Details

sample80.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 62.473122%

Results

10.0ms	194×	body	80	valid
8.0ms	28×	body	2560	valid
3.0ms	9×	body	5120	valid
2.0ms	8×	body	1280	valid
1.0ms	7×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	8
1	24	8
2	30	8
3	35	8
4	35	8

prune3.0ms

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: 38.4b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.0b	(+ (* re re) (* im im))
1.5b	(- (sqrt (+ (* re re) (* im im))) re)
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
5×	`add-cube-cbrt` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`sqrt-pow1`
2×	`flip3--` `flip3-+` `pow1/2` `associate-*r/` `flip--` `flip-+` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `diff-log` `pow-prod-down` `sum-log` `distribute-lft-out--`

Counts

4 → 54

Calls

4 calls:

8.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(+ (* re re) (* im im))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
5.0ms	(+ (* re re) (* im im))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
10.0ms	(sqrt (+ (* re re) (* im im)))

simplify106.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	260	458
1	982	428
2	3667	421
3	5001	420

prune120.0ms

Filtered

52 candidates to 66 candidates (-26.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	60	6	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	6	67

Merged error: 17.1b

Counts

67 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
8.6b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
30.1b	(sqrt (+ (* re re) (* im im)))
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
51×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `difference-of-squares`

Counts

4 → 126

Calls

4 calls:

17.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
14.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series25.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	261	1112
1	935	975
2	5001	951

prune136.0ms

Filtered

75 candidates to 138 candidates (-84.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	137	7	144

Merged error: 17.1b

Counts

144 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (sqrt (+ (* re re) (* im im))) re)
1.5b	(- (sqrt (+ (* re re) (* im im))) re)
30.1b	(sqrt (+ (* re re) (* im im)))
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series25.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify84.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 4 (77.0ms)

Iter	Nodes	Cost
0	135	456
1	332	432
2	839	424
3	2503	422
4	5002	420

prune133.0ms

Filtered

56 candidates to 72 candidates (-28.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	72	7	79

Merged error: 17.1b

Counts

79 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

30.1b	(sqrt (+ (* re re) (* im im)))
30.1b	(sqrt (+ (* re re) (* im im)))
30.1b	(sqrt (+ (* re re) (* im im)))
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series23.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify140.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 5 (135.0ms)

Iter	Nodes	Cost
0	89	400
1	215	388
2	503	388
3	1265	388
4	4227	388
5	5002	384

prune109.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	72	7	79

Merged error: 17.1b

Counts

79 → 7

regimes600.0ms

Accuracy

57.6% (9.0b remaining)

Error of 26.8b against oracle of 17.8b and baseline of 39.1b

bsearch68.0ms

Steps

Iters	Range	Point
9	7.902638540703399e-250	9.888311763283355e-241	1.0047013286056985e-249
10	-2.8691530181618067e-284	-1.1799496549931445e-295	-1.6166635324987067e-294
10	-4.76090289411841e+166	-5.18007515342894e+152	-6.793106322448464e+152

Iters

Range

Point

7.902638540703399e-250

9.888311763283355e-241

1.0047013286056985e-249

-2.8691530181618067e-284

-1.1799496549931445e-295

-1.6166635324987067e-294

-4.76090289411841e+166

-5.18007515342894e+152

-6.793106322448464e+152

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	34
1	55	34
2	55	34

end0.0ms

sample1.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 62.473122%

Results

290.0ms	6002×	body	80	valid
197.0ms	698×	body	2560	valid
115.0ms	492×	body	1280	valid
110.0ms	306×	body	5120	valid
50.0ms	282×	body	640	valid
21.0ms	155×	body	320	valid
6.0ms	65×	body	160	valid

Details

sample80.0ms

simplify7.0ms

prune3.0ms

localize11.0ms

rewrite23.0ms

series46.0ms

simplify106.0ms

prune120.0ms

localize13.0ms

rewrite43.0ms

series25.0ms

simplify46.0ms

prune136.0ms

localize16.0ms

rewrite23.0ms

series25.0ms

simplify84.0ms

prune133.0ms

localize23.0ms

rewrite17.0ms

series23.0ms

simplify140.0ms

prune109.0ms

regimes600.0ms

bsearch68.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling