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

sample97.0ms

Algorithm

intervals

Results

37.0ms	383×	body	80	nan
25.0ms	256×	body	80	valid
4.0ms	37×	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: 26.8b

Counts

2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

4.5b	(* n (* (pow (/ l Om) 2.0) (- U* U)))
6.4b	(* (pow (/ l Om) 2.0) (- U* U))
7.9b	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
19.0b	(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

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)))
13.0ms	(* (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)))))))
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:

125.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
124.0ms	(* (pow (/ l Om) 2.0) (- U* U))
330.0ms	(* 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)))))))))

simplify51.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5048	2227

prune296.0ms

Filtered

83 candidates to 120 candidates (-44.6%)

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: 21.6b

Counts

122 → 15

localize22.0ms

Local error

Found 4 expressions with local error:

4.5b	(* n (* (pow (/ l Om) 2.0) (- U* U)))
6.4b	(* (pow (/ l Om) 2.0) (- U* U))
7.5b	(* (* n U) (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
19.0b	(sqrt (* 2.0 (* (* n U) (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log`
25×	`add-sqr-sqrt`
21×	`pow1` `associate-l`
19×	`*-un-lft-identity`
16×	`prod-exp` `add-cbrt-cube`
15×	`add-cube-cbrt` `unpow-prod-down`
12×	`associate-*r/`
10×	`times-frac` `associate-r` `pow-prod-down`
7×	`cbrt-unprod`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
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` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 107

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))))))
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:

124.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
120.0ms	(* (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))))))
2.1s	(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

119 → 119

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5047	2214

prune259.0ms

Filtered

79 candidates to 119 candidates (-50.6%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	117	17	134

Merged error: 21.6b

Counts

134 → 17

localize20.0ms

Local error

Found 4 expressions with local error:

4.5b	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))))
6.8b	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
7.9b	(* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))
19.0b	(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)))))))))

rewrite72.0ms

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:

16.0ms	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))))
11.0ms	(* (- 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)))))))
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)))))))))

series2.4s

Counts

4 → 12

Calls

4 calls:

129.0ms	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))))
90.0ms	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
328.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))
1.9s	(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)))))))))

simplify44.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4972	2719
1	4972	2719

prune304.0ms

Filtered

84 candidates to 131 candidates (-56.0%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	2	13	15
Picked	1	0	1
Done	0	1	1
Total	132	16	148

Merged error: 20.4b

Counts

148 → 16

localize20.0ms

Local error

Found 4 expressions with local error:

5.3b	(* n (pow (/ l Om) (/ 2.0 2)))
6.8b	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
7.9b	(* n (* U (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om)))))))
19.0b	(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)))))))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
35×	`associate-r`
30×	`unpow-prod-down`
25×	`add-exp-log` `*-un-lft-identity`
23×	`add-cube-cbrt`
20×	`times-frac`
19×	`pow1`
13×	`add-cbrt-cube`
11×	`associate-l` `prod-exp`
10×	`associate-*r/`
9×	`pow-prod-down`
8×	`unswap-sqr`
5×	`cbrt-unprod`
4×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `pow-exp` `add-log-exp` `sqr-pow`
3×	`*-commutative`
2×	`pow-to-exp` `flip3-+` `sqrt-div` `div-exp` `associate-*l/` `flip-+` `div-inv`
1×	`flip3--` `pow1/2` `sqrt-prod` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 117

Calls

4 calls:

9.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
13.0ms	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
18.0ms	(* n (* U (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om)))))))
18.0ms	(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)))))))))

series2.4s

Counts

4 → 12

Calls

4 calls:

47.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
89.0ms	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
330.0ms	(* n (* U (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om)))))))
1.9s	(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)))))))))

simplify67.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4960	2511
1	4960	2511

prune271.0ms

Filtered

98 candidates to 129 candidates (-31.6%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	129	16	145

Merged error: 20.4b

Counts

145 → 16

regimes1.5s

Accuracy

43% (4.2b remaining)

Error of 26.7b against oracle of 22.5b and baseline of 29.8b

bsearch2.0ms

simplify18.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	764	127
1	764	127

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.2s	12826×	body	80	nan
758.0ms	8000×	body	80	valid
115.0ms	1182×	body	80	invalid

Details

analyze2.3s

sample97.0ms

simplify40.0ms

prune16.0ms

localize18.0ms

rewrite58.0ms

series2.5s

simplify51.0ms

prune296.0ms

localize22.0ms

rewrite56.0ms

series2.7s

simplify52.0ms

prune259.0ms

localize20.0ms

rewrite72.0ms

series2.4s

simplify44.0ms

prune304.0ms

localize20.0ms

rewrite63.0ms

series2.4s

simplify67.0ms

prune271.0ms

regimes1.5s

bsearch2.0ms

simplify18.0ms

end0.0ms

sample2.8s

Profiling