Details

analyze2.5s

Algorithm: search

sample96.0ms

Algorithm

intervals

Results

35.0ms	375×	body	80	nan
27.0ms	256×	body	80	valid
4.0ms	41×	body	80	invalid

simplify120.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	14
1	153	14
2	652	14
3	3624	14
4	5002	14

prune5.0ms

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: 33.9b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

5.2b	(* n (pow (/ l Om) 2.0))
8.9b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.3b	(/ (* l l) Om)
18.5b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
24×	`add-sqr-sqrt`
23×	`pow1`
20×	`associate-r/` `associate-r*` `add-cbrt-cube`
16×	`add-cube-cbrt` `*-un-lft-identity`
15×	`unpow-prod-down`
13×	`times-frac`
12×	`pow-prod-down`
11×	`prod-exp`
10×	`flip3--` `flip--`
8×	`frac-sub` `cbrt-unprod`
6×	`sqrt-div`
4×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-pow1` `associate-l` `associate--l+` `add-log-exp` `unswap-sqr`
3×	`div-exp` `associate-/r*`
2×	`cbrt-undiv` `pow-exp` `*-commutative` `div-inv` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `associate-/l*`

Counts

4 → 112

Calls

4 calls:

11.0ms	(* n (pow (/ l Om) 2.0))
12.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
5.0ms	(/ (* l l) Om)
10.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series2.3s

Counts

4 → 12

Calls

4 calls:

43.0ms	(* n (pow (/ l Om) 2.0))
355.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
3.0ms	(/ (* l l) Om)
1.9s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify127.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1026	1602
1	4925	1447
2	5001	1447

prune318.0ms

Filtered

88 candidates to 124 candidates (-40.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	112	12	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	12	125

Merged error: 22.4b

Counts

125 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

5.0b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.2b	(* n (pow (/ l Om) 2.0))
8.9b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.5b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

11.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.0ms	(* n (pow (/ l Om) 2.0))
12.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series2.4s

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
42.0ms	(* n (pow (/ l Om) 2.0))
364.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
1.9s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1071	1765
1	5001	1602

prune295.0ms

Filtered

87 candidates to 131 candidates (-50.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	125	6	131
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	129	14	143

Merged error: 21.4b

Counts

143 → 14

localize24.0ms

Local error

Found 4 expressions with local error:

8.9b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (sqrt (pow (/ l Om) 2.0))) (sqrt (pow (/ l Om) 2.0))) (- U U*))))
15.1b	(sqrt (pow (/ l Om) 2.0))
15.1b	(sqrt (pow (/ l Om) 2.0))
18.5b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (sqrt (pow (/ l Om) 2.0))) (sqrt (pow (/ l Om) 2.0))) (- U U*)))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

35×	`sqrt-prod`
30×	`unpow-prod-down`
29×	`add-sqr-sqrt`
23×	`pow1`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac` `associate-*r/`
13×	`add-exp-log` `add-cbrt-cube`
12×	`pow-prod-down`
10×	`flip3--` `flip--`
8×	`rem-sqrt-square` `frac-sub`
6×	`sqrt-pow1` `sqrt-div` `prod-exp` `cbrt-unprod`
4×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate--l+` `add-log-exp` `sqr-pow`
3×	`pow1/2` `associate-r`
2×	`div-inv`
1×	`associate-l` `*-commutative`

Counts

4 → 114

Calls

4 calls:

12.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (sqrt (pow (/ l Om) 2.0))) (sqrt (pow (/ l Om) 2.0))) (- U U*))))
4.0ms	(sqrt (pow (/ l Om) 2.0))
4.0ms	(sqrt (pow (/ l Om) 2.0))
10.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (sqrt (pow (/ l Om) 2.0))) (sqrt (pow (/ l Om) 2.0))) (- U U*)))))

series2.3s

Counts

4 → 12

Calls

4 calls:

357.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (sqrt (pow (/ l Om) 2.0))) (sqrt (pow (/ l Om) 2.0))) (- U U*))))
46.0ms	(sqrt (pow (/ l Om) 2.0))
48.0ms	(sqrt (pow (/ l Om) 2.0))
1.9s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (sqrt (pow (/ l Om) 2.0))) (sqrt (pow (/ l Om) 2.0))) (- U U*)))))

simplify114.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	970	2051
1	4229	1801
2	5003	1765

prune400.0ms

Filtered

97 candidates to 126 candidates (-29.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	124	16	140

Merged error: 21.4b

Counts

140 → 16

localize21.0ms

Local error

Found 4 expressions with local error:

5.0b	(* (neg (- U U)) ( n (pow (/ l Om) 2.0)))
5.2b	(* n (pow (/ l Om) 2.0))
6.0b	(* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (neg (- U U)) ( n (pow (/ l Om) 2.0)))))) U)
18.5b	(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (neg (- U U)) ( n (pow (/ l Om) 2.0)))))) U) 1))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
31×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
21×	`associate-r`
20×	`add-cbrt-cube`
19×	`prod-exp`
18×	`add-cube-cbrt` `associate-l`
16×	`unpow-prod-down`
15×	`pow1`
10×	`times-frac` `cbrt-unprod`
7×	`pow-prod-down`
5×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `sqrt-prod`
4×	`associate-*l/` `pow-exp` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`*-commutative`
2×	`pow-to-exp` `rem-sqrt-square` `flip3--` `associate-*r/` `div-exp` `flip--` `distribute-neg-frac` `distribute-lft-out--` `difference-of-squares`
1×	`distribute-lft-neg-out` `neg-mul-1` `sqrt-pow1` `pow1/2` `div-inv`

Counts

4 → 110

Calls

4 calls:

12.0ms	(* (neg (- U U)) ( n (pow (/ l Om) 2.0)))
9.0ms	(* n (pow (/ l Om) 2.0))
15.0ms	(* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (neg (- U U)) ( n (pow (/ l Om) 2.0)))))) U)
3.0ms	(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (neg (- U U)) ( n (pow (/ l Om) 2.0)))))) U) 1))

series3.8s

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (neg (- U U)) ( n (pow (/ l Om) 2.0)))
42.0ms	(* n (pow (/ l Om) 2.0))
338.0ms	(* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (neg (- U U)) ( n (pow (/ l Om) 2.0)))))) U)
3.3s	(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (neg (- U U)) ( n (pow (/ l Om) 2.0)))))) U) 1))

simplify110.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	832	1407
1	3998	1220
2	5001	1215

prune230.0ms

Filtered

90 candidates to 122 candidates (-35.6%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	4	10	14
Picked	1	0	1
Done	0	1	1
Total	121	17	138

Merged error: 18.9b

Counts

138 → 17

regimes1.6s

Accuracy

31.9% (8.6b remaining)

Error of 28.4b against oracle of 19.7b and baseline of 32.4b

bsearch12.0s

Steps

Iters	Range		Point
8	8.010811663920977e-244	3.2221030128664845e-241	2.0842367652555688e-243
5	1.872281020423449e-270	4.601102883692136e-270	3.3518662346370392e-270
6	-8.667954530780272e-279	-8.792215268180793e-280	-2.8864814563598238e-279
8	-1.353631402271787e-61	-4.5126018857808774e-64	-6.581444501142788e-62

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	73
1	80	73
2	86	73
3	86	73

end0.0ms

analyze2.3s

Algorithm: search

sample3.1s

Algorithm

intervals

Results

1.5s	12730×	body	80	nan
761.0ms	8000×	body	80	valid
118.0ms	1198×	body	80	invalid

Details

analyze2.5s

sample96.0ms

simplify120.0ms

prune5.0ms

localize19.0ms

rewrite42.0ms

series2.3s

simplify127.0ms

prune318.0ms

localize20.0ms

rewrite46.0ms

series2.4s

simplify43.0ms

prune295.0ms

localize24.0ms

rewrite36.0ms

series2.3s

simplify114.0ms

prune400.0ms

localize21.0ms

rewrite43.0ms

series3.8s

simplify110.0ms

prune230.0ms

regimes1.6s

bsearch12.0s

simplify3.0ms

end0.0ms

analyze2.3s

sample3.1s

Profiling