Details

sample87.0ms

Algorithm

intervals

Results

30.0ms	465×	body	80	nan
24.0ms	299×	body	80	valid

simplify125.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	14
1	155	14
2	684	14
3	3898	14
4	5001	14

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize19.0ms

Local error

Found 4 expressions with local error:

5.4b	(* n (pow (/ l Om) 2.0))
6.2b	(/ (* l l) Om)
10.9b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.8b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`add-exp-log`
23×	`pow1`
20×	`add-cube-cbrt` `-un-lft-identity` `associate-r/` `associate-r` `add-cbrt-cube`
15×	`unpow-prod-down`
13×	`times-frac`
12×	`prod-diff` `pow-prod-down`
11×	`prod-exp`
10×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `associate--l+` `flip--`
8×	`frac-sub` `cbrt-unprod`
6×	`sqrt-div`
4×	`expm1-log1p-u` `sub-neg` `sqrt-pow1` `associate-l` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`div-exp` `associate-/r*`
2×	`cbrt-undiv` `pow-exp` `*-commutative` `div-inv` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `associate-/l*`

Counts

4 → 132

Calls

4 calls:

17.0ms	(* n (pow (/ l Om) 2.0))
3.0ms	(/ (* l l) Om)
50.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
44.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.3s

Counts

4 → 12

Calls

4 calls:

136.0ms	(* n (pow (/ l Om) 2.0))
19.0ms	(/ (* l l) Om)
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.8s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1079	1948
1	5001	1746

prune594.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 23.8b

localize18.0ms

Local error

Found 4 expressions with local error:

5.4b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.4b	(* n (pow (/ l Om) 2.0))
10.9b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.8b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite139.0ms

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:

26.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
14.0ms	(* n (pow (/ l Om) 2.0))
52.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
40.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.5s

Counts

4 → 12

Calls

4 calls:

365.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
148.0ms	(* n (pow (/ l Om) 2.0))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.7s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1227	2457
1	5002	2136

prune626.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.1b

localize20.0ms

Local error

Found 4 expressions with local error:

5.4b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.4b	(* n (pow (/ l Om) 2.0))
5.7b	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
20.8b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

51×	`distribute-rgt-in` `distribute-lft-in`
44×	`add-sqr-sqrt`
42×	`prod-diff`
38×	`add-exp-log`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt` `associate-*r/`
31×	`pow1`
23×	`associate-r` `add-cbrt-cube`
21×	`prod-exp`
20×	`associate--l+`
17×	`pow-prod-down`
15×	`unpow-prod-down`
12×	`cbrt-unprod`
11×	`flip3--` `flip--`
10×	`sub-neg` `times-frac`
8×	`frac-sub`
6×	`sqrt-div`
5×	`sqrt-pow1` `associate-l`
4×	`expm1-log1p-u` `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 → 179

Calls

4 calls:

24.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
15.0ms	(* n (pow (/ l Om) 2.0))
58.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
67.0ms	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series6.9s

Counts

4 → 12

Calls

4 calls:

362.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
144.0ms	(* n (pow (/ l Om) 2.0))
1.3s	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.1s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify57.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1404	2979
1	5001	2579

prune614.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 17.6b

localize22.0ms

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*))
5.6b	(* n (pow (/ l Om) (/ 2.0 2)))
5.7b	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
20.8b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

rewrite276.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-exp-log`
69×	`prod-exp`
51×	`distribute-rgt-in` `distribute-lft-in`
44×	`add-sqr-sqrt`
42×	`prod-diff`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt` `associate-*r/`
31×	`pow1`
27×	`add-cbrt-cube`
23×	`associate-r`
20×	`pow-exp` `associate--l+`
17×	`pow-prod-down`
15×	`unpow-prod-down` `cbrt-unprod`
11×	`flip3--` `flip--`
10×	`pow-to-exp` `sub-neg` `times-frac` `div-exp`
8×	`frac-sub`
6×	`sqrt-div`
5×	`sqrt-pow1` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 196

Calls

4 calls:

84.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
15.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
84.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
82.0ms	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

series6.6s

Counts

4 → 12

Calls

4 calls:

371.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
159.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.3s	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
4.7s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

simplify74.0ms

Algorithm

egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1530	4198
1	5002	3368

prune642.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.9b

regimes707.0ms

Accuracy

14.9% (11.2b remaining)

Error of 29.5b against oracle of 18.2b and baseline of 31.4b

bsearch388.0ms

Steps

Iters	Range		Point
5	29184922253.33966	70347099364.66205	65976789463.48323
7	7.203753371045093e-284	1.498389736052345e-281	9.142704392468657e-283
9	-6.598336758836399e-272	-9.841880362584622e-278	-9.948594652063987e-278
4	-9.40172093679925e-112	-4.705308269382675e-112	-6.911969950309971e-112

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	91	108
1	95	108
2	102	108
3	102	108

end0.0ms

sample2.4s

Algorithm

intervals

Results

984.0ms	14972×	body	80	nan
607.0ms	9184×	body	80	valid