Details

sample220.0ms

Algorithm

intervals

Results

101.0ms	475×	body	80	nan
41.0ms	298×	body	80	valid

simplify3.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	21	28
1	49	28
2	154	27
3	664	27
4	4143	27
done	5000	27

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize38.0ms

Local error

Found 4 expressions with local error:

7.8b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.0b	(/ (* l l) Om)
10.3b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.7b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite439.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
30×	`prod-diff`
26×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`pow1`
24×	`add-cube-cbrt`
23×	`add-cbrt-cube`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`associate--l+` `cbrt-unprod`
8×	`associate-r` `frac-sub`
6×	`sub-neg` `sqrt-div`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `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 → 141

Calls

4 calls:

58.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
13.0ms	(/ (* l l) Om)
196.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
163.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series8.6s

Counts

4 → 12

Calls

4 calls:

540.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
24.0ms	(/ (* l l) Om)
1.7s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
6.3s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify652.0ms

Counts

153 → 153

Iterations

Useful iterations: done (645.0ms)

Iter	Nodes	Cost
0	411	4799
1	1278	4444
done	5000	3908

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 22.5b

localize58.0ms

Local error

Found 4 expressions with local error:

6.0b	(* n (pow (/ l Om) 2.0))
7.8b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.3b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.7b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite494.0ms

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:

48.0ms	(* n (pow (/ l Om) 2.0))
68.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
194.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
168.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.9s

Counts

4 → 12

Calls

4 calls:

207.0ms	(* n (pow (/ l Om) 2.0))
518.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.9s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.3s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify872.0ms

Counts

169 → 169

Iterations

Useful iterations: done (863.0ms)

Iter	Nodes	Cost
0	442	5038
1	1316	4661
done	5001	4111

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 21.5b

localize69.0ms

Local error

Found 4 expressions with local error:

3.8b	(* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (* (- U U*) n) (pow (/ l Om) 2.0)))) U))
5.8b	(* (- t (fma (* l (/ l Om)) 2.0 (* (* (- U U*) n) (pow (/ l Om) 2.0)))) U)
10.7b	(* (* (- U U*) n) (pow (/ l Om) 2.0))
18.7b	(sqrt (* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (* (- U U*) n) (pow (/ l Om) 2.0)))) U)))

rewrite268.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-exp-log`
31×	`pow1`
23×	`add-cbrt-cube`
21×	`associate-r` `prod-exp`
18×	`add-sqr-sqrt`
17×	`pow-prod-down`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`unpow-prod-down`
12×	`cbrt-unprod`
10×	`associate-*l/`
9×	`times-frac`
7×	`associate-l`
5×	`sqrt-pow1`
4×	`expm1-log1p-u` `flip3--` `associate-*r/` `pow-exp` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-to-exp` `sqrt-div` `div-exp`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `sqr-pow`

Counts

4 → 108

Calls

4 calls:

76.0ms	(* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (* (- U U*) n) (pow (/ l Om) 2.0)))) U))
37.0ms	(* (- t (fma (* l (/ l Om)) 2.0 (* (* (- U U*) n) (pow (/ l Om) 2.0)))) U)
74.0ms	(* (* (- U U*) n) (pow (/ l Om) 2.0))
77.0ms	(sqrt (* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (* (- U U*) n) (pow (/ l Om) 2.0)))) U)))

series20.6s

Counts

4 → 12

Calls

4 calls:

1.5s	(* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (* (- U U*) n) (pow (/ l Om) 2.0)))) U))
1.0s	(* (- t (fma (* l (/ l Om)) 2.0 (* (* (- U U*) n) (pow (/ l Om) 2.0)))) U)
513.0ms	(* (* (- U U*) n) (pow (/ l Om) 2.0))
17.6s	(sqrt (* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (* (- U U*) n) (pow (/ l Om) 2.0)))) U)))

simplify2.5s

Counts

120 → 120

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	282	3077
1	754	2952
2	3909	2537
done	5000	2521

prune1.1s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 18.6b

localize39.0ms

Local error

Found 4 expressions with local error:

3.8b	(* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (* (* (- U U*) n) (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))))) U))
5.8b	(* (- t (fma (* l (/ l Om)) 2.0 (* (* (* (- U U*) n) (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))))) U)
11.5b	(* (* (- U U*) n) (pow (/ l Om) (/ 2.0 2)))
18.7b	(sqrt (* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (* (* (- U U*) n) (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))))) U)))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-exp-log`
31×	`pow1`
23×	`add-cbrt-cube`
21×	`associate-r` `prod-exp`
18×	`add-sqr-sqrt`
17×	`pow-prod-down`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`unpow-prod-down`
12×	`cbrt-unprod`
10×	`associate-*l/`
9×	`times-frac`
7×	`associate-l`
5×	`sqrt-pow1`
4×	`expm1-log1p-u` `flip3--` `associate-*r/` `pow-exp` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-to-exp` `sqrt-div` `div-exp`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `sqr-pow`

Counts

4 → 108

Calls

4 calls:

61.0ms	(* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (* (* (- U U*) n) (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))))) U))
47.0ms	(* (- t (fma (* l (/ l Om)) 2.0 (* (* (* (- U U*) n) (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))))) U)
106.0ms	(* (* (- U U*) n) (pow (/ l Om) (/ 2.0 2)))
79.0ms	(sqrt (* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (* (* (- U U*) n) (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))))) U)))

series20.9s

Counts

4 → 12

Calls

4 calls:

1.5s	(* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (* (* (- U U*) n) (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))))) U))
901.0ms	(* (- t (fma (* l (/ l Om)) 2.0 (* (* (* (- U U*) n) (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))))) U)
541.0ms	(* (* (- U U*) n) (pow (/ l Om) (/ 2.0 2)))
18.0s	(sqrt (* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (* (* (- U U*) n) (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))))) U)))

simplify3.0s

Counts

120 → 120

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	295	4063
1	798	3401
2	4070	2914
done	5000	2898

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 18.5b

regimes1.5s

Accuracy

7.2% (10.4b remaining)

Error of 29.4b against oracle of 19.1b and baseline of 30.3b

bsearch219.0ms

Steps

Iters	Range		Point
8	1.4311168842449665e+196	9.446012968415954e+198	1.4483498882880329e+196

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	69
1	45	69
done	45	69

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.7s	14815×	body	80	nan
1.8s	9208×	body	80	valid