Details

analyze324.0ms

Algorithm: search

sample34.0ms

Algorithm

intervals

Results

9.0ms	185×	body	80	valid
7.0ms	24×	body	2560	valid
3.0ms	19×	body	640	valid
3.0ms	14×	body	1280	valid
3.0ms	8×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	3×	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: 36.3b

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)
26.6b	(sqrt (+ (* re re) (* im im)))

rewrite22.0ms

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))
7.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
22.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
10.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify94.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (88.0ms)

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

prune127.0ms

Filtered

52 candidates to 63 candidates (-21.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	54	9	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	9	64

Merged error: 19.1b

Counts

64 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (sqrt (+ (* re re) (* im im))) re)
1.0b	(+ (sqrt (+ (* re re) (* im im))) re)
26.6b	(sqrt (+ (* re re) (* im im)))
26.6b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

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

simplify83.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	141	396
1	358	372
2	866	364
3	2557	362
4	5001	362

prune113.0ms

Filtered

58 candidates to 66 candidates (-13.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	66	9	75

Merged error: 19.1b

Counts

75 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (sqrt (+ (* re re) (* im im))) re)
26.6b	(sqrt (+ (* re re) (* im im)))
26.6b	(sqrt (+ (* re re) (* im im)))
26.6b	(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:

6.0ms	(+ (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)))

series24.0ms

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 (28.0ms)

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

prune175.0ms

Filtered

61 candidates to 69 candidates (-13.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	69	9	78

Merged error: 19.1b

Counts

78 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
6.4b	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
27.5b	(cbrt (+ (* re re) (* im im)))
27.5b	(cbrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`sqrt-prod`
6×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`associate-l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/`
1×	`+-commutative` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod`

Counts

4 → 65

Calls

4 calls:

8.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
8.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
3.0ms	(cbrt (+ (* re re) (* im im)))
3.0ms	(cbrt (+ (* re re) (* im im)))

series106.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
31.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
20.0ms	(cbrt (+ (* re re) (* im im)))
20.0ms	(cbrt (+ (* re re) (* im im)))

simplify126.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (116.0ms)

Iter	Nodes	Cost
0	355	1000
1	1235	940
2	4815	899
3	5002	885

prune118.0ms

Filtered

66 candidates to 77 candidates (-16.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	2	4	6
Picked	1	0	1
Done	2	0	2
Total	78	8	86

Merged error: 19.1b

Counts

86 → 8

regimes268.0ms

Accuracy

60.1% (8.5b remaining)

Error of 26.5b against oracle of 18.0b and baseline of 39.3b

bsearch75.0ms

Steps

Iters	Range		Point
10	1.517122326187752e+104	4.830195718898959e+114	3.780963997997663e+114
9	3.2891403426719287e-264	3.5708605022620106e-255	3.463695368610397e-264

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	36
1	44	36

end0.0ms

analyze321.0ms

Algorithm: search

sample938.0ms

Algorithm

intervals

Results

293.0ms	6033×	body	80	valid
201.0ms	699×	body	2560	valid
117.0ms	474×	body	1280	valid
99.0ms	284×	body	5120	valid
53.0ms	278×	body	640	valid
21.0ms	154×	body	320	valid
8.0ms	78×	body	160	valid

Details

analyze324.0ms

sample34.0ms

simplify5.0ms

prune3.0ms

localize10.0ms

rewrite22.0ms

series43.0ms

simplify94.0ms

prune127.0ms

localize12.0ms

rewrite23.0ms

series25.0ms

simplify83.0ms

prune113.0ms

localize15.0ms

rewrite19.0ms

series24.0ms

simplify84.0ms

prune175.0ms

localize13.0ms

rewrite25.0ms

series106.0ms

simplify126.0ms

prune118.0ms

regimes268.0ms

bsearch75.0ms

simplify2.0ms

end0.0ms

analyze321.0ms

sample938.0ms

Profiling