Details

sample128.0ms

Algorithm

intervals

Results

57.0ms	546×	body	80	nan
29.0ms	295×	body	80	valid

simplify116.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 36.5b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

5.9b	(* n (pow (/ l Om) 2.0))
8.2b	(/ (* l l) Om)
13.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
16.6b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite41.0ms

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*)))))

series6.3s

Counts

4 → 12

Calls

4 calls:

144.0ms	(* 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*)))))

simplify123.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 1 (23.0ms)

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

prune477.0ms

Filtered

124 candidates to 87 candidates (70.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	111	13	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	13	125

Merged error: 19.1b

Counts

125 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

3.9b	(- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
5.9b	(* n (pow (/ l Om) 2.0))
13.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
16.6b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

24×	`associate-*r/`
23×	`pow1`
22×	`add-sqr-sqrt`
21×	`add-exp-log`
20×	`associate-r`
15×	`unpow-prod-down` `flip3--` `add-cbrt-cube` `flip--`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow-prod-down` `frac-sub`
10×	`times-frac` `prod-exp`
9×	`add-log-exp`
8×	`sub-neg`
7×	`cbrt-unprod`
6×	`distribute-rgt-in` `distribute-lft-in` `sqrt-div` `associate--l+`
4×	`sqrt-pow1` `associate-l` `associate--r+` `unswap-sqr`
3×	`diff-log`
2×	`pow-exp` `*-commutative` `sqr-pow`
1×	`associate--l-` `pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `div-inv`

Counts

4 → 115

Calls

4 calls:

7.0ms	(- (- t (* 2.0 (* l (/ l Om)))) (* (* 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*)))))

series6.9s

Counts

4 → 12

Calls

4 calls:

664.0ms	(- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
149.0ms	(* 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*))))
4.7s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify130.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	936	1902
1	4637	1737
2	5001	1737

prune485.0ms

Filtered

127 candidates to 89 candidates (70.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	122	5	127
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	127	13	140

Merged error: 17.9b

Counts

140 → 13

localize24.0ms

Local error

Found 4 expressions with local error:

3.9b	(- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
5.9b	(* n (pow (/ l Om) 2.0))
7.9b	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
16.6b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

36×	`associate-*r/`
29×	`pow1`
24×	`add-exp-log`
21×	`add-sqr-sqrt`
18×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `add-cbrt-cube`
16×	`pow-prod-down`
15×	`unpow-prod-down` `flip3--` `flip--`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`sub-neg` `prod-exp` `frac-sub`
10×	`times-frac` `associate--l+`
9×	`cbrt-unprod` `add-log-exp`
6×	`sqrt-div`
5×	`sqrt-pow1`
4×	`associate-l` `associate--r+` `unswap-sqr`
3×	`diff-log`
2×	`pow-exp` `*-commutative` `sqr-pow`
1×	`associate--l-` `pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `div-inv`

Counts

4 → 125

Calls

4 calls:

7.0ms	(- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
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*)))))
11.0ms	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series7.2s

Counts

4 → 12

Calls

4 calls:

858.0ms	(- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
142.0ms	(* 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*))))))

simplify126.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1004	2064
1	4590	1867
2	5001	1867

prune476.0ms

Filtered

137 candidates to 88 candidates (64.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	131	6	137
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	137	13	150

Merged error: 16.2b

Counts

150 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

3.9b	(- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
4.9b	(* n (pow (/ l Om) (/ 2.0 2)))
7.9b	(* (* 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*)))))
16.6b	(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*))))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

36×	`associate-*r/`
29×	`pow1`
24×	`add-exp-log`
21×	`add-sqr-sqrt`
18×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `add-cbrt-cube`
16×	`pow-prod-down`
15×	`unpow-prod-down` `flip3--` `flip--`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`sub-neg` `prod-exp` `frac-sub`
10×	`times-frac` `associate--l+`
9×	`cbrt-unprod` `add-log-exp`
6×	`sqrt-div`
5×	`sqrt-pow1`
4×	`associate-l` `associate--r+` `unswap-sqr`
3×	`diff-log`
2×	`pow-exp` `*-commutative` `sqr-pow`
1×	`associate--l-` `pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `div-inv`

Counts

4 → 125

Calls

4 calls:

7.0ms	(- (- 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)))
13.0ms	(* (* 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	(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*))))))

series6.8s

Counts

4 → 12

Calls

4 calls:

659.0ms	(- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
157.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
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*)))))
4.7s	(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*))))))

simplify139.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	1031	2632
1	4727	2247
2	5001	2234

prune456.0ms

Filtered

137 candidates to 89 candidates (65.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	137	13	150

Merged error: 16.2b

Counts

150 → 13

regimes491.0ms

Accuracy

5.2% (11.3b remaining)

Error of 30.0b against oracle of 18.7b and baseline of 30.7b

bsearch103.0ms

Steps

Iters	Range		Point
6	4.3236642318716767e-278	2.1777929378670944e-277	1.9876102665034602e-277

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	34
1	46	34

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.5s	14999×	body	80	nan
912.0ms	9154×	body	80	valid