Details

Time bar (total: 32.8s)

sample92.0ms

Algorithm
intervals
Results
27.0ms442×body80nan
22.0ms291×body80valid

simplify118.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04914
115314
265214
3362414
4500214
done500214

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.4b

localize23.0ms

Local error

Found 4 expressions with local error:

7.0b
(/ (* l l) Om)
7.9b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite254.0ms

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:
9.0ms
(/ (* l l) Om)
44.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
120.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
77.0ms
(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:
19.0ms
(/ (* l l) Om)
371.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* 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*)))))

simplify122.0ms

Counts
115 → 115
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09371544
147641385
250011385
done50011385

prune458.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 25.2b

localize20.0ms

Local error

Found 4 expressions with local error:

5.5b
(* n (pow (/ l Om) 2.0))
7.9b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite275.0ms

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))
45.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
122.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
78.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.8s

Counts
4 → 12
Calls
4 calls:
158.0ms
(* n (pow (/ l Om) 2.0))
386.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify43.0ms

Counts
131 → 131
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
09871664
150011508
done50011508

prune503.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 24.3b

localize20.0ms

Local error

Found 4 expressions with local error:

5.5b
(* n (pow (/ l Om) 2.0))
7.9b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite276.0ms

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:
25.0ms
(* n (pow (/ l Om) 2.0))
44.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
121.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
79.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.9s

Counts
4 → 12
Calls
4 calls:
145.0ms
(* n (pow (/ l Om) 2.0))
356.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.5s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify41.0ms

Counts
131 → 131
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09871664
150011508
done50011508

prune478.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 24.3b

localize24.0ms

Local error

Found 4 expressions with local error:

19.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (cbrt (* n (pow (/ l Om) 2.0))) (cbrt (* n (pow (/ l Om) 2.0)))) (cbrt (* n (pow (/ l Om) 2.0)))) (- U U*)))))
30.4b
(cbrt (* n (pow (/ l Om) 2.0)))
30.4b
(cbrt (* n (pow (/ l Om) 2.0)))
30.4b
(cbrt (* n (pow (/ l Om) 2.0)))

rewrite244.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1
10×associate-*r/
6×sqrt-div pow-prod-down
5×flip3-- flip--
4×add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity sqrt-pow1 frac-sub add-cbrt-cube add-log-exp
3×cbrt-prod pow1/3
1×pow1/2 sqrt-prod
Counts
4 → 46
Calls
4 calls:
218.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (cbrt (* n (pow (/ l Om) 2.0))) (cbrt (* n (pow (/ l Om) 2.0)))) (cbrt (* n (pow (/ l Om) 2.0)))) (- U U*)))))
7.0ms
(cbrt (* n (pow (/ l Om) 2.0)))
7.0ms
(cbrt (* n (pow (/ l Om) 2.0)))
10.0ms
(cbrt (* n (pow (/ l Om) 2.0)))

series5.6s

Counts
4 → 12
Calls
4 calls:
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (cbrt (* n (pow (/ l Om) 2.0))) (cbrt (* n (pow (/ l Om) 2.0)))) (cbrt (* n (pow (/ l Om) 2.0)))) (- U U*)))))
206.0ms
(cbrt (* n (pow (/ l Om) 2.0)))
207.0ms
(cbrt (* n (pow (/ l Om) 2.0)))
210.0ms
(cbrt (* n (pow (/ l Om) 2.0)))

simplify62.0ms

Counts
58 → 58
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0524955
12265904
25001898
done5001898

prune280.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 24.3b

regimes480.0ms

Accuracy

14.6% (7.8b remaining)

Error of 30.5b against oracle of 22.7b and baseline of 31.9b

bsearch346.0ms

Steps
ItersRangePoint
10
1.9644764314368125e+189
2.5386666659135918e+200
2.7244659562007136e+192
8
4.165409530078807e-176
3.982339784349315e-172
1.070028174441902e-172
7
1.3959854711839468e-305
3.997870835751917e-304
5.921596680002773e-305

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
05158
15429
25729
35729
done5729

end0.0ms

sample2.7s

Algorithm
intervals
Results
919.0ms14645×body80nan
589.0ms9159×body80valid