Details

sample119.0ms

Algorithm

intervals

Results

9.0ms	200×	body	80	valid
6.0ms	23×	body	2560	valid
3.0ms	13×	body	1280	valid
2.0ms	6×	body	5120	valid
1.0ms	8×	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: 36.4b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

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

series41.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
23.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify92.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (86.0ms)

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

prune123.0ms

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: 18.3b

Counts

64 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
27.8b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
12.0ms	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
23.0ms	(* (sqrt 2.0) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify40.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	324	640
1	1367	605
2	5002	595

prune135.0ms

Filtered

61 candidates to 83 candidates (-36.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	81	11	92

Merged error: 18.3b

Counts

92 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
27.8b	(sqrt (+ (* re re) (* im im)))
27.8b	(sqrt (+ (* re re) (* im im)))
27.8b	(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)))

simplify80.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (27.0ms)

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

prune122.0ms

Filtered

61 candidates to 69 candidates (-13.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	69	11	80

Merged error: 18.3b

Counts

80 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (* 2.0 (+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)))
5.3b	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
28.7b	(cbrt (+ (* re re) (* im im)))
28.7b	(cbrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 50

Calls

4 calls:

9.0ms	(sqrt (* 2.0 (+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)))
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)))

series122.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(sqrt (* 2.0 (+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)))
30.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
20.0ms	(cbrt (+ (* re re) (* im im)))
21.0ms	(cbrt (+ (* re re) (* im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	526	982
1	1905	904
2	5001	882

prune129.0ms

Filtered

59 candidates to 62 candidates (-5.1%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	61	12	73

Merged error: 18.3b

Counts

73 → 12

regimes447.0ms

Accuracy

57.6% (8.7b remaining)

Error of 26.7b against oracle of 18.1b and baseline of 38.5b

bsearch52.0ms

Steps

Iters	Range	Point
7	2.20140649672281e+130	1.0677592813206312e+132	6.532690006172032e+130
8	1.8593062270909148e-280	2.109665093495661e-277	2.8300128607351077e-279
8	-3.2022453028888753e-217	-1.075787534348924e-220	-1.415313427309286e-220

Iters

Range

Point

2.20140649672281e+130

1.0677592813206312e+132

6.532690006172032e+130

1.8593062270909148e-280

2.109665093495661e-277

2.8300128607351077e-279

-3.2022453028888753e-217

-1.075787534348924e-220

-1.415313427309286e-220

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	33
1	52	33

end0.0ms

sample1.0s

Algorithm

intervals

Results

288.0ms	6072×	body	80	valid
186.0ms	681×	body	2560	valid
110.0ms	482×	body	1280	valid
100.0ms	296×	body	5120	valid
43.0ms	244×	body	640	valid
19.0ms	144×	body	320	valid
7.0ms	81×	body	160	valid

Details

sample119.0ms

simplify5.0ms

prune3.0ms

localize10.0ms

rewrite25.0ms

series41.0ms

simplify92.0ms

prune123.0ms

localize13.0ms

rewrite27.0ms

series41.0ms

simplify40.0ms

prune135.0ms

localize15.0ms

rewrite19.0ms

series24.0ms

simplify80.0ms

prune122.0ms

localize16.0ms

rewrite25.0ms

series122.0ms

simplify49.0ms

prune129.0ms

regimes447.0ms

bsearch52.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling