Details

sample298.0ms

Algorithm

intervals

Results

96.0ms	503×	body	80	nan
32.0ms	279×	body	80	valid

simplify3.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3869
3	632
2	152
1	49
0	21

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.9b

localize101.0ms

Local error

Found 4 expressions with local error:

5.7b	(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
6.5b	(* (* n (pow (/ l Om) 2.0)) (- U* U))
7.0b	(* n (pow (/ l Om) 2.0))
19.2b	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
25×	`add-sqr-sqrt` `pow1` `associate-r`
20×	`add-cbrt-cube`
19×	`prod-exp`
17×	`*-un-lft-identity`
15×	`unpow-prod-down` `add-cube-cbrt`
13×	`pow-prod-down`
10×	`times-frac` `cbrt-unprod`
6×	`associate-*r/`
5×	`associate-l`
4×	`sqrt-pow1` `associate-*l/` `pow-exp` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`distribute-rgt-in` `pow-to-exp` `sub-neg` `distribute-lft-in` `flip3-+` `sqrt-div` `div-exp` `flip-+` `sqr-pow`
1×	`flip3--` `pow1/2` `sqrt-prod` `div-inv` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 103

Calls

4 calls:

569.0ms	(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
40.0ms	(* (* n (pow (/ l Om) 2.0)) (- U* U))
35.0ms	(* n (pow (/ l Om) 2.0))
442.0ms	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

series17.6s

Counts

4 → 12

Calls

4 calls:

1.7s	(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
887.0ms	(* (* n (pow (/ l Om) 2.0)) (- U* U))
238.0ms	(* n (pow (/ l Om) 2.0))
14.8s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

simplify3.0s

Counts

115 → 115

Iterations

Iter	Nodes
done	5001
2	4120
1	713
0	260

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 21.2b

localize74.0ms

Local error

Found 4 expressions with local error:

4.6b	(* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))))
5.7b	(* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
6.5b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
19.2b	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

rewrite5.0s

Algorithm

rewrite-expression-head

Rules

96×	`add-exp-log`
66×	`prod-exp`
30×	`pow1`
27×	`add-cbrt-cube`
18×	`pow-exp`
16×	`pow-prod-down`
15×	`cbrt-unprod`
12×	`associate-r`
11×	`*-un-lft-identity`
9×	`add-sqr-sqrt` `pow-to-exp` `div-exp`
8×	`associate-*r/`
7×	`add-cube-cbrt`
4×	`sqrt-pow1` `associate-*l/` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `associate-l` `*-commutative` `flip-+`
2×	`sub-neg` `sqrt-div`
1×	`flip3--` `pow1/2` `sqrt-prod` `flip--` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 106

Calls

4 calls:

1.2s	(* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))))
1.8s	(* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
207.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
1.8s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

series15.7s

Counts

4 → 12

Calls

4 calls:

1.1s	(* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))))
1.1s	(* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
390.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
13.1s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

simplify2.3s

Counts

118 → 118

Iterations

Iter	Nodes
done	5001
2	4764
1	746
0	248

prune671.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.7b

localize87.0ms

Local error

Found 4 expressions with local error:

6.5b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
6.5b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
19.2b	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))
19.2b	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

rewrite2.5s

Algorithm

rewrite-expression-head

Rules

160×	`add-exp-log`
114×	`prod-exp`
36×	`pow-exp`
28×	`pow1`
22×	`add-cbrt-cube`
18×	`pow-to-exp` `div-exp`
14×	`pow-prod-down`
12×	`cbrt-unprod`
10×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*`
8×	`sqrt-pow1` `associate-*r/`
6×	`add-cube-cbrt`
4×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div` `associate-*l/` `add-log-exp`
2×	`flip3-+` `flip3--` `pow1/2` `associate-l` `*-commutative` `sqrt-prod` `flip-+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 120

Calls

4 calls:

118.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
116.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
1.1s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))
1.1s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

series20.4s

Counts

4 → 12

Calls

4 calls:

372.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
375.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
9.8s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))
9.9s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

simplify1.5s

Counts

132 → 132

Iterations

Iter	Nodes
done	5000
2	2404
1	478
0	165

prune826.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 20.7b

localize43.0ms

Local error

Found 4 expressions with local error:

4.5b	(* (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))) U)
6.5b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
7.1b	(* (* 2.0 n) (* (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))) U))
19.2b	(sqrt (* (* 2.0 n) (* (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))) U)))

rewrite2.8s

Algorithm

rewrite-expression-head

Rules

96×	`add-exp-log`
66×	`prod-exp`
33×	`pow1`
27×	`add-cbrt-cube`
18×	`pow-prod-down` `pow-exp`
15×	`cbrt-unprod`
11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`pow-to-exp` `div-exp` `associate-r`
7×	`add-cube-cbrt`
6×	`associate-l` `associate-l/` `associate-r/`
5×	`sqrt-pow1`
4×	`add-log-exp`
3×	`flip3-+` `*-commutative` `flip-+`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
1×	`flip3--` `pow1/2` `sqrt-prod` `flip--` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

1.1s	(* (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))) U)
113.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
806.0ms	(* (* 2.0 n) (* (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))) U))
805.0ms	(sqrt (* (* 2.0 n) (* (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))) U)))

series12.1s

Counts

4 → 12

Calls

4 calls:

1.0s	(* (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))) U)
373.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
1.1s	(* (* 2.0 n) (* (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))) U))
9.6s	(sqrt (* (* 2.0 n) (* (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))) U)))

simplify1.8s

Counts

118 → 118

Iterations

Iter	Nodes
done	5002
2	4139
1	710
0	242

prune537.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 18.3b

regimes1.1s

Accuracy

29.3% (8.9b remaining)

Error of 27.4b against oracle of 18.5b and baseline of 31.1b

bsearch304.0ms

Steps

Iters	Range		Point
8	1.431076248367481e-295	3.6191111494565633e-292	4.990611334173369e-293
10	-3.0632372757179626e+150	-3.319013425719186e+133	-1.0845919563821882e+140

simplify18.0ms

Iterations

Iter	Nodes
done	67
3	67
2	60
1	54
0	39

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.1s	14889×	body	80	nan
1.3s	9174×	body	80	valid