Details

analyze2.2s

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

sample102.0ms

Algorithm

intervals

Results

40.0ms	437×	body	80	nan
24.0ms	256×	body	80	valid
5.0ms	46×	body	80	invalid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5030	28

prune18.0ms

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: 27.8b

Counts

2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

5.2b	(* n (* (pow (/ l Om) 2.0) (- U* U)))
5.7b	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
7.5b	(* (pow (/ l Om) 2.0) (- U* U))
20.3b	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

rewrite60.0ms

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:

14.0ms	(* 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)))))))
11.0ms	(* (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:

129.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
336.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
124.0ms	(* (pow (/ l Om) 2.0) (- U* U))
2.0s	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

simplify56.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4980	2233
1	4980	2233

prune327.0ms

Filtered

85 candidates to 120 candidates (-41.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	106	14	120
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	107	15	122

Merged error: 25.0b

Counts

122 → 15

localize23.0ms

Local error

Found 4 expressions with local error:

5.2b	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))))
5.7b	(* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))
7.4b	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
20.3b	(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

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:

17.0ms	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (- 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)))))))
12.0ms	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
19.0ms	(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)))))))))

series2.7s

Counts

4 → 12

Calls

4 calls:

130.0ms	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))))
339.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))
89.0ms	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
2.2s	(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)))))))))

simplify88.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4958	2714
1	4958	2714

prune320.0ms

Filtered

84 candidates to 131 candidates (-56.0%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	131	15	146

Merged error: 25.0b

Counts

146 → 15

localize26.0ms

Local error

Found 4 expressions with local error:

4.4b	(* U (* (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))) (cbrt n)))
5.2b	(* n (* (pow (/ l Om) 2.0) (- U* U)))
7.5b	(* (pow (/ l Om) 2.0) (- U* U))
20.3b	(sqrt (* 2.0 (* (* (cbrt n) (cbrt n)) (* U (* (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))) (cbrt n))))))

rewrite64.0ms

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:

15.0ms	(* U (* (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))) (cbrt n)))
11.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
11.0ms	(* (pow (/ l Om) 2.0) (- U* U))
22.0ms	(sqrt (* 2.0 (* (* (cbrt n) (cbrt n)) (* U (* (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))) (cbrt n))))))

series2.5s

Counts

4 → 12

Calls

4 calls:

469.0ms	(* U (* (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))) (cbrt n)))
129.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
124.0ms	(* (pow (/ l Om) 2.0) (- U* U))
1.8s	(sqrt (* 2.0 (* (* (cbrt n) (cbrt n)) (* U (* (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))) (cbrt n))))))

simplify72.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4979	2161
1	4979	2161

prune309.0ms

Filtered

87 candidates to 120 candidates (-37.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	0	13	13
Picked	1	0	1
Done	0	1	1
Total	119	16	135

Merged error: 24.0b

Counts

135 → 16

localize22.0ms

Local error

Found 4 expressions with local error:

4.4b	(* U (* (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om))))) (cbrt n)))
6.4b	(* n (pow (/ l Om) 2.0))
8.1b	(* (* n (pow (/ l Om) 2.0)) (- U* U))
20.3b	(sqrt (* 2.0 (* (* (cbrt n) (cbrt n)) (* U (* (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om))))) (cbrt n))))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

18.0ms	(* U (* (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om))))) (cbrt n)))
9.0ms	(* n (pow (/ l Om) 2.0))
11.0ms	(* (* n (pow (/ l Om) 2.0)) (- U* U))
22.0ms	(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:

473.0ms	(* U (* (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om))))) (cbrt n)))
42.0ms	(* n (pow (/ l Om) 2.0))
129.0ms	(* (* n (pow (/ l Om) 2.0)) (- U* U))
1.8s	(sqrt (* 2.0 (* (* (cbrt n) (cbrt n)) (* U (* (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* 2.0 (* l (/ l Om))))) (cbrt n))))))

simplify45.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5691	1990

prune204.0ms

Filtered

83 candidates to 114 candidates (-37.3%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	114	16	130

Merged error: 24.0b

Counts

130 → 16

regimes1.4s

Accuracy

34.3% (5.1b remaining)

Error of 28.3b against oracle of 23.1b and baseline of 31.0b

bsearch1.0ms

simplify12.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	719	168
1	719	168

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.2s	13055×	body	80	nan
774.0ms	8000×	body	80	valid
119.0ms	1183×	body	80	invalid

Details

analyze2.2s

sample102.0ms

simplify38.0ms

prune18.0ms

localize18.0ms

rewrite60.0ms

series2.5s

simplify56.0ms

prune327.0ms

localize23.0ms

rewrite75.0ms

series2.7s

simplify88.0ms

prune320.0ms

localize26.0ms

rewrite64.0ms

series2.5s

simplify72.0ms

prune309.0ms

localize22.0ms

rewrite64.0ms

series2.4s

simplify45.0ms

prune204.0ms

regimes1.4s

bsearch1.0ms

simplify12.0ms

end0.0ms

sample2.9s

Profiling