Details

sample0.0hr

Algorithm

intervals

Results

0.0hr	502×	body	80	nan
0.0hr	291×	body	80	valid

simplify0.0hr

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0hr)

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

prune0.0hr

Filtered

1 candidates to 0 candidates (100.0%)

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: 33.3b

Counts

2 → 1

localize0.0hr

Local error

Found 4 expressions with local error:

6.4b	(* n (pow (/ l Om) 2.0))
8.2b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
9.9b	(/ (* l l) Om)
19.7b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite0.0hr

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:

0.0hr	(* n (pow (/ l Om) 2.0))
0.0hr	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
0.0hr	(/ (* l l) Om)
0.0hr	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(* n (pow (/ l Om) 2.0))
0.0hr	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
0.0hr	(/ (* l l) Om)
0.0hr	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify0.0hr

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 1 (0.0hr)

Iter	Nodes	Cost
0	1026	1598
1	4937	1447
2	5001	1447

prune0.0hr

Filtered

124 candidates to 88 candidates (29.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	110	14	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	14	125

Merged error: 22.0b

Counts

125 → 14

localize0.0hr

Local error

Found 4 expressions with local error:

6.4b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.4b	(* n (pow (/ l Om) 2.0))
8.2b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.7b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite0.0hr

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:

0.0hr	(* (* n (pow (/ l Om) 2.0)) (- U U*))
0.0hr	(* n (pow (/ l Om) 2.0))
0.0hr	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
0.0hr	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(* (* n (pow (/ l Om) 2.0)) (- U U*))
0.0hr	(* n (pow (/ l Om) 2.0))
0.0hr	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
0.0hr	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify0.0hr

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (0.0hr)

Iter	Nodes	Cost
0	1071	1769
1	5001	1602

prune0.0hr

Filtered

131 candidates to 86 candidates (34.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	133	12	145

Merged error: 20.3b

Counts

145 → 12

localize0.0hr

Local error

Found 4 expressions with local error:

6.4b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.4b	(* n (pow (/ l Om) 2.0))
7.5b	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
19.7b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite0.0hr

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:

0.0hr	(* (* n (pow (/ l Om) 2.0)) (- U U*))
0.0hr	(* n (pow (/ l Om) 2.0))
0.0hr	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
0.0hr	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(* (* n (pow (/ l Om) 2.0)) (- U U*))
0.0hr	(* n (pow (/ l Om) 2.0))
0.0hr	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
0.0hr	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify0.0hr

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 1 (0.0hr)

Iter	Nodes	Cost
0	1136	1922
1	5001	1732

prune0.0hr

Filtered

141 candidates to 85 candidates (39.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	134	7	141
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	138	15	153

Merged error: 16.4b

Counts

153 → 15

localize0.0hr

Local error

Found 4 expressions with local error:

6.4b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
8.2b	(* (* (* 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*))))
9.9b	(/ (* l l) Om)
19.7b	(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*)))))

rewrite0.0hr

Algorithm

rewrite-expression-head

Rules

96×	`add-exp-log`
64×	`prod-exp`
27×	`add-cbrt-cube`
25×	`pow1`
22×	`associate-*r/`
18×	`pow-exp`
13×	`pow-prod-down` `cbrt-unprod`
11×	`flip3--` `div-exp` `flip--`
10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`pow-to-exp`
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` `associate-/r*`
2×	`cbrt-undiv` `associate-l` `*-commutative`
1×	`frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 120

Calls

4 calls:

0.0hr	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
0.0hr	(* (* (* 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*))))
0.0hr	(/ (* l l) Om)
0.0hr	(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*)))))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
0.0hr	(* (* (* 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*))))
0.0hr	(/ (* l l) Om)
0.0hr	(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*)))))

simplify0.0hr

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 1 (0.0hr)

Iter	Nodes	Cost
0	1109	2291
1	5002	1933

prune0.0hr

Filtered

132 candidates to 75 candidates (43.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	129	3	132
Fresh	2	11	13
Picked	1	0	1
Done	1	0	1
Total	133	14	147

Merged error: 15.7b

Counts

147 → 14

regimes0.0hr

Accuracy

14.2% (12.6b remaining)

Error of 30.7b against oracle of 18.1b and baseline of 32.8b

bsearch0.0hr

Steps

Iters	Range		Point
10	-6.505642589348379e-301	2.851972393828784e-297	4.929420577321347e-302

simplify0.0hr

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0hr)

Iter	Nodes	Cost
0	49	34
1	49	34

end0.0hr

sample0.0hr

Algorithm

intervals

Results

0.0hr	14996×	body	80	nan
0.0hr	9192×	body	80	valid

Details

sample0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

regimes0.0hr

bsearch0.0hr

simplify0.0hr

end0.0hr

sample0.0hr

Profiling