Details

sample445.0ms

Algorithm

intervals

Results

40.0ms	294×	body	80	valid
37.0ms	526×	body	80	nan

simplify123.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	49	14
1	153	14
2	652	14
3	3624	14
4	5002	14

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.4b

localize29.0ms

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*)))))

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
24×	`add-sqr-sqrt`
23×	`pow1`
20×	`associate-r/` `associate-r*` `add-cbrt-cube`
16×	`add-cube-cbrt` `*-un-lft-identity`
15×	`unpow-prod-down`
13×	`times-frac`
12×	`pow-prod-down`
11×	`prod-exp`
10×	`flip3--` `flip--`
8×	`frac-sub` `cbrt-unprod`
6×	`sqrt-div`
4×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-pow1` `associate-l` `associate--l+` `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 → 112

Calls

4 calls:

25.0ms	(* n (pow (/ l Om) 2.0))
10.0ms	(/ (* l l) Om)
125.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
86.0ms	(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))
18.0ms	(/ (* 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*)))))

simplify124.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	964	1525
1	4793	1370
2	5001	1370

prune510.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 23.7b

localize22.0ms

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*)))))

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
25×	`pow1` `add-sqr-sqrt` `associate-r`
22×	`associate-*r/`
20×	`add-cbrt-cube`
19×	`prod-exp`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `unpow-prod-down`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`times-frac` `cbrt-unprod`
8×	`frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
5×	`associate-l`
4×	`sqrt-pow1` `pow-exp` `associate--l+` `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 → 119

Calls

4 calls:

45.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
23.0ms	(* n (pow (/ l Om) 2.0))
123.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
79.0ms	(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:

362.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
151.0ms	(* 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*))))
4.9s	(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

131 → 131

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	987	1668
1	5001	1508

prune481.0ms

Pruning

13 alts after pruning (13 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*))))))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log` `add-sqr-sqrt` `associate-*r/`
25×	`associate-r`
21×	`pow1`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`unpow-prod-down`
14×	`prod-exp`
13×	`add-cbrt-cube`
11×	`flip3--` `flip--`
10×	`times-frac` `pow-prod-down`
8×	`frac-sub`
7×	`associate-l`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
5×	`sqrt-pow1` `cbrt-unprod` `unswap-sqr`
4×	`pow-exp` `associate--l+` `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 → 117

Calls

4 calls:

85.0ms	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
44.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
23.0ms	(* n (pow (/ l Om) 2.0))
101.0ms	(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:

833.0ms	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
359.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
141.0ms	(* n (pow (/ l Om) 2.0))
5.0s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify116.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	893	1489
1	4546	1394
2	5001	1394

prune495.0ms

Pruning

15 alts after pruning (15 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*))))))

rewrite721.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 141

Calls

4 calls:

249.0ms	(* (* 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*)))))
144.0ms	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
146.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
175.0ms	(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*))))
368.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
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*))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1077	3086
1	5001	2593

prune481.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 19.8b

regimes663.0ms

Accuracy

23.8% (9.8b remaining)

Error of 28.1b against oracle of 18.3b and baseline of 31.1b

bsearch195.0ms

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	71	56
1	77	56
2	78	56
3	78	56

end0.0ms

sample2.8s

Algorithm

intervals

Results

987.0ms	15161×	body	80	nan
606.0ms	9201×	body	80	valid