Details

sample1.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 72.674561%

Results

10.0ms	195×	body	80	valid
6.0ms	23×	body	2560	valid
4.0ms	11×	body	5120	valid
2.0ms	11×	body	1280	valid
2.0ms	9×	body	640	valid
0.0ms	3×	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: 39.6b

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)))
0.8b	(- (sqrt (+ (* re re) (* im im))) re)
30.0b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

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:

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

series44.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
25.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify108.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (102.0ms)

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

prune114.0ms

Filtered

52 candidates to 66 candidates (-26.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	61	5	66
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	6	67

Merged error: 18.9b

Counts

67 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
5.6b	(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
31.1b	(cbrt (+ (* re re) (* im im)))
31.1b	(cbrt (+ (* re re) (* im im)))

rewrite26.0ms

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`
3×	`flip3-+` `associate-l` `flip-+` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 66

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)))
5.0ms	(cbrt (+ (* re re) (* im im)))

series111.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
30.0ms	(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
21.0ms	(cbrt (+ (* re re) (* im im)))
23.0ms	(cbrt (+ (* re re) (* im im)))

simplify117.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	341	1002
1	1180	942
2	4515	900
3	5002	886

prune136.0ms

Filtered

66 candidates to 78 candidates (-18.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	76	8	84

Merged error: 18.8b

Counts

84 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

31.1b	(cbrt (+ (* re re) (* im im)))
31.1b	(cbrt (+ (* re re) (* im im)))
31.1b	(cbrt (+ (* re re) (* im im)))
31.1b	(cbrt (+ (* re re) (* im im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))
3.0ms	(cbrt (+ (* re re) (* im im)))
3.0ms	(cbrt (+ (* re re) (* im im)))

series87.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt (+ (* re re) (* im im)))
21.0ms	(cbrt (+ (* re re) (* im im)))
21.0ms	(cbrt (+ (* re re) (* im im)))
22.0ms	(cbrt (+ (* re re) (* im im)))

simplify45.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (38.0ms)

Iter	Nodes	Cost
0	151	560
1	426	524
2	1225	500
3	5002	468

prune127.0ms

Filtered

56 candidates to 64 candidates (-14.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	64	8	72

Merged error: 18.8b

Counts

72 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

31.1b	(cbrt (+ (* re re) (* im im)))
31.1b	(cbrt (+ (* re re) (* im im)))
31.1b	(cbrt (+ (* re re) (* im im)))
33.3b	(pow (+ (* re re) (* im im)) 1/3)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `flip3-+` `pow1/3` `flip-+`
1×	`pow-to-exp` `pow-pow` `unpow1/3` `pow-exp` `sqr-pow`

Counts

4 → 57

Calls

4 calls:

4.0ms	(cbrt (+ (* re re) (* im im)))
3.0ms	(cbrt (+ (* re re) (* im im)))
3.0ms	(cbrt (+ (* re re) (* im im)))
5.0ms	(pow (+ (* re re) (* im im)) 1/3)

series87.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt (+ (* re re) (* im im)))
22.0ms	(cbrt (+ (* re re) (* im im)))
21.0ms	(cbrt (+ (* re re) (* im im)))
23.0ms	(pow (+ (* re re) (* im im)) 1/3)

simplify80.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	200	539
1	682	479
2	2623	435
3	5001	407

prune148.0ms

Filtered

59 candidates to 69 candidates (-16.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	4	4
Picked	1	0	1
Done	0	3	3
Total	69	8	77

Merged error: 18.8b

Counts

77 → 8

regimes698.0ms

Accuracy

55.8% (9.3b remaining)

Error of 26.8b against oracle of 17.5b and baseline of 38.6b

bsearch53.0ms

Steps

Iters	Range	Point
7	9.713458418191775e-164	2.3030690137822174e-161	9.927723549652797e-164
9	3.101302953318024e-301	5.411045921540497e-294	1.3487210264843393e-296
4	-1.4725401500926607e+124	-9.648099655221202e+123	-1.341156763099232e+124

Iters

Range

Point

9.713458418191775e-164

2.3030690137822174e-161

9.927723549652797e-164

3.101302953318024e-301

5.411045921540497e-294

1.3487210264843393e-296

-1.4725401500926607e+124

-9.648099655221202e+123

-1.341156763099232e+124

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	27
1	53	27
2	53	27

end0.0ms

sample2.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 72.674561%

Results

301.0ms	6025×	body	80	valid
196.0ms	710×	body	2560	valid
106.0ms	471×	body	1280	valid
98.0ms	296×	body	5120	valid
45.0ms	260×	body	640	valid
23.0ms	161×	body	320	valid
7.0ms	77×	body	160	valid

Details

sample1.4s

simplify7.0ms

prune3.0ms

localize10.0ms

rewrite24.0ms

series44.0ms

simplify108.0ms

prune114.0ms

localize14.0ms

rewrite26.0ms

series111.0ms

simplify117.0ms

prune136.0ms

localize23.0ms

rewrite15.0ms

series87.0ms

simplify45.0ms

prune127.0ms

localize26.0ms

rewrite16.0ms

series87.0ms

simplify80.0ms

prune148.0ms

regimes698.0ms

bsearch53.0ms

simplify2.0ms

end0.0ms

sample2.4s

Profiling