Details

analyze2.3s

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

sample106.0ms

Algorithm

intervals

Results

43.0ms	461×	body	80	nan
25.0ms	256×	body	80	valid
4.0ms	43×	body	80	invalid

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

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: 27.2b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

5.2b	(* (pow (/ l Om) 2.0) (- U U*))
5.8b	(* n (* (pow (/ l Om) 2.0) (- U U*)))
8.2b	(* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))
17.2b	(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:

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

series2.7s

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (pow (/ l Om) 2.0) (- U U*))
126.0ms	(* n (* (pow (/ l Om) 2.0) (- U U*)))
340.0ms	(* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))
2.1s	(sqrt (* 2.0 (* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))))

simplify59.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5015	2266

prune327.0ms

Filtered

84 candidates to 120 candidates (-42.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	108	12	120
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	110	12	122

Merged error: 22.2b

Counts

122 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

6.1b	(* n (pow (/ l Om) 2.0))
6.1b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.2b	(* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
17.2b	(sqrt (* 2.0 (* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log`
25×	`add-sqr-sqrt`
23×	`associate-r`
21×	`pow1`
17×	`*-un-lft-identity`
16×	`prod-exp` `add-cbrt-cube`
15×	`add-cube-cbrt` `unpow-prod-down`
12×	`associate-*r/`
10×	`times-frac` `pow-prod-down`
7×	`associate-l` `cbrt-unprod`
6×	`sub-neg`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`sqrt-pow1` `pow-exp` `add-log-exp` `unswap-sqr`
3×	`flip3--` `*-commutative` `flip--`
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 → 102

Calls

4 calls:

8.0ms	(* n (pow (/ l Om) 2.0))
11.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
13.0ms	(* n (* U (- t (+ (* 2.0 (* l (/ l Om))) (* (* n (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*))))))))

series2.4s

Counts

4 → 12

Calls

4 calls:

42.0ms	(* n (pow (/ l Om) 2.0))
130.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
324.0ms	(* 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*))))))))

simplify37.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5003	2088

prune222.0ms

Filtered

74 candidates to 114 candidates (-54.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	115	11	126

Merged error: 22.2b

Counts

126 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

6.1b	(* n (pow (/ l Om) 2.0))
6.1b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
13.1b	(* (* n U) (- t (+ (* 2.0 (* l (/ l Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
17.2b	(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

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

Counts

4 → 102

Calls

4 calls:

8.0ms	(* n (pow (/ l Om) 2.0))
11.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
11.0ms	(* (* 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:

42.0ms	(* n (pow (/ l Om) 2.0))
126.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
335.0ms	(* (* 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*)))))))

simplify75.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4978	2038
1	4978	2038

prune239.0ms

Filtered

75 candidates to 114 candidates (-52.0%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	111	14	125

Merged error: 22.2b

Counts

125 → 14

localize32.0ms

Local error

Found 4 expressions with local error:

14.0b	(cbrt (- t (+ (* 2.0 (* l (/ l Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
14.0b	(cbrt (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))
14.0b	(cbrt (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))
17.2b	(sqrt (* 2.0 (* (* n (* U (* (cbrt (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U)))))) (cbrt (- t (+ ( 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U))))))))) (cbrt (- t (+ ( 2.0 (* l (/ l Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

82×	`associate-*r/`
60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`sqrt-div`
25×	`pow1`
15×	`cbrt-prod` `pow-prod-down`
14×	`associate-*l/`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`sqrt-pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `distribute-lft-out--` `difference-of-squares`
1×	`pow1/2` `sqrt-prod`

Counts

4 → 86

Calls

4 calls:

6.0ms	(cbrt (- t (+ (* 2.0 (* l (/ l Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.0ms	(cbrt (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))
7.0ms	(cbrt (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))
34.0ms	(sqrt (* 2.0 (* (* n (* U (* (cbrt (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U)))))) (cbrt (- t (+ ( 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U))))))))) (cbrt (- t (+ ( 2.0 (* l (/ l Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))))

series2.7s

Counts

4 → 12

Calls

4 calls:

281.0ms	(cbrt (- t (+ (* 2.0 (* l (/ l Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
278.0ms	(cbrt (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))
273.0ms	(cbrt (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))
1.9s	(sqrt (* 2.0 (* (* n (* U (* (cbrt (- t (+ (* 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U)))))) (cbrt (- t (+ ( 2.0 (* l (/ l Om))) (* n (* (pow (/ l Om) 2.0) (- U U))))))))) (cbrt (- t (+ ( 2.0 (* l (/ l Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))))

simplify75.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4948	6337
1	4948	6337

prune279.0ms

Filtered

61 candidates to 98 candidates (-60.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	0	12	12
Picked	1	0	1
Done	0	1	1
Total	96	16	112

Merged error: 22.2b

Counts

112 → 16

regimes1.0s

Accuracy

-1.3% (7.7b remaining)

Error of 32.4b against oracle of 24.6b and baseline of 32.2b

bsearch7.0s

Steps

Iters	Range		Point
9	-3.968518119498483e-291	-1.2842063325732417e-299	-7.178830274298204e-295
7	-7.320794103193871e-225	-1.450778450117527e-226	-1.5437202692128072e-226

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	80
1	71	80

end0.0ms

analyze2.3s

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

sample2.9s

Algorithm

intervals

Results

1.2s	12838×	body	80	nan
763.0ms	8000×	body	80	valid
122.0ms	1190×	body	80	invalid

Details

analyze2.3s

sample106.0ms

simplify66.0ms

prune17.0ms

localize19.0ms

rewrite50.0ms

series2.7s

simplify59.0ms

prune327.0ms

localize18.0ms

rewrite48.0ms

series2.4s

simplify37.0ms

prune222.0ms

localize20.0ms

rewrite44.0ms

series2.4s

simplify75.0ms

prune239.0ms

localize32.0ms

rewrite60.0ms

series2.7s

simplify75.0ms

prune279.0ms

regimes1.0s

bsearch7.0s

simplify2.0ms

end0.0ms

analyze2.3s

sample2.9s

Profiling