Details

sample87.0ms

Algorithm

intervals

Results

29.0ms	428×	body	80	nan
25.0ms	304×	body	80	valid

simplify120.0ms

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: 36.1b

localize19.0ms

Local error

Found 4 expressions with local error:

7.2b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.2b	(/ (* l l) Om)
8.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.6b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite51.0ms

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:

11.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.0ms	(/ (* l l) Om)
14.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
16.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.4s

Counts

4 → 12

Calls

4 calls:

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

simplify47.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1176	2335
1	5001	2011

prune556.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 23.8b

localize18.0ms

Local error

Found 4 expressions with local error:

6.2b	(* n (pow (/ l Om) 2.0))
7.2b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.6b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite57.0ms

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:

12.0ms	(* n (pow (/ l Om) 2.0))
12.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
13.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
13.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.6s

Counts

4 → 12

Calls

4 calls:

149.0ms	(* n (pow (/ l Om) 2.0))
373.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
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

169 → 169

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1229	2457
1	5001	2136

prune605.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.4b

localize18.0ms

Local error

Found 4 expressions with local error:

4.4b	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.2b	(* n (pow (/ l Om) 2.0))
7.2b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
21.6b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite63.0ms

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:

18.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
9.0ms	(* n (pow (/ l Om) 2.0))
12.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
16.0ms	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series6.7s

Counts

4 → 12

Calls

4 calls:

1.3s	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
141.0ms	(* n (pow (/ l Om) 2.0))
358.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
4.9s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify60.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1406	2979
1	5001	2579

prune593.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 17.8b

localize20.0ms

Local error

Found 4 expressions with local error:

4.4b	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
6.5b	(* n (pow (/ l Om) (/ 2.0 2)))
7.2b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
21.6b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

rewrite71.0ms

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:

18.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
9.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
17.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
17.0ms	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

series6.6s

Counts

4 → 12

Calls

4 calls:

1.3s	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
165.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
360.0ms	(* (* (* 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 (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

simplify72.0ms

Algorithm

egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1532	4198
1	5001	3368

prune609.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 17.6b

regimes505.0ms

Accuracy

27.7% (9.0b remaining)

Error of 27.5b against oracle of 18.6b and baseline of 31.0b

bsearch94.0ms

Steps

Iters	Range		Point
7	-2.5892607296053433e-308	2.395002724385006e-307	4.43445988456375e-310

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	39
1	45	39

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	15020×	body	80	nan
668.0ms	9201×	body	80	valid