Details

sample103.0ms

Algorithm

intervals

Results

42.0ms	526×	body	80	nan
22.0ms	305×	body	80	valid

simplify124.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	49	14
1	155	14
2	684	14
3	3898	14
4	5001	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: 34.1b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

6.5b	(/ (* l l) Om)
8.4b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.7b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
30×	`prod-diff`
26×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`pow1`
24×	`add-cube-cbrt`
23×	`add-cbrt-cube`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`associate--l+` `cbrt-unprod`
8×	`associate-r` `frac-sub`
6×	`sub-neg` `sqrt-div`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `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 → 141

Calls

4 calls:

5.0ms	(/ (* l l) Om)
12.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
13.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
13.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.4s

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (* l l) Om)
367.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.6s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1176	2335
1	5001	2011

prune538.0ms

Filtered

153 candidates to 92 candidates (60.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	137	16	153
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	138	16	154

Merged error: 24.0b

Counts

154 → 16

localize19.0ms

Local error

Found 4 expressions with local error:

5.6b	(* n (pow (/ l Om) 2.0))
8.4b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.7b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
35×	`add-exp-log`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`prod-diff`
25×	`pow1` `associate-r`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
20×	`add-cbrt-cube`
19×	`prod-exp`
15×	`unpow-prod-down`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`times-frac` `associate--l+` `cbrt-unprod`
8×	`frac-sub`
6×	`sub-neg` `sqrt-div`
5×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `pow-exp` `log1p-expm1-u` `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 → 157

Calls

4 calls:

8.0ms	(* n (pow (/ l Om) 2.0))
12.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
13.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
13.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.7s

Counts

4 → 12

Calls

4 calls:

149.0ms	(* n (pow (/ l Om) 2.0))
371.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
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*)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1229	2457
1	5001	2136

prune548.0ms

Filtered

169 candidates to 103 candidates (60.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	165	4	169
Fresh	6	9	15
Picked	1	0	1
Done	0	0	0
Total	172	13	185

Merged error: 22.6b

Counts

185 → 13

localize27.0ms

Local error

Found 4 expressions with local error:

5.7b	(* n (pow (/ l Om) (/ 2.0 2)))
8.4b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.5b	(* (* (* 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*))))
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*)))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
41×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`prod-diff`
25×	`pow1` `associate-r`
24×	`add-cbrt-cube`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
20×	`pow-exp`
15×	`unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
11×	`flip3--` `flip--`
10×	`pow-to-exp` `times-frac` `div-exp` `associate--l+`
8×	`frac-sub`
6×	`sub-neg` `sqrt-div`
5×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `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 → 174

Calls

4 calls:

9.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
17.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
14.0ms	(* (* (* 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*))))
14.0ms	(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:

158.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
367.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
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*))))
4.9s	(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*)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1355	3515
1	5002	2841

prune570.0ms

Filtered

186 candidates to 107 candidates (57.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	186	13	199

Merged error: 22.6b

Counts

199 → 13

localize24.0ms

Local error

Found 4 expressions with local error:

5.6b	(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
6.1b	(* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (- U U)) ( n (pow (/ l Om) (* 2 (/ 2.0 2)))))))) U)
8.4b	(* (- (- U U)) ( n (pow (/ l Om) (* 2 (/ 2.0 2)))))
19.7b	(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (- U U)) ( n (pow (/ l Om) (* 2 (/ 2.0 2)))))))) U) 1))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
31×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
21×	`associate-r`
20×	`add-cbrt-cube`
19×	`prod-exp`
18×	`add-cube-cbrt` `associate-l`
16×	`unpow-prod-down`
15×	`pow1`
10×	`times-frac` `cbrt-unprod`
7×	`pow-prod-down`
5×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `sqrt-prod`
4×	`expm1-log1p-u` `associate-*l/` `pow-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`*-commutative`
2×	`pow-to-exp` `rem-sqrt-square` `flip3--` `associate-*r/` `div-exp` `flip--` `distribute-neg-frac` `distribute-lft-out--` `difference-of-squares`
1×	`distribute-lft-neg-out` `neg-mul-1` `sqrt-pow1` `pow1/2` `div-inv`

Counts

4 → 118

Calls

4 calls:

10.0ms	(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
16.0ms	(* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (- U U)) ( n (pow (/ l Om) (* 2 (/ 2.0 2)))))))) U)
12.0ms	(* (- (- U U)) ( n (pow (/ l Om) (* 2 (/ 2.0 2)))))
4.0ms	(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (- U U)) ( n (pow (/ l Om) (* 2 (/ 2.0 2)))))))) U) 1))

series11.4s

Counts

4 → 12

Calls

4 calls:

148.0ms	(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
1.1s	(* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (- U U)) ( n (pow (/ l Om) (* 2 (/ 2.0 2)))))))) U)
258.0ms	(* (- (- U U)) ( n (pow (/ l Om) (* 2 (/ 2.0 2)))))
9.9s	(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (- U U)) ( n (pow (/ l Om) (* 2 (/ 2.0 2)))))))) U) 1))

simplify115.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	778	1671
1	3861	1446
2	5002	1440

prune704.0ms

Filtered

130 candidates to 96 candidates (73.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	124	6	130
Fresh	2	9	11
Picked	1	0	1
Done	1	0	1
Total	128	15	143

Merged error: 20.3b

Counts

143 → 15

regimes850.0ms

Accuracy

25.3% (8.5b remaining)

Error of 27.4b against oracle of 18.9b and baseline of 30.3b

bsearch3.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	98
1	76	98
2	83	98
3	88	98
4	88	98

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	14844×	body	80	nan
700.0ms	9160×	body	80	valid