Details

sample98.0ms

Algorithm

intervals

Results

35.0ms	464×	body	80	nan
26.0ms	303×	body	80	valid

simplify123.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize24.0ms

Local error

Found 4 expressions with local error:

5.6b	(* n (pow (/ l Om) 2.0))
8.2b	(/ (* l l) Om)
12.3b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.9b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite47.0ms

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:

9.0ms	(* n (pow (/ l Om) 2.0))
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*))))
14.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.5s

Counts

4 → 12

Calls

4 calls:

157.0ms	(* n (pow (/ l Om) 2.0))
20.0ms	(/ (* l l) Om)
1.4s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
5.0s	(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

144 → 144

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1079	1948
1	5001	1746

prune622.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 24.9b

localize18.0ms

Local error

Found 4 expressions with local error:

4.8b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.6b	(* n (pow (/ l Om) 2.0))
12.3b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.9b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite62.0ms

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)) (- U U*))
10.0ms	(* n (pow (/ l Om) 2.0))
19.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
14.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.9s

Counts

4 → 12

Calls

4 calls:

387.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
149.0ms	(* n (pow (/ l Om) 2.0))
1.4s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
5.0s	(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 (29.0ms)

Iter	Nodes	Cost
0	1229	2457
1	5001	2136

prune636.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 23.7b

localize19.0ms

Local error

Found 4 expressions with local error:

5.6b	(* n (pow (/ l Om) 2.0))
5.6b	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.4b	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.9b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

50×	`distribute-rgt-in` `distribute-lft-in`
42×	`associate-*r/`
37×	`add-sqr-sqrt`
36×	`prod-diff`
31×	`pow1`
30×	`associate--l+`
27×	`add-cube-cbrt` `*-un-lft-identity`
26×	`add-exp-log`
21×	`associate-r`
20×	`add-cbrt-cube`
17×	`pow-prod-down`
15×	`unpow-prod-down` `flip3--` `flip--`
13×	`prod-exp`
12×	`sub-neg` `frac-sub`
10×	`times-frac` `cbrt-unprod`
7×	`associate-l`
6×	`sqrt-div`
5×	`sqrt-pow1` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-exp` `sqr-pow`
1×	`pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `div-inv`

Counts

4 → 177

Calls

4 calls:

10.0ms	(* n (pow (/ l Om) 2.0))
15.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
16.0ms	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.0ms	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series7.6s

Counts

4 → 12

Calls

4 calls:

148.0ms	(* n (pow (/ l Om) 2.0))
1.4s	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
880.0ms	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
5.2s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify63.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1234	3268
1	5001	2916

prune678.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 20.9b

localize22.0ms

Local error

Found 4 expressions with local error:

5.6b	(* (* 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*)))))
6.4b	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
6.6b	(* n (pow (/ l Om) (/ 2.0 2)))
18.9b	(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*))))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

50×	`distribute-rgt-in` `distribute-lft-in`
42×	`associate-*r/`
37×	`add-sqr-sqrt`
36×	`prod-diff`
31×	`pow1`
30×	`associate--l+`
27×	`add-cube-cbrt` `*-un-lft-identity`
26×	`add-exp-log`
21×	`associate-r`
20×	`add-cbrt-cube`
17×	`pow-prod-down`
15×	`unpow-prod-down` `flip3--` `flip--`
13×	`prod-exp`
12×	`sub-neg` `frac-sub`
10×	`times-frac` `cbrt-unprod`
7×	`associate-l`
6×	`sqrt-div`
5×	`sqrt-pow1` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-exp` `sqr-pow`
1×	`pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `div-inv`

Counts

4 → 177

Calls

4 calls:

15.0ms	(* (* 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*)))))
12.0ms	(* 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)))
18.0ms	(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:

1.4s	(* (* 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*)))))
900.0ms	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
171.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
4.9s	(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*))))))

simplify69.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1259	4267
1	5002	3638

prune686.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 20.9b

regimes657.0ms

Accuracy

25.8% (9.4b remaining)

Error of 28.0b against oracle of 18.5b and baseline of 31.2b

bsearch251.0ms

Steps

Iters	Range	Point
4	1.6033137569180996e-165	2.738753508717326e-165	1.629919832483336e-165
7	1.1016495202129172e-206	1.1965738267793967e-204	9.659136402608944e-205
7	-3.220166757189285e-306	-3.260847540779377e-308	-3.3187788874505696e-308

Iters

Range

Point

1.6033137569180996e-165

2.738753508717326e-165

1.629919832483336e-165

1.1016495202129172e-206

1.1965738267793967e-204

9.659136402608944e-205

-3.220166757189285e-306

-3.260847540779377e-308

-3.3187788874505696e-308

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	68
1	54	68

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	14756×	body	80	nan
708.0ms	9192×	body	80	valid