Details

sample425.0ms

Algorithm

intervals

Results

58.0ms	526×	body	80	nan
19.0ms	294×	body	80	valid

simplify126.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.4b

localize22.0ms

Local error

Found 4 expressions with local error:

6.5b	(* n (pow (/ l Om) 2.0))
7.2b	(/ (* l l) Om)
9.8b	(* (* (* 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*)))))

rewrite274.0ms

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:

25.0ms	(* n (pow (/ l Om) 2.0))
10.0ms	(/ (* l l) Om)
128.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
105.0ms	(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:

149.0ms	(* 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*)))))

simplify45.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1079	1952
1	5001	1746

prune576.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 23.7b

localize19.0ms

Local error

Found 4 expressions with local error:

6.2b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.5b	(* n (pow (/ l Om) 2.0))
9.8b	(* (* (* 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*)))))

rewrite303.0ms

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:

45.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
24.0ms	(* n (pow (/ l Om) 2.0))
126.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
98.0ms	(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:

370.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
143.0ms	(* n (pow (/ l Om) 2.0))
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*)))))

simplify47.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1229	2461
1	5001	2136

prune569.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 22.9b

localize18.0ms

Local error

Found 4 expressions with local error:

5.5b	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
6.2b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.5b	(* n (pow (/ l Om) 2.0))
20.8b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
32×	`add-cube-cbrt`
30×	`prod-diff`
28×	`add-exp-log` `associate-*r/`
25×	`associate-r`
21×	`pow1` `distribute-rgt-in` `distribute-lft-in`
15×	`unpow-prod-down`
14×	`prod-exp`
13×	`add-cbrt-cube`
11×	`flip3--` `flip--`
10×	`times-frac` `pow-prod-down` `associate--l+`
8×	`frac-sub`
7×	`associate-l`
6×	`sub-neg` `sqrt-div`
5×	`sqrt-pow1` `cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u` `add-log-exp`
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 → 155

Calls

4 calls:

89.0ms	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
45.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
22.0ms	(* n (pow (/ l Om) 2.0))
140.0ms	(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:

985.0ms	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
368.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
144.0ms	(* n (pow (/ l Om) 2.0))
4.8s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify46.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1100	2222
1	5002	1963

prune564.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 20.2b

localize21.0ms

Local error

Found 4 expressions with local error:

4.8b	(* (* 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*)))))
5.5b	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
6.2b	(* (* (* 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 (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

rewrite762.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-exp-log`
66×	`prod-exp`
61×	`distribute-rgt-in` `distribute-lft-in`
54×	`prod-diff`
44×	`associate-*r/`
35×	`add-sqr-sqrt`
33×	`pow1` `*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`associate--l+`
27×	`add-cbrt-cube`
18×	`pow-prod-down` `pow-exp`
16×	`flip3--` `flip--`
15×	`cbrt-unprod`
14×	`sub-neg`
12×	`frac-sub`
9×	`pow-to-exp` `div-exp` `associate-r`
6×	`sqrt-div`
5×	`sqrt-pow1` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
1×	`pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 203

Calls

4 calls:

254.0ms	(* (* 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*)))))
145.0ms	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
140.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
212.0ms	(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*))))))

series7.4s

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*)))))
873.0ms	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
374.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
4.8s	(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*))))))

simplify66.0ms

Algorithm

egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1430	5142
1	5001	4118

prune598.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 19.0b

regimes664.0ms

Accuracy

23.1% (10.2b remaining)

Error of 28.1b against oracle of 17.9b and baseline of 31.1b

bsearch194.0ms

Steps

Iters	Range		Point
7	1.105638821755816e-154	3.735054536702864e-153	1.1204463845939562e-154
8	-6.83442747679948e-170	-1.319183411070151e-173	-5.08941887732029e-171

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	56
1	71	56
2	78	56
3	78	56

end0.0ms

sample2.7s

Algorithm

intervals

Results

956.0ms	15161×	body	80	nan
577.0ms	9201×	body	80	valid