-inv
Counts
4 → 221
Calls
4 calls:
73.0ms
(* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*))))
24.0ms
(* n (pow (/ l Om) 2.0))
285.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*)))) (cbrt (- U U*)))))
190.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*)))) (cbrt (- U U*))))))

series6.6s

Counts
4 → 12
Calls
4 calls:
247.0ms
(* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*))))
156.0ms
(* n (pow (/ l Om) 2.0))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*)))) (cbrt (- U U*)))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*)))) (cbrt (- U U*))))))

simplify96.0ms

Counts
233 → 233
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
018358044
150027730
done50027730

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 18.6b

regimes505.0ms

Accuracy

24.8% (7.4b remaining)

Error of 29.0b against oracle of 21.5b and baseline of 31.4b

bsearch225.0ms

Steps
ItersRangePoint
8
1.6397680076746226e+69
5.136335325147995e+72
4.089192710274501e+70
9
-4.488326589292748e-67
-7.23706028840217e-73
-1.2841079021870823e-68

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05547
16447
26747
36747
done6747

end0.0ms

sample2.6s

Algorithm
intervals
Results
910.0ms15130×body80nan
546.0ms9212×body80valid