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

sample156.0ms

Algorithm

intervals

Results

22.0ms

256×

body

valid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5186	28

prune16.0ms

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: 26.8b

Counts

2 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

5.1b	(* (pow (/ l Om) 2.0) (- U* U))
5.4b	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
5.5b	(* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
17.8b	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

11.0ms	(* (pow (/ l Om) 2.0) (- U* U))
15.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
14.0ms	(* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
15.0ms	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

series2.9s

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (pow (/ l Om) 2.0) (- U* U))
362.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
332.0ms	(* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
2.0s	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

simplify44.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	6589	2534

prune312.0ms

Filtered

87 candidates to 117 candidates (-34.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	103	14	117
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	104	15	119

Merged error: 21.8b

Counts

119 → 15

localize23.0ms

Local error

Found 4 expressions with local error:

5.1b	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
5.4b	(* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))
5.5b	(* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om))))))
17.8b	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

12.0ms	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
19.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))
18.0ms	(* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om))))))
22.0ms	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))))

series2.8s

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
357.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))
333.0ms	(* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om))))))
2.0s	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))))

simplify66.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4963	2785
1	4963	2785

prune316.0ms

Filtered

88 candidates to 115 candidates (-30.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	4	10	14
Picked	0	1	1
Done	0	0	0
Total	116	14	130

Merged error: 21.0b

Counts

130 → 14

localize25.0ms

Local error

Found 4 expressions with local error:

12.1b	(cbrt (/ l Om))
12.1b	(cbrt (/ l Om))
12.1b	(cbrt (/ l Om))
17.8b	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0) (* (- U* U) (pow (cbrt (/ l Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))))

rewrite30.0ms

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:

3.0ms	(cbrt (/ l Om))
4.0ms	(cbrt (/ l Om))
3.0ms	(cbrt (/ l Om))
17.0ms	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0) (* (- U* U) (pow (cbrt (/ l Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))))

series2.1s

Counts

4 → 12

Calls

4 calls:

13.0ms	(cbrt (/ l Om))
13.0ms	(cbrt (/ l Om))
14.0ms	(cbrt (/ l Om))
2.1s	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0) (* (- U* U) (pow (cbrt (/ l Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))))

simplify43.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4973	1399
1	4973	1399

prune253.0ms

Filtered

79 candidates to 93 candidates (-17.7%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	93	14	107

Merged error: 21.0b

Counts

107 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

5.1b	(* (pow (/ l Om) 2.0) (- U* U))
5.4b	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
5.5b	(* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
17.8b	(sqrt (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

11.0ms	(* (pow (/ l Om) 2.0) (- U* U))
17.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
14.0ms	(* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
14.0ms	(sqrt (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))))

series2.2s

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (pow (/ l Om) 2.0) (- U* U))
356.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
331.0ms	(* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
1.4s	(sqrt (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))))

simplify40.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	6018	2493

prune233.0ms

Filtered

91 candidates to 116 candidates (-27.5%)

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	111	5	116
Fresh	2	9	11
Picked	0	1	1
Done	0	2	2
Total	113	17	130

Merged error: 17.8b

Counts

130 → 17

regimes1.1s

Accuracy

31.1% (8.2b remaining)

Error of 28.3b against oracle of 20.1b and baseline of 32.0b

bsearch129.0ms

Steps

Iters	Range		Point
9	-2.980172525730764e-302	5.467241652945337e-308	4.2789353869314e-311
5	-1.4517173759372536e-71	-4.376425235204081e-72	-1.0972760249323405e-71

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	218	119
1	218	119

end0.0ms

sample4.5s

Algorithm

intervals

Results

729.0ms

8000×

body

valid

Details

analyze2.3s

sample156.0ms

simplify39.0ms

prune16.0ms

localize22.0ms

rewrite58.0ms

series2.9s

simplify44.0ms

prune312.0ms

localize23.0ms

rewrite75.0ms

series2.8s

simplify66.0ms

prune316.0ms

localize25.0ms

rewrite30.0ms

series2.1s

simplify43.0ms

prune253.0ms

localize21.0ms

rewrite59.0ms

series2.2s

simplify40.0ms

prune233.0ms

regimes1.1s

bsearch129.0ms

simplify3.0ms

end0.0ms

sample4.5s

Profiling