Details

analyze2.5s

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

40.0ms	394×	body	80	nan
25.0ms	256×	body	80	valid
3.0ms	30×	body	80	invalid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (38.0ms)

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: 27.3b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

5.9b	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
5.9b	(* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
6.8b	(* n (* (pow (/ l Om) 2.0) (- U* U)))
18.0b	(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

25×	`add-exp-log`
23×	`pow1`
16×	`associate-*r/` `add-cbrt-cube`
13×	`prod-exp`
11×	`pow-prod-down`
10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
8×	`add-cube-cbrt`
7×	`cbrt-unprod`
6×	`associate-r`
4×	`sub-neg` `sqrt-pow1` `add-log-exp`
3×	`flip3-+` `*-commutative` `flip-+`
2×	`sqrt-div` `pow-exp`
1×	`pow-to-exp` `flip3--` `pow1/2` `div-exp` `sqrt-prod` `flip--` `distribute-lft-out` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

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

328.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
303.0ms	(* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
127.0ms	(* 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)))))))))

simplify39.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	6423	2359

prune247.0ms

Filtered

67 candidates to 100 candidates (-49.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	88	12	100
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	89	13	102

Merged error: 23.5b

Counts

102 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

5.9b	(* U (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om))))))
6.0b	(* n (pow (/ l Om) 2.0))
6.1b	(* (* n (pow (/ l Om) 2.0)) (- U* U))
18.0b	(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

28×	`add-exp-log` `add-sqr-sqrt`
26×	`associate-r`
20×	`*-un-lft-identity`
18×	`pow1`
16×	`add-cube-cbrt`
15×	`unpow-prod-down`
14×	`prod-exp`
13×	`add-cbrt-cube`
10×	`times-frac` `associate-*r/`
8×	`pow-prod-down`
7×	`associate-l`
5×	`cbrt-unprod` `unswap-sqr`
4×	`sqrt-pow1` `pow-exp` `add-log-exp`
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:

14.0ms	(* U (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om))))))
9.0ms	(* n (pow (/ l Om) 2.0))
11.0ms	(* (* n (pow (/ l Om) 2.0)) (- U* U))
14.0ms	(sqrt (* 2.0 (* n (* U (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om)))))))))

series2.3s

Counts

4 → 12

Calls

4 calls:

303.0ms	(* U (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om))))))
41.0ms	(* n (pow (/ l Om) 2.0))
125.0ms	(* (* 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)))))))))

simplify39.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5835	2000

prune242.0ms

Filtered

77 candidates to 113 candidates (-46.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	114	12	126

Merged error: 23.3b

Counts

126 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

5.9b	(* n (* U (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* 2.0 (* l (/ l Om)))))))
5.9b	(* U (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* 2.0 (* l (/ l Om))))))
6.1b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
18.0b	(sqrt (* 2.0 (* n (* U (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* 2.0 (* l (/ l Om)))))))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-exp-log`
61×	`prod-exp`
23×	`pow1`
20×	`add-cbrt-cube`
18×	`pow-exp`
14×	`associate-*r/`
12×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`pow-prod-down`
10×	`associate-r` `cbrt-unprod`
9×	`pow-to-exp` `div-exp`
8×	`add-cube-cbrt`
7×	`associate-l`
6×	`distribute-rgt-in` `distribute-lft-in`
4×	`sqrt-pow1` `add-log-exp`
3×	`flip3-+` `*-commutative` `flip-+`
2×	`sub-neg` `sqrt-div`
1×	`flip3--` `pow1/2` `sqrt-prod` `flip--` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

20.0ms	(* n (* U (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* 2.0 (* l (/ l Om)))))))
18.0ms	(* U (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* 2.0 (* l (/ l Om))))))
16.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
21.0ms	(sqrt (* 2.0 (* n (* U (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* 2.0 (* l (/ l Om)))))))))

series2.6s

Counts

4 → 12

Calls

4 calls:

321.0ms	(* n (* U (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* 2.0 (* l (/ l Om)))))))
308.0ms	(* U (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* 2.0 (* l (/ l Om))))))
130.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
1.9s	(sqrt (* 2.0 (* n (* U (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* 2.0 (* l (/ l Om)))))))))

simplify57.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5006	2958

prune242.0ms

Filtered

72 candidates to 117 candidates (-62.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	118	11	129

Merged error: 22.8b

Counts

129 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

5.1b	(* n (pow (/ l Om) (/ 2.0 2)))
6.1b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
9.7b	(* (* n U) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* 2.0 (* l (/ l Om))))))
18.0b	(sqrt (* 2.0 (* (* n U) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* 2.0 (* l (/ l Om))))))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

8.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
16.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
18.0ms	(* (* n U) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* 2.0 (* l (/ l Om))))))
18.0ms	(sqrt (* 2.0 (* (* n U) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* 2.0 (* l (/ l Om))))))))

series2.4s

Counts

4 → 12

Calls

4 calls:

49.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
128.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
330.0ms	(* (* n U) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* 2.0 (* l (/ l Om))))))
1.9s	(sqrt (* 2.0 (* (* n U) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* 2.0 (* l (/ l Om))))))))

simplify72.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4985	2681
1	4985	2681

prune225.0ms

Filtered

82 candidates to 130 candidates (-58.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	127	3	130
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	128	13	141

Merged error: 22.8b

Counts

141 → 13

regimes825.0ms

Accuracy

12.3% (6.2b remaining)

Error of 29.8b against oracle of 23.6b and baseline of 30.6b

bsearch52.0ms

Steps

Iters	Range		Point
7	-1.323600137395367e-103	-1.5107670254750874e-105	-3.1921428213769144e-104

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	108	83
1	108	83

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.2s	12859×	body	80	nan
785.0ms	8000×	body	80	valid
114.0ms	1163×	body	80	invalid

Details

analyze2.5s

sample98.0ms

simplify40.0ms

prune16.0ms

localize19.0ms

rewrite58.0ms

series2.6s

simplify39.0ms

prune247.0ms

localize19.0ms

rewrite54.0ms

series2.3s

simplify39.0ms

prune242.0ms

localize21.0ms

rewrite80.0ms

series2.6s

simplify57.0ms

prune242.0ms

localize23.0ms

rewrite65.0ms

series2.4s

simplify72.0ms

prune225.0ms

regimes825.0ms

bsearch52.0ms

simplify2.0ms

end0.0ms

sample2.9s

Profiling