Details

sample131.0ms

Algorithm

intervals

Results

48.0ms	500×	body	80	nan
26.0ms	301×	body	80	valid

simplify119.0ms

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

prune7.0ms

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

localize22.0ms

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*)))))

rewrite40.0ms

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:

10.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
4.0ms	(/ (* 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*)))))

series2.4s

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.0ms	(/ (* l l) Om)
349.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
1.9s	(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

115 → 115

Iterations

Useful iterations: 1 (25.0ms)

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

prune1.1s

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

localize19.0ms

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*)))))

rewrite42.0ms

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*)))
10.0ms	(* (* 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*)))))

series2.6s

Counts

4 → 12

Calls

4 calls:

202.0ms	(- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
126.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
347.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
1.9s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify123.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	971	2014
1	4611	1827
2	5001	1827

prune879.0ms

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*))))))

rewrite51.0ms

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:

11.0ms	(* n (* (pow (/ l Om) 2.0) (- U U*)))
13.0ms	(* (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*))))))

series2.7s

Counts

4 → 12

Calls

4 calls:

126.0ms	(* n (* (pow (/ l Om) 2.0) (- U U*)))
121.0ms	(* (pow (/ l Om) 2.0) (- U U*))
349.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))
2.1s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))

simplify129.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 1 (25.0ms)

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

prune1.6s

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*)))))))

rewrite60.0ms

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:

16.0ms	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
11.0ms	(* (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*))))))
10.0ms	(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*)))))))

series2.5s

Counts

4 → 12

Calls

4 calls:

125.0ms	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
123.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
351.0ms	(* (* (* 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*))))))
1.9s	(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*)))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1301	2832
1	5002	2417

prune1.9s

Filtered

166 candidates to 94 candidates (43.4%)

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

regimes1.7s

Accuracy

28.4% (6.7b remaining)

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

bsearch4.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	47
1	54	47

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.3s	14722×	body	80	nan
825.0ms	9219×	body	80	valid

Details

sample131.0ms

simplify119.0ms

prune7.0ms

localize22.0ms

rewrite40.0ms

series2.4s

simplify126.0ms

prune1.1s

localize19.0ms

rewrite42.0ms

series2.6s

simplify123.0ms

prune879.0ms

localize19.0ms

rewrite51.0ms

series2.7s

simplify129.0ms

prune1.6s

localize21.0ms

rewrite60.0ms

series2.5s

simplify54.0ms

prune1.9s

regimes1.7s

bsearch4.0ms

simplify2.0ms

end0.0ms

sample3.5s

Profiling