Details

sample175.0ms

Algorithm

intervals

Results

57.0ms	474×	body	80	nan
51.0ms	294×	body	80	valid

simplify3.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (32.0ms)

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: 31.1b

localize46.0ms

Local error

Found 4 expressions with local error:

7.0b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.1b	(/ (* l l) Om)
10.3b	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
15.8b	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

rewrite317.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
25×	`pow1`
24×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`add-cbrt-cube`
20×	`add-cube-cbrt`
18×	`prod-diff`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`cbrt-unprod`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `times-frac` `div-exp` `associate-/r*` `flip--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `associate-r/` `pow-exp` `-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`pow-to-exp` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `div-inv` `associate-/l*`

Counts

4 → 115

Calls

4 calls:

89.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
18.0ms	(/ (* l l) Om)
104.0ms	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
98.0ms	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

series4.0s

Counts

4 → 12

Calls

4 calls:

383.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
20.0ms	(/ (* l l) Om)
940.0ms	(* (- 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)))

simplify490.0ms

Counts

127 → 127

Iterations

Useful iterations: done (486.0ms)

Iter	Nodes	Cost
0	281	3038
1	798	2788
done	5000	2386

prune586.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.2b

localize54.0ms

Local error

Found 4 expressions with local error:

6.3b	(* n (pow (/ l Om) 2.0))
7.0b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.3b	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
15.8b	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

rewrite279.0ms

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:

46.0ms	(* n (pow (/ l Om) 2.0))
85.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
73.0ms	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
65.0ms	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

series3.8s

Counts

4 → 12

Calls

4 calls:

163.0ms	(* n (pow (/ l Om) 2.0))
385.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
926.0ms	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
2.3s	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

simplify2.6s

Counts

143 → 143

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	314	3277
1	841	3008
2	4509	2611
done	5000	2607

prune734.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 19.0b

localize29.0ms

Local error

Found 4 expressions with local error:

5.8b	(* n (pow (/ l Om) (/ 2.0 2)))
7.0b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.3b	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
15.8b	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

rewrite408.0ms

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:

27.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
209.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
95.0ms	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
66.0ms	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

series3.9s

Counts

4 → 12

Calls

4 calls:

192.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
455.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
898.0ms	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
2.3s	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

simplify557.0ms

Counts

160 → 160

Iterations

Useful iterations: done (547.0ms)

Iter	Nodes	Cost
0	349	5166
1	949	3930
done	5000	3432

prune782.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 18.7b

localize41.0ms

Local error

Found 4 expressions with local error:

5.8b	(* n (pow (/ l Om) (/ 2.0 2)))
6.4b	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
10.3b	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U) (pow (/ l Om) (/ 2.0 2)))))) ( (* 2.0 n) U))
15.8b	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U) (pow (/ l Om) (/ 2.0 2)))))) ( (* 2.0 n) U)))

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
35×	`associate-r`
30×	`unpow-prod-down`
29×	`add-exp-log`
27×	`*-un-lft-identity`
23×	`pow1` `add-cube-cbrt`
20×	`times-frac`
17×	`add-cbrt-cube`
14×	`prod-exp`
13×	`associate-l`
12×	`pow-prod-down`
8×	`cbrt-unprod` `unswap-sqr`
6×	`associate-*l/`
4×	`expm1-log1p-u` `sqrt-pow1` `pow-exp` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`flip3--` `*-commutative` `flip--`
2×	`pow-to-exp` `sqrt-div` `div-exp` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`pow1/2` `sqrt-prod`

Counts

4 → 126

Calls

4 calls:

41.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
55.0ms	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
87.0ms	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U) (pow (/ l Om) (/ 2.0 2)))))) ( (* 2.0 n) U))
58.0ms	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U) (pow (/ l Om) (/ 2.0 2)))))) ( (* 2.0 n) U)))

series5.1s

Counts

4 → 12

Calls

4 calls:

257.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.2s	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
1.1s	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U) (pow (/ l Om) (/ 2.0 2)))))) ( (* 2.0 n) U))
2.5s	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U) (pow (/ l Om) (/ 2.0 2)))))) ( (* 2.0 n) U)))

simplify2.3s

Counts

138 → 138

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	286	3399
1	701	3221
2	3281	2583
done	5001	2578

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 18.2b

regimes840.0ms

Accuracy

18.6% (7.7b remaining)

Error of 28.3b against oracle of 20.6b and baseline of 30.1b

bsearch526.0ms

Steps

Iters	Range		Point
9	8.545262035761832e+98	3.657084440728184e+106	1.1482528827886977e+101
9	3.0592371436044766e-118	4.3786494054231285e-113	3.611795465534093e-116

simplify16.0ms

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	44	173
1	57	173
done	57	173

end0.0ms

sample6.9s

Algorithm

intervals

Results

3.0s	14931×	body	80	nan
1.9s	9212×	body	80	valid