Details

sample132.0ms

Algorithm

intervals

Results

46.0ms	500×	body	80	nan
28.0ms	301×	body	80	valid

simplify120.0ms

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

prune5.0ms

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: 36.0b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

6.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.5b	(/ (* l l) Om)
11.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.1b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite44.0ms

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:

14.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
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*)))))

series2.5s

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.0ms	(/ (* l l) Om)
366.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
2.0s	(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

115 → 115

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1004	1621
1	4896	1448
2	5001	1448

prune423.0ms

Filtered

115 candidates to 75 candidates (34.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	100	15	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	15	116

Merged error: 26.2b

Counts

116 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

4.5b	(- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
6.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
11.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.1b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log`
26×	`associate-*r/`
25×	`pow1`
18×	`add-cbrt-cube`
16×	`flip3--` `flip--`
15×	`prod-exp`
13×	`pow-prod-down`
12×	`frac-sub`
10×	`sub-neg`
9×	`cbrt-unprod` `add-log-exp`
8×	`distribute-rgt-in` `add-sqr-sqrt` `-un-lft-identity` `distribute-lft-in` `associate-r*`
6×	`add-cube-cbrt` `sqrt-div` `associate--l+`
4×	`sqrt-pow1` `associate--r+`
3×	`diff-log`
2×	`associate-l` `pow-exp` `*-commutative`
1×	`associate--l-` `pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 106

Calls

4 calls:

6.0ms	(- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
11.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series2.7s

Counts

4 → 12

Calls

4 calls:

211.0ms	(- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
131.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
383.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
2.0s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify128.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	971	2018
1	4599	1827
2	5002	1827

prune283.0ms

Filtered

118 candidates to 76 candidates (35.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	113	5	118
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	118	15	133

Merged error: 25.0b

Counts

133 → 15

localize19.0ms

Local error

Found 4 expressions with local error:

5.2b	(* n (* (pow (/ l Om) 2.0) (- U U*)))
6.0b	(* (pow (/ l Om) 2.0) (- U U*))
11.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))
20.1b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
34×	`associate-*r/`
25×	`pow1` `add-sqr-sqrt`
21×	`associate-l`
20×	`add-cbrt-cube`
19×	`prod-exp`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `unpow-prod-down`
14×	`distribute-rgt-in` `distribute-lft-in`
13×	`pow-prod-down`
12×	`flip3--` `flip--`
10×	`sub-neg` `times-frac` `cbrt-unprod`
9×	`associate-r`
8×	`frac-sub`
6×	`sqrt-div`
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 → 129

Calls

4 calls:

13.0ms	(* n (* (pow (/ l Om) 2.0) (- U U*)))
11.0ms	(* (pow (/ l Om) 2.0) (- U U*))
12.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))
10.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))

series2.6s

Counts

4 → 12

Calls

4 calls:

130.0ms	(* n (* (pow (/ l Om) 2.0) (- U U*)))
129.0ms	(* (pow (/ l Om) 2.0) (- U U*))
364.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))
2.0s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))

simplify126.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1104	1912
1	4866	1718
2	5002	1718

prune319.0ms

Filtered

141 candidates to 90 candidates (36.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	0	14	14
Picked	1	0	1
Done	0	0	0
Total	140	16	156

Merged error: 24.4b

Counts

156 → 16

localize21.0ms

Local error

Found 4 expressions with local error:

5.2b	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
6.7b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
11.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) (/ 2.0 2)) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
20.1b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) (/ 2.0 2)) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
44×	`associate-*r/`
30×	`distribute-rgt-in` `distribute-lft-in`
25×	`pow1` `add-sqr-sqrt`
24×	`add-cbrt-cube`
21×	`associate-l`
20×	`pow-exp`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `unpow-prod-down`
14×	`sub-neg`
13×	`pow-prod-down` `cbrt-unprod`
12×	`flip3--` `flip--`
10×	`pow-to-exp` `times-frac` `div-exp`
9×	`associate-r`
8×	`frac-sub`
6×	`sqrt-div`
4×	`sqrt-pow1` `associate--l+` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 154

Calls

4 calls:

17.0ms	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
13.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
13.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) (/ 2.0 2)) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
11.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) (/ 2.0 2)) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))))

series2.6s

Counts

4 → 12

Calls

4 calls:

131.0ms	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
125.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
369.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) (/ 2.0 2)) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
2.0s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) (/ 2.0 2)) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))))

simplify57.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1301	2828
1	5002	2413

prune299.0ms

Filtered

166 candidates to 93 candidates (44.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	168	14	182

Merged error: 23.7b

Counts

182 → 14

regimes1.4s

Accuracy

28.4% (6.7b remaining)

Error of 28.5b against oracle of 21.8b and baseline of 31.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	47
1	54	47

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.4s	14722×	body	80	nan
859.0ms	9219×	body	80	valid

Details

sample132.0ms

simplify120.0ms

prune5.0ms

localize18.0ms

rewrite44.0ms

series2.5s

simplify124.0ms

prune423.0ms

localize21.0ms

rewrite44.0ms

series2.7s

simplify128.0ms

prune283.0ms

localize19.0ms

rewrite52.0ms

series2.6s

simplify126.0ms

prune319.0ms

localize21.0ms

rewrite62.0ms

series2.6s

simplify57.0ms

prune299.0ms

regimes1.4s

bsearch1.0ms

simplify2.0ms

end0.0ms

sample3.7s

Profiling