Details

analyze2.4s

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

sample100.0ms

Algorithm

intervals

Results

42.0ms	382×	body	80	nan
25.0ms	256×	body	80	valid
4.0ms	38×	body	80	invalid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5186	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: 27.5b

Counts

2 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

6.0b	(* (pow (/ l Om) 2.0) (- U* U))
6.0b	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
7.3b	(* n (* (pow (/ l Om) 2.0) (- U* U)))
19.2b	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

rewrite55.0ms

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

series2.7s

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (pow (/ l Om) 2.0) (- U* U))
328.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
129.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
2.1s	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

simplify52.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5048	2227

prune283.0ms

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: 24.4b

Counts

122 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

5.1b	(* n (pow (/ l Om) 2.0))
6.0b	(* n (* U (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om)))))))
6.2b	(* (* n (pow (/ l Om) 2.0)) (- U* U))
19.2b	(sqrt (* 2.0 (* n (* U (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om)))))))))

rewrite55.0ms

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:

9.0ms	(* n (pow (/ l Om) 2.0))
17.0ms	(* n (* 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))
15.0ms	(sqrt (* 2.0 (* n (* U (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om)))))))))

series2.4s

Counts

4 → 12

Calls

4 calls:

42.0ms	(* n (pow (/ l Om) 2.0))
335.0ms	(* n (* U (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om)))))))
124.0ms	(* (* 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)))))))))

simplify40.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	6599	2066

prune255.0ms

Filtered

74 candidates to 114 candidates (-54.1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	112	16	128

Merged error: 23.9b

Counts

128 → 16

localize24.0ms

Local error

Found 4 expressions with local error:

5.5b	(* U (* (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))) (cbrt n)))
6.0b	(* (pow (/ l Om) 2.0) (- U* U))
7.3b	(* n (* (pow (/ l Om) 2.0) (- U* U)))
19.2b	(sqrt (* 2.0 (* (* (cbrt n) (cbrt n)) (* U (* (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))) (cbrt n))))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

41×	`pow1`
31×	`add-exp-log`
26×	`pow-prod-down`
25×	`add-sqr-sqrt`
23×	`associate-l`
17×	`*-un-lft-identity`
16×	`prod-exp`
15×	`add-cube-cbrt` `unpow-prod-down` `add-cbrt-cube`
14×	`associate-*r/`
10×	`times-frac`
8×	`sqrt-pow1`
7×	`associate-r` `cbrt-unprod`
6×	`sub-neg`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-*l/` `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:

17.0ms	(* U (* (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))) (cbrt n)))
11.0ms	(* (pow (/ l Om) 2.0) (- U* U))
11.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
21.0ms	(sqrt (* 2.0 (* (* (cbrt n) (cbrt n)) (* U (* (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))) (cbrt n))))))

series2.4s

Counts

4 → 12

Calls

4 calls:

454.0ms	(* U (* (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))) (cbrt n)))
120.0ms	(* (pow (/ l Om) 2.0) (- U* U))
124.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
1.7s	(sqrt (* 2.0 (* (* (cbrt n) (cbrt n)) (* U (* (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))) (cbrt n))))))

simplify39.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	6201	2218

prune301.0ms

Filtered

86 candidates to 120 candidates (-39.5%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	116	4	120
Fresh	1	13	14
Picked	1	0	1
Done	0	1	1
Total	118	18	136

Merged error: 23.9b

Counts

136 → 18

localize28.0ms

Local error

Found 4 expressions with local error:

3.7b	(* (* (cbrt n) (cbrt n)) (* (* (cbrt U) (cbrt U)) (* (cbrt n) (* (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))) (cbrt U)))))
6.0b	(* (pow (/ l Om) 2.0) (- U* U))
7.3b	(* n (* (pow (/ l Om) 2.0) (- U* U)))
19.2b	(sqrt (* 2.0 (* (* (cbrt n) (cbrt n)) (* (* (cbrt U) (cbrt U)) (* (cbrt n) (* (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))) (cbrt U)))))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

153×	`pow1`
118×	`pow-prod-down`
91×	`add-exp-log`
64×	`prod-exp`
55×	`cbrt-unprod`
38×	`add-cbrt-cube`
24×	`add-sqr-sqrt`
21×	`associate-l`
20×	`associate-*r/`
16×	`*-un-lft-identity` `sqrt-pow1`
15×	`unpow-prod-down`
14×	`add-cube-cbrt`
10×	`times-frac`
7×	`associate-r`
6×	`sub-neg`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-*l/` `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 → 150

Calls

4 calls:

31.0ms	(* (* (cbrt n) (cbrt n)) (* (* (cbrt U) (cbrt U)) (* (cbrt n) (* (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))) (cbrt U)))))
12.0ms	(* (pow (/ l Om) 2.0) (- U* U))
11.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
33.0ms	(sqrt (* 2.0 (* (* (cbrt n) (cbrt n)) (* (* (cbrt U) (cbrt U)) (* (cbrt n) (* (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))) (cbrt U)))))))

series2.5s

Counts

4 → 12

Calls

4 calls:

346.0ms	(* (* (cbrt n) (cbrt n)) (* (* (cbrt U) (cbrt U)) (* (cbrt n) (* (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))) (cbrt U)))))
122.0ms	(* (pow (/ l Om) 2.0) (- U* U))
125.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
1.9s	(sqrt (* 2.0 (* (* (cbrt n) (cbrt n)) (* (* (cbrt U) (cbrt U)) (* (cbrt n) (* (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))) (cbrt U)))))))

simplify63.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5124	3446

prune197.0ms

Filtered

83 candidates to 162 candidates (-95.2%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	0	16	16
Picked	1	0	1
Done	0	1	1
Total	162	18	180

Merged error: 23.9b

Counts

180 → 18

regimes1.6s

Accuracy

50.4% (3.9b remaining)

Error of 27.3b against oracle of 23.4b and baseline of 31.2b

bsearch2.0ms

simplify19.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	892	156
1	892	156

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.2s	12267×	body	80	nan
815.0ms	8000×	body	80	valid
125.0ms	1172×	body	80	invalid

Details

analyze2.4s

sample100.0ms

simplify39.0ms

prune17.0ms

localize22.0ms

rewrite55.0ms

series2.7s

simplify52.0ms

prune283.0ms

localize19.0ms

rewrite55.0ms

series2.4s

simplify40.0ms

prune255.0ms

localize24.0ms

rewrite65.0ms

series2.4s

simplify39.0ms

prune301.0ms

localize28.0ms

rewrite95.0ms

series2.5s

simplify63.0ms

prune197.0ms

regimes1.6s

bsearch2.0ms

simplify19.0ms

end0.0ms

sample2.9s

Profiling