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

sample98.0ms

Algorithm

intervals

Results

41.0ms	389×	body	80	nan
24.0ms	256×	body	80	valid
3.0ms	34×	body	80	invalid

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: 26.7b

Counts

2 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

5.8b	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
6.4b	(* (pow (/ l Om) 2.0) (- U* U))
6.8b	(* n (* (pow (/ l Om) 2.0) (- U* U)))
17.6b	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

rewrite57.0ms

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×	`times-frac` `pow-prod-down`
9×	`distribute-rgt-in` `distribute-lft-in`
7×	`associate-r` `cbrt-unprod`
6×	`sub-neg`
4×	`sqrt-pow1` `pow-exp` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`pow-to-exp` `flip3--` `flip3-+` `sqrt-div` `div-exp` `flip--` `flip-+` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 108

Calls

4 calls:

15.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
11.0ms	(* (pow (/ l Om) 2.0) (- U* U))
11.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
16.0ms	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

series2.5s

Counts

4 → 12

Calls

4 calls:

337.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
125.0ms	(* (pow (/ l Om) 2.0) (- U* U))
132.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
1.9s	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5048	2227

prune288.0ms

Filtered

83 candidates to 120 candidates (-44.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	107	13	120
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	108	14	122

Merged error: 24.0b

Counts

122 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

5.6b	(* (* n (pow (/ l Om) 2.0)) (- U* U))
5.8b	(* n (* U (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om)))))))
6.4b	(* n (pow (/ l Om) 2.0))
17.6b	(sqrt (* 2.0 (* n (* U (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om)))))))))

rewrite57.0ms

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`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`sqrt-pow1` `pow-exp` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`pow-to-exp` `sub-neg` `flip3-+` `sqrt-div` `div-exp` `flip-+` `sqr-pow`
1×	`flip3--` `pow1/2` `sqrt-prod` `flip--` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 102

Calls

4 calls:

12.0ms	(* (* n (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)))))))
9.0ms	(* n (pow (/ l Om) 2.0))
15.0ms	(sqrt (* 2.0 (* n (* U (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om)))))))))

series2.6s

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (* n (pow (/ l Om) 2.0)) (- U* U))
337.0ms	(* n (* U (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om)))))))
42.0ms	(* n (pow (/ l Om) 2.0))
2.0s	(sqrt (* 2.0 (* n (* U (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om)))))))))

simplify39.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	6599	2066

prune233.0ms

Filtered

74 candidates to 114 candidates (-54.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	3	10	13
Picked	0	1	1
Done	0	0	0
Total	114	14	128

Merged error: 23.7b

Counts

128 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

5.6b	(* (* n (pow (/ l Om) 2.0)) (- U* U))
6.4b	(* n (pow (/ l Om) 2.0))
9.7b	(* (* n U) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om))))))
17.6b	(sqrt (* 2.0 (* (* n U) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om))))))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log`
26×	`associate-r`
25×	`add-sqr-sqrt`
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×	`sqrt-pow1` `pow-exp` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`distribute-rgt-in` `pow-to-exp` `sub-neg` `distribute-lft-in` `flip3-+` `sqrt-div` `div-exp` `flip-+` `sqr-pow`
1×	`flip3--` `pow1/2` `sqrt-prod` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 101

Calls

4 calls:

11.0ms	(* (* n (pow (/ l Om) 2.0)) (- U* U))
9.0ms	(* n (pow (/ l Om) 2.0))
15.0ms	(* (* n 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))))))))

series2.5s

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (* n (pow (/ l Om) 2.0)) (- U* U))
43.0ms	(* n (pow (/ l Om) 2.0))
345.0ms	(* (* n U) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om))))))
1.9s	(sqrt (* 2.0 (* (* n U) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om))))))))

simplify69.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4974	2029
1	4974	2029

prune253.0ms

Filtered

76 candidates to 113 candidates (-48.7%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	111	16	127

Merged error: 23.5b

Counts

127 → 16

localize25.0ms

Local error

Found 4 expressions with local error:

5.8b	(* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))
6.8b	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))))
7.2b	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
17.6b	(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)))))))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

20.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))
17.0ms	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))))
12.0ms	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
20.0ms	(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)))))))))

series2.5s

Counts

4 → 12

Calls

4 calls:

341.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))
131.0ms	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))))
93.0ms	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
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)))))))))

simplify41.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4972	2719
1	4972	2719

prune215.0ms

Filtered

83 candidates to 131 candidates (-57.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	2	11	13
Picked	1	0	1
Done	1	1	2
Total	133	14	147

Merged error: 22.2b

Counts

147 → 14

regimes940.0ms

Accuracy

0.2% (8.5b remaining)

Error of 31.5b against oracle of 22.9b and baseline of 31.5b

bsearch292.0ms

Steps

Iters	Range		Point
8	3.075580053479308e-73	3.421937567266123e-69	6.559726813680222e-73
9	1.426262406368397e-280	3.8086540723714405e-274	1.8007965386908381e-276
7	-1.6227800475589376e-188	-9.48915817225894e-191	-2.502409614250465e-190

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	196	150
1	196	150

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.3s	12944×	body	80	nan
787.0ms	8000×	body	80	valid
120.0ms	1223×	body	80	invalid

Details

analyze2.6s

sample98.0ms

simplify39.0ms

prune16.0ms

localize21.0ms

rewrite57.0ms

series2.5s

simplify54.0ms

prune288.0ms

localize18.0ms

rewrite57.0ms

series2.6s

simplify39.0ms

prune233.0ms

localize20.0ms

rewrite53.0ms

series2.5s

simplify69.0ms

prune253.0ms

localize25.0ms

rewrite74.0ms

series2.5s

simplify41.0ms

prune215.0ms

regimes940.0ms

bsearch292.0ms

simplify3.0ms

end0.0ms

sample2.9s

Profiling