Details

sample83.0ms

Algorithm

intervals

Results

28.0ms	415×	body	80	nan
23.0ms	292×	body	80	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	21	28
1	49	28
2	151	27
3	601	27
4	3048	27
done	5000	27

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.0b

localize19.0ms

Local error

Found 4 expressions with local error:

5.5b	(* (* 2.0 n) (* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
5.8b	(* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
8.0b	(/ (* l l) Om)
23.2b	(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

55×	`distribute-rgt-in` `distribute-lft-in`
54×	`prod-diff`
48×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
44×	`add-cube-cbrt`
31×	`pow1`
23×	`add-exp-log` `add-cbrt-cube`
17×	`pow-prod-down`
10×	`associate-*r/` `prod-exp` `cbrt-unprod`
6×	`sub-neg` `associate-r`
5×	`sqrt-pow1`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `times-frac` `associate-/r*` `flip--`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `*-commutative`
1×	`frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 157

Calls

4 calls:

24.0ms	(* (* 2.0 n) (* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
11.0ms	(* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
3.0ms	(/ (* l l) Om)
31.0ms	(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

series6.6s

Counts

4 → 12

Calls

4 calls:

1.2s	(* (* 2.0 n) (* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
998.0ms	(* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
24.0ms	(/ (* l l) Om)
4.4s	(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

simplify1.0s

Counts

169 → 169

Iterations

Useful iterations: 2 (431.0ms)

Iter	Nodes	Cost
0	351	10299
1	911	6962
2	3080	5322
done	5000	5322

prune492.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 24.5b

localize18.0ms

Local error

Found 4 expressions with local error:

5.4b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.5b	(* (* 2.0 n) (* U (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
5.8b	(* U (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
23.2b	(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

72×	`prod-diff`
66×	`distribute-rgt-in` `distribute-lft-in`
61×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
55×	`add-cube-cbrt`
33×	`pow1`
32×	`add-exp-log`
23×	`add-cbrt-cube`
18×	`pow-prod-down` `prod-exp`
12×	`associate-*r/` `cbrt-unprod`
11×	`associate-r`
8×	`sub-neg`
5×	`sqrt-pow1` `associate-l`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`sqrt-div` `pow-exp` `distribute-lft-out--` `difference-of-squares`
1×	`pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `unswap-sqr`

Counts

4 → 182

Calls

4 calls:

26.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
22.0ms	(* (* 2.0 n) (* U (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
14.0ms	(* U (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
31.0ms	(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

series6.7s

Counts

4 → 12

Calls

4 calls:

364.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.2s	(* (* 2.0 n) (* U (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
810.0ms	(* U (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.3s	(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

simplify1.5s

Counts

194 → 194

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	423	11342
1	1123	7816
2	3884	6070
done	5001	6052

prune503.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 23.3b

localize19.0ms

Local error

Found 4 expressions with local error:

4.4b	(* n (pow (/ l Om) 2.0))
5.4b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.9b	(* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
23.2b	(sqrt (* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 153

Calls

4 calls:

17.0ms	(* n (pow (/ l Om) 2.0))
25.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
28.0ms	(* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
32.0ms	(sqrt (* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series6.4s

Counts

4 → 12

Calls

4 calls:

153.0ms	(* n (pow (/ l Om) 2.0))
382.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.2s	(* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.7s	(sqrt (* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify1.7s

Counts

165 → 165

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	414	5992
1	1070	4615
2	4058	3806
done	5001	3788

prune548.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 19.6b

localize26.0ms

Local error

Found 4 expressions with local error:

5.4b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
5.5b	(* n (pow (/ l Om) (/ 2.0 2)))
8.9b	(* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
23.2b	(sqrt (* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 170

Calls

4 calls:

87.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
18.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
28.0ms	(* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
28.0ms	(sqrt (* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

series6.1s

Counts

4 → 12

Calls

4 calls:

370.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
167.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.2s	(* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
4.3s	(sqrt (* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

simplify1.8s

Counts

182 → 182

Iterations

Useful iterations: 2 (941.0ms)

Iter	Nodes	Cost
0	450	8991
1	1196	5778
2	4552	4779
done	5000	4779

prune548.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 19.6b

regimes655.0ms

Accuracy

25.4% (10.3b remaining)

Error of 28.6b against oracle of 18.3b and baseline of 32.1b

bsearch342.0ms

Steps

Iters	Range	Point
7	-3.239627375911032e-303	-4.3939532820442994e-305	-4.448978028228541e-305
9	-1.9715372945094305e-273	-2.231092121831226e-282	-9.22772670345822e-280
9	-7.445858345606715e-226	-2.8340931239319175e-232	-1.0046679677178109e-230

Iters

Range

Point

-3.239627375911032e-303

-4.3939532820442994e-305

-4.448978028228541e-305

-1.9715372945094305e-273

-2.231092121831226e-282

-9.22772670345822e-280

-7.445858345606715e-226

-2.8340931239319175e-232

-1.0046679677178109e-230

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	60	217
1	78	217
done	78	217

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.0s	15017×	body	80	nan
633.0ms	9185×	body	80	valid