Details

sample93.0ms

Algorithm

intervals

Results

33.0ms	464×	body	80	nan
26.0ms	303×	body	80	valid

simplify115.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize25.0ms

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*)))))

rewrite40.0ms

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:

9.0ms	(* n (pow (/ l Om) 2.0))
5.0ms	(/ (* l l) Om)
12.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.0ms	(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:

137.0ms	(* n (pow (/ l Om) 2.0))
23.0ms	(/ (* 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

prune540.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 24.9b

localize24.0ms

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*)))))

rewrite48.0ms

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:

12.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.0ms	(* n (pow (/ l Om) 2.0))
12.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.0ms	(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:

369.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
145.0ms	(* 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*)))))

simplify44.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	987	1664
1	5001	1508

prune529.0ms

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*))))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

9.0ms	(* n (pow (/ l Om) 2.0))
13.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
15.0ms	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
11.0ms	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series7.5s

Counts

4 → 12

Calls

4 calls:

143.0ms	(* n (pow (/ l Om) 2.0))
1.5s	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
877.0ms	(* 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*))))))

simplify133.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1003	2155
1	4972	1934
2	5001	1934

prune541.0ms

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*))))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

17.0ms	(* (* 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*)))))
11.0ms	(* 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)))
12.0ms	(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*))))))

series7.1s

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*)))))
868.0ms	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
168.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
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*))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1028	2758
1	5001	2381

prune558.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 20.9b

regimes662.0ms

Accuracy

25.8% (9.4b remaining)

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

bsearch424.0ms

Steps

Iters	Range		Point
9	1.2863883229368928e-170	1.6033137569180996e-165	4.378446049639009e-170
7	7.611550461155143e-252	1.8515651458783057e-250	1.7265773238547077e-250
7	-3.220166757189285e-306	-3.260847540779377e-308	-3.3187788874505696e-308
8	-1.3806876679235032e-250	-2.5767314769870796e-254	-1.4515776824764508e-252

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	95
1	78	95
2	88	95
3	88	95

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	14756×	body	80	nan
683.0ms	9192×	body	80	valid