Details

sample255.0ms

Algorithm

intervals

Results

122.0ms	512×	body	80	nan
44.0ms	289×	body	80	valid

simplify2.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	21	28
1	49	28
2	154	27
3	642	27
4	3239	27
done	5000	27

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize25.0ms

Local error

Found 4 expressions with local error:

6.5b	(* n (pow (/ l Om) 2.0))
7.2b	(/ (* l l) Om)
10.1b	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
19.3b	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log` `add-sqr-sqrt`
23×	`pow1`
20×	`add-cbrt-cube`
18×	`-un-lft-identity` `associate-r*`
16×	`add-cube-cbrt`
15×	`unpow-prod-down`
13×	`times-frac`
12×	`pow-prod-down`
11×	`prod-exp`
8×	`associate-l` `cbrt-unprod`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-*l/` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`div-exp` `associate-/r*`
2×	`cbrt-undiv` `flip3--` `sqrt-div` `pow-exp` `*-commutative` `flip--` `div-inv` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 106

Calls

4 calls:

30.0ms	(* n (pow (/ l Om) 2.0))
10.0ms	(/ (* l l) Om)
66.0ms	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
70.0ms	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

series3.9s

Counts

4 → 12

Calls

4 calls:

213.0ms	(* n (pow (/ l Om) 2.0))
21.0ms	(/ (* l l) Om)
1.0s	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
2.6s	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

simplify1.2s

Counts

118 → 118

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	251	2234
1	589	2131
2	1949	1847
done	5001	1842

prune699.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.3b

localize37.0ms

Local error

Found 4 expressions with local error:

5.8b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.5b	(* n (pow (/ l Om) 2.0))
10.1b	(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
19.3b	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
35×	`add-exp-log`
31×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`pow1`
23×	`associate-r`
20×	`add-cbrt-cube`
19×	`prod-exp`
18×	`prod-diff`
15×	`unpow-prod-down`
13×	`pow-prod-down`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`times-frac` `cbrt-unprod`
9×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-*l/` `pow-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`flip3--` `*-commutative` `flip--`
2×	`pow-to-exp` `sub-neg` `sqrt-div` `associate-*r/` `div-exp` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv`

Counts

4 → 131

Calls

4 calls:

54.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
24.0ms	(* n (pow (/ l Om) 2.0))
63.0ms	(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
62.0ms	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

series4.5s

Counts

4 → 12

Calls

4 calls:

531.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
203.0ms	(* n (pow (/ l Om) 2.0))
1.0s	(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
2.8s	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

simplify1.7s

Counts

143 → 143

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	313	3277
1	762	2989
2	2550	2595
done	5001	2566

prune745.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.6b

localize62.0ms

Local error

Found 4 expressions with local error:

3.6b	(* n (pow (/ l Om) (/ 2.0 2)))
5.8b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.1b	(* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
19.3b	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

rewrite469.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
39×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`pow1`
24×	`add-cbrt-cube`
23×	`associate-r`
20×	`pow-exp`
18×	`prod-diff`
15×	`unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow-to-exp` `times-frac` `div-exp`
9×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-*l/` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`flip3--` `*-commutative` `flip--`
2×	`sub-neg` `sqrt-div` `associate-*r/` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv`

Counts

4 → 148

Calls

4 calls:

42.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
226.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
124.0ms	(* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
68.0ms	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

series5.1s

Counts

4 → 12

Calls

4 calls:

227.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
572.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.1s	(* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
3.2s	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

simplify2.4s

Counts

160 → 160

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	348	5166
1	853	3924
2	2947	3412
done	5000	3383

prune809.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.6b

localize52.0ms

Local error

Found 4 expressions with local error:

11.6b	(cbrt (/ l Om))
11.6b	(cbrt (/ l Om))
11.6b	(cbrt (/ l Om))
19.3b	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U)))) ( (* 2.0 n) U)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
27×	`times-frac`
25×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
14×	`pow1`
6×	`pow-prod-down`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3` `div-inv`
2×	`sqrt-div` `associate-*l/`
1×	`flip3--` `pow1/2` `sqrt-prod` `flip--`

Counts

4 → 89

Calls

4 calls:

8.0ms	(cbrt (/ l Om))
4.0ms	(cbrt (/ l Om))
4.0ms	(cbrt (/ l Om))
97.0ms	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U)))) ( (* 2.0 n) U)))

series3.2s

Counts

4 → 12

Calls

4 calls:

102.0ms	(cbrt (/ l Om))
75.0ms	(cbrt (/ l Om))
92.0ms	(cbrt (/ l Om))
2.9s	(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U)))) ( (* 2.0 n) U)))

simplify1.6s

Counts

101 → 101

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	133	1553
1	237	1440
2	568	1372
3	2336	1351
done	5000	1324

prune771.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.6b

regimes815.0ms

Accuracy

14.8% (8.8b remaining)

Error of 29.3b against oracle of 20.5b and baseline of 30.9b

bsearch186.0ms

Steps

Iters	Range		Point
8	2.4864886162434826e+38	5.64601237047726e+41	1.1096816485837593e+40

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	73
1	45	73
done	45	73

end0.0ms

sample7.2s

Algorithm

intervals

Results

3.6s	15106×	body	80	nan
1.6s	9162×	body	80	valid