Details

sample667.0ms

Algorithm

intervals

Results

226.0ms	281×	body	10240	exit
84.0ms	892×	body	80	nan
29.0ms	296×	body	80	valid

simplify121.0ms

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: 35.1b

localize28.0ms

Local error

Found 4 expressions with local error:

6.2b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.2b	(/ (* l l) Om)
10.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.6b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
25×	`pow1`
23×	`add-cbrt-cube`
22×	`associate-*r/`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`add-sqr-sqrt` `*-un-lft-identity` `cbrt-unprod`
8×	`add-cube-cbrt` `associate-r` `frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
4×	`sqrt-pow1` `associate--l+` `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 → 103

Calls

4 calls:

22.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.0ms	(/ (* l l) Om)
51.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
32.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.1s

Counts

4 → 12

Calls

4 calls:

348.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
17.0ms	(/ (* l l) Om)
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.5s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify121.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	937	1548
1	4752	1385
2	5002	1385

prune443.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 22.3b

localize18.0ms

Local error

Found 4 expressions with local error:

5.7b	(* n (pow (/ l Om) 2.0))
6.2b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.6b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite120.0ms

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:

14.0ms	(* n (pow (/ l Om) 2.0))
23.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
45.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
32.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.2s

Counts

4 → 12

Calls

4 calls:

134.0ms	(* n (pow (/ l Om) 2.0))
349.0ms	(* (* 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*))))
4.5s	(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

131 → 131

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	987	1668
1	5001	1508

prune463.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.3b

localize19.0ms

Local error

Found 4 expressions with local error:

5.7b	(* n (pow (/ l Om) 2.0))
6.2b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.6b	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
18.6b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-exp-log`
34×	`associate-*r/`
31×	`pow1`
24×	`add-sqr-sqrt`
23×	`associate-r` `add-cbrt-cube`
21×	`prod-exp`
18×	`distribute-rgt-in` `distribute-lft-in`
17×	`pow-prod-down`
16×	`*-un-lft-identity`
15×	`unpow-prod-down`
14×	`add-cube-cbrt`
12×	`cbrt-unprod`
11×	`flip3--` `flip--`
10×	`sub-neg` `times-frac`
8×	`associate--l+` `frac-sub`
6×	`sqrt-div`
5×	`sqrt-pow1` `associate-l`
4×	`pow-exp` `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 → 129

Calls

4 calls:

15.0ms	(* n (pow (/ l Om) 2.0))
22.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
50.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
35.0ms	(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:

134.0ms	(* n (pow (/ l Om) 2.0))
348.0ms	(* (* 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*)))))
4.7s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify42.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1052	1826
1	5001	1638

prune477.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 17.9b

localize21.0ms

Local error

Found 4 expressions with local error:

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*))
6.6b	(* (* 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*)))))
18.6b	(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*))))))

rewrite257.0ms

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:

46.0ms	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
79.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
74.0ms	(* (* 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*)))))
51.0ms	(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*))))))

series6.9s

Counts

4 → 12

Calls

4 calls:

813.0ms	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
348.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.2s	(* (* 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*)))))
4.5s	(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*))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1077	3086
1	5001	2593

prune457.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 17.3b

regimes542.0ms

Accuracy

31.6% (9.0b remaining)

Error of 26.9b against oracle of 17.9b and baseline of 31.0b

bsearch291.0ms

Steps

Iters	Range		Point
10	-1.4311343096859104e-297	2.3760210479683207e-307	1.9800560136077e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	39
1	45	39

end0.0ms

sample12.1s

Algorithm

intervals

Results

6.9s	9205×	body	10240	exit
2.8s	30158×	body	80	nan
791.0ms	9250×	body	80	valid