Details

analyze2.6s

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	98.1%	1.9%	7
0%	98.1%	1.9%	8
0%	97.8%	2.2%	9
0%	96.8%	3.2%	10
0%	96.3%	3.7%	11
0%	94.3%	5.7%	12
0.4%	92.1%	7.5%	13
0.6%	90.8%	8.6%	14

sample100.0ms

Algorithm

intervals

Results

37.0ms	368×	body	80	nan
29.0ms	256×	body	80	valid
4.0ms	36×	body	80	invalid

simplify62.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5159	28

prune17.0ms

Filtered

1 candidates to 1 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: 29.0b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

6.0b	(* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))
6.1b	(* n (* (pow (/ l Om) 2.0) (- U U*)))
7.2b	(* (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*)))))))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log`
25×	`add-sqr-sqrt`
23×	`associate-l`
21×	`pow1`
17×	`*-un-lft-identity`
16×	`associate-*r/` `prod-exp` `add-cbrt-cube`
15×	`add-cube-cbrt` `unpow-prod-down`
10×	`sub-neg` `times-frac` `pow-prod-down`
9×	`distribute-rgt-in` `distribute-lft-in`
7×	`associate-r` `cbrt-unprod`
4×	`flip3--` `sqrt-pow1` `pow-exp` `flip--` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`pow-to-exp` `sqrt-div` `div-exp` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 108

Calls

4 calls:

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

series2.6s

Counts

4 → 12

Calls

4 calls:

348.0ms	(* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))
129.0ms	(* n (* (pow (/ l Om) 2.0) (- U U*)))
125.0ms	(* (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*)))))))))

simplify95.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5015	2266

prune323.0ms

Filtered

84 candidates to 120 candidates (-42.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	106	14	120
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	107	15	122

Merged error: 26.2b

Counts

122 → 15

localize25.0ms

Local error

Found 4 expressions with local error:

14.8b	(cbrt (/ l Om))
14.8b	(cbrt (/ l Om))
14.8b	(cbrt (/ l Om))
20.1b	(sqrt (* 2.0 (* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0) (* (- U U*) (pow (cbrt (/ l Om)) 2.0))))))))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
27×	`times-frac`
25×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
14×	`pow1`
6×	`associate-*r/` `pow-prod-down`
4×	`add-exp-log` `sqrt-pow1` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-div` `pow1/3` `div-inv`
2×	`sqrt-div`
1×	`flip3--` `pow1/2` `sqrt-prod` `flip--`

Counts

4 → 81

Calls

4 calls:

2.0ms	(cbrt (/ l Om))
2.0ms	(cbrt (/ l Om))
3.0ms	(cbrt (/ l Om))
11.0ms	(sqrt (* 2.0 (* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0) (* (- U U*) (pow (cbrt (/ l Om)) 2.0))))))))))

series2.0s

Counts

4 → 12

Calls

4 calls:

12.0ms	(cbrt (/ l Om))
15.0ms	(cbrt (/ l Om))
13.0ms	(cbrt (/ l Om))
2.0s	(sqrt (* 2.0 (* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0) (* (- U U*) (pow (cbrt (/ l Om)) 2.0))))))))))

simplify38.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5215	1385

prune281.0ms

Filtered

79 candidates to 93 candidates (-17.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	93	15	108

Merged error: 26.2b

Counts

108 → 15

localize25.0ms

Local error

Found 4 expressions with local error:

7.2b	(* (pow (/ l Om) 2.0) (- U U*))
20.1b	(sqrt (* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))))
20.1b	(sqrt (* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))))
20.1b	(sqrt (* 2.0 (* (sqrt (* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U)))))))) (sqrt ( n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

13.0ms	(* (pow (/ l Om) 2.0) (- U U*))
10.0ms	(sqrt (* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))))
10.0ms	(sqrt (* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))))
30.0ms	(sqrt (* 2.0 (* (sqrt (* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U)))))))) (sqrt ( n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))))))

series4.8s

Counts

4 → 12

Calls

4 calls:

134.0ms	(* (pow (/ l Om) 2.0) (- U U*))
1.3s	(sqrt (* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))))
1.3s	(sqrt (* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))))
2.0s	(sqrt (* 2.0 (* (sqrt (* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U)))))))) (sqrt ( n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))))))

simplify84.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4992	2893
1	4992	2893

prune373.0ms

Filtered

76 candidates to 103 candidates (-35.5%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	102	16	118

Merged error: 26.2b

Counts

118 → 16

localize21.0ms

Local error

Found 4 expressions with local error:

6.0b	(* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))
6.1b	(* n (* (pow (/ l Om) 2.0) (- U U*)))
7.2b	(* (pow (/ l Om) 2.0) (- U U*))
20.1b	(sqrt (* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log`
25×	`add-sqr-sqrt`
23×	`associate-l`
17×	`pow1` `*-un-lft-identity`
16×	`prod-exp` `add-cbrt-cube`
15×	`add-cube-cbrt` `unpow-prod-down`
14×	`associate-*r/`
10×	`sub-neg` `times-frac`
9×	`distribute-rgt-in` `distribute-lft-in`
7×	`associate-r` `pow-prod-down` `cbrt-unprod`
4×	`flip3--` `pow-exp` `flip--` `add-log-exp` `unswap-sqr`
3×	`sqrt-pow1` `*-commutative`
2×	`pow-to-exp` `sqrt-div` `div-exp` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 107

Calls

4 calls:

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

series2.0s

Counts

4 → 12

Calls

4 calls:

346.0ms	(* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))
135.0ms	(* n (* (pow (/ l Om) 2.0) (- U U*)))
129.0ms	(* (pow (/ l Om) 2.0) (- U U*))
1.4s	(sqrt (* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4958	2191
1	4958	2191

prune218.0ms

Filtered

84 candidates to 119 candidates (-41.7%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	2	11	13
Picked	1	0	1
Done	0	2	2
Total	118	17	135

Merged error: 20.8b

Counts

135 → 17

regimes1.6s

Accuracy

28.7% (7.6b remaining)

Error of 28.8b against oracle of 21.2b and baseline of 31.8b

bsearch4.5s

Steps

Iters	Range		Point
10	-2.2744309850859972e-306	8.428806888926738e-293	5.8001105639268e-310

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	75
1	53	75

end0.0ms

analyze2.4s

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	98.1%	1.9%	7
0%	98.1%	1.9%	8
0%	97.8%	2.2%	9
0%	96.8%	3.2%	10
0%	96.3%	3.7%	11
0%	94.3%	5.7%	12
0.4%	92.1%	7.5%	13
0.6%	90.8%	8.6%	14

sample3.0s

Algorithm

intervals

Results

1.3s	12651×	body	80	nan
825.0ms	8000×	body	80	valid
127.0ms	1190×	body	80	invalid

Details

analyze2.6s

sample100.0ms

simplify62.0ms

prune17.0ms

localize19.0ms

rewrite50.0ms

series2.6s

simplify95.0ms

prune323.0ms

localize25.0ms

rewrite21.0ms

series2.0s

simplify38.0ms

prune281.0ms

localize25.0ms

rewrite66.0ms

series4.8s

simplify84.0ms

prune373.0ms

localize21.0ms

rewrite50.0ms

series2.0s

simplify58.0ms

prune218.0ms

regimes1.6s

bsearch4.5s

simplify1.0ms

end0.0ms

analyze2.4s

sample3.0s

Profiling