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

sample107.0ms

Algorithm

intervals

Results

47.0ms	474×	body	80	nan
24.0ms	256×	body	80	valid
4.0ms	42×	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: 26.5b

Counts

2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

5.9b	(* n (* (pow (/ l Om) 2.0) (- U* U)))
6.2b	(* (pow (/ l Om) 2.0) (- U* U))
6.8b	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
19.2b	(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

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:

11.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
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)))))))
17.0ms	(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:

128.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
124.0ms	(* (pow (/ l Om) 2.0) (- U* U))
339.0ms	(* n (* 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)))))))))

simplify53.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5048	2227

prune278.0ms

Filtered

83 candidates to 120 candidates (-44.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	108	12	120
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	109	13	122

Merged error: 21.6b

Counts

122 → 13

localize28.0ms

Local error

Found 4 expressions with local error:

13.1b	(cbrt (/ l Om))
13.1b	(cbrt (/ l Om))
13.1b	(cbrt (/ l Om))
19.2b	(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)))))))))

rewrite27.0ms

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))
2.0ms	(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)))))))))

series2.2s

Counts

4 → 12

Calls

4 calls:

14.0ms	(cbrt (/ l Om))
15.0ms	(cbrt (/ l Om))
23.0ms	(cbrt (/ l Om))
2.2s	(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)))))))))

simplify38.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4973	1399
1	4973	1399

prune247.0ms

Filtered

79 candidates to 93 candidates (-17.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	93	13	106

Merged error: 21.6b

Counts

106 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

4.2b	(* n (pow (/ l Om) 2.0))
6.2b	(* (* n (pow (/ l Om) 2.0)) (- U* U))
6.8b	(* n (* U (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om)))))))
19.2b	(sqrt (* 2.0 (* n (* U (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om)))))))))

rewrite54.0ms

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:

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

43.0ms	(* n (pow (/ l Om) 2.0))
127.0ms	(* (* n (pow (/ l Om) 2.0)) (- U* U))
342.0ms	(* n (* 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)))))))))

simplify47.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	6599	2066

prune233.0ms

Filtered

75 candidates to 114 candidates (-52.0%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	113	14	127

Merged error: 21.3b

Counts

127 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

4.2b	(* n (pow (/ l Om) 2.0))
6.2b	(* (* n (pow (/ l Om) 2.0)) (- U* U))
8.2b	(* (* n U) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om))))))
19.2b	(sqrt (* 2.0 (* (* n U) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om))))))))

rewrite54.0ms

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))
11.0ms	(* (* n (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))))))
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:

45.0ms	(* n (pow (/ l Om) 2.0))
128.0ms	(* (* n (pow (/ l Om) 2.0)) (- U* U))
339.0ms	(* (* n 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))))))))

simplify63.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4974	2029
1	4974	2029

prune171.0ms

Filtered

76 candidates to 113 candidates (-48.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	2	9	11
Picked	1	0	1
Done	0	2	2
Total	114	13	127

Merged error: 21.3b

Counts

127 → 13

regimes1.3s

Accuracy

51.3% (4.1b remaining)

Error of 28.5b against oracle of 24.4b and baseline of 32.9b

bsearch1.0ms

simplify19.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	892	159
1	892	159

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.2s	12823×	body	80	nan
750.0ms	8000×	body	80	valid
125.0ms	1195×	body	80	invalid

Details

analyze2.3s

sample107.0ms

simplify39.0ms

prune16.0ms

localize18.0ms

rewrite58.0ms

series2.5s

simplify53.0ms

prune278.0ms

localize28.0ms

rewrite27.0ms

series2.2s

simplify38.0ms

prune247.0ms

localize18.0ms

rewrite54.0ms

series2.5s

simplify47.0ms

prune233.0ms

localize18.0ms

rewrite54.0ms

series2.5s

simplify63.0ms

prune171.0ms

regimes1.3s

bsearch1.0ms

simplify19.0ms

end0.0ms

sample2.8s

Profiling