Details

sample1.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 74.609375%

Results

12.0ms	195×	body	80	valid
6.0ms	22×	body	2560	valid
4.0ms	11×	body	5120	valid
3.0ms	15×	body	1280	valid
1.0ms	7×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	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: 37.5b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.0b	(+ (sqrt (+ (* re re) (* im im))) re)
28.0b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
8.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (* re re) (* im im))
25.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify97.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	277	428
1	1024	399
2	3458	393
3	5002	391

prune118.0ms

Filtered

52 candidates to 63 candidates (-21.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	7	64

Merged error: 16.5b

Counts

64 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (sqrt (+ (* re re) (* im im))) re)
28.0b	(sqrt (+ (* re re) (* im im)))
28.0b	(sqrt (+ (* re re) (* im im)))
28.0b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `sqrt-prod`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log` `distribute-lft-out`

Counts

4 → 57

Calls

4 calls:

7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
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)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify84.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	141	392
1	358	380
2	866	376
3	2557	375
4	5001	375

prune183.0ms

Filtered

61 candidates to 69 candidates (-13.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	69	7	76

Merged error: 16.5b

Counts

76 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

14.6b	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
28.0b	(sqrt (+ (* re re) (* im im)))
28.0b	(sqrt (+ (* re re) (* im im)))
28.0b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `sqrt-prod`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log` `distribute-lft-out`

Counts

4 → 57

Calls

4 calls:

9.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series25.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (exp (log (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify86.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 4 (79.0ms)

Iter	Nodes	Cost
0	148	441
1	379	399
2	892	395
3	2614	394
4	5001	393

prune188.0ms

Filtered

62 candidates to 69 candidates (-11.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	69	7	76

Merged error: 16.5b

Counts

76 → 7

localize31.0ms

Local error

Found 4 expressions with local error:

28.0b	(sqrt (+ (* re re) (* im im)))
28.0b	(sqrt (+ (* re re) (* im im)))
28.0b	(sqrt (+ (* re re) (* im im)))
28.0b	(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)))

series26.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify144.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 5 (138.0ms)

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

prune169.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	72	7	79

Merged error: 16.5b

Counts

79 → 7

regimes648.0ms

Accuracy

56.6% (9.1b remaining)

Error of 27.2b against oracle of 18.1b and baseline of 39.0b

bsearch103.0ms

Steps

Iters	Range	Point
8	9.03567328328406e+126	2.8337051363940888e+131	8.325258196494308e+130
10	-4.4587291624847184e-241	-7.768456259363856e-259	-2.606775090128557e-250
10	-2.827145857664849e-159	-4.602855931631007e-171	-5.789437331010863e-171

Iters

Range

Point

9.03567328328406e+126

2.8337051363940888e+131

8.325258196494308e+130

-4.4587291624847184e-241

-7.768456259363856e-259

-2.606775090128557e-250

-2.827145857664849e-159

-4.602855931631007e-171

-5.789437331010863e-171

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	26
1	47	26

end0.0ms

sample2.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 74.609375%

Results

290.0ms	6037×	body	80	valid
185.0ms	666×	body	2560	valid
108.0ms	469×	body	1280	valid
102.0ms	305×	body	5120	valid
53.0ms	293×	body	640	valid
22.0ms	154×	body	320	valid
7.0ms	76×	body	160	valid

Details

sample1.0s

simplify5.0ms

prune3.0ms

localize10.0ms

rewrite23.0ms

series46.0ms

simplify97.0ms

prune118.0ms

localize15.0ms

rewrite19.0ms

series25.0ms

simplify84.0ms

prune183.0ms

localize22.0ms

rewrite23.0ms

series25.0ms

simplify86.0ms

prune188.0ms

localize31.0ms

rewrite17.0ms

series26.0ms

simplify144.0ms

prune169.0ms

regimes648.0ms

bsearch103.0ms

simplify2.0ms

end0.0ms

sample2.0s

Profiling