Details

sample37.0ms

Algorithm

intervals

Results

11.0ms	188×	body	80	valid
9.0ms	33×	body	2560	valid
3.0ms	14×	body	1280	valid
2.0ms	7×	body	5120	valid
1.0ms	8×	body	640	valid
1.0ms	6×	body	320	valid

simplify8.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

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: 37.4b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.3b	(- (sqrt (+ (* re re) (* im im))) re)
27.5b	(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:

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

series282.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
172.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
45.0ms	(- (sqrt (+ (* re re) (* im im))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify97.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	258	459
1	938	422
2	3098	412
3	5001	410

prune172.0ms

Filtered

66 candidates to 52 candidates (78.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	58	8	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	8	67

Merged error: 18.7b

Counts

67 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(- (sqrt (+ (* re re) (* im im))) re)
0.4b	(* (sqrt 2.0) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
15.0ms	(* (sqrt 2.0) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* re re) (* im im))
49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
175.0ms	(* (sqrt 2.0) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify139.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	314	691
1	1267	648
2	4889	633
3	5001	633

prune205.0ms

Filtered

88 candidates to 62 candidates (70.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	86	10	96

Merged error: 18.5b

Counts

96 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
6.8b	(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
28.5b	(cbrt (+ (* re re) (* im im)))
28.5b	(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)
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
82.0ms	(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
93.0ms	(cbrt (+ (* re re) (* im im)))
95.0ms	(cbrt (+ (* re re) (* im im)))

simplify147.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	307	930
1	1159	870
2	4797	842
3	5002	842

prune274.0ms

Filtered

78 candidates to 64 candidates (82.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	74	4	78
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	77	11	88

Merged error: 18.5b

Counts

88 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

28.5b	(cbrt (+ (* re re) (* im im)))
28.5b	(cbrt (+ (* re re) (* im im)))
28.5b	(cbrt (+ (* re re) (* im im)))
28.5b	(cbrt (+ (* re re) (* im im)))

rewrite19.0ms

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

series371.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (+ (* re re) (* im im)))
92.0ms	(cbrt (+ (* re re) (* im im)))
93.0ms	(cbrt (+ (* re re) (* im im)))
94.0ms	(cbrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	123	488
1	408	452
2	1386	444
3	5001	444

prune284.0ms

Filtered

64 candidates to 60 candidates (93.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	64	11	75

Merged error: 18.5b

Counts

75 → 11

regimes291.0ms

Accuracy

58.8% (8.8b remaining)

Error of 26.3b against oracle of 17.5b and baseline of 38.9b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	42
1	49	42

end0.0ms

sample872.0ms

Algorithm

intervals

Results

282.0ms	6034×	body	80	valid
176.0ms	669×	body	2560	valid
102.0ms	314×	body	5120	valid
99.0ms	460×	body	1280	valid
45.0ms	269×	body	640	valid
21.0ms	166×	body	320	valid
7.0ms	88×	body	160	valid

Details

sample37.0ms

simplify8.0ms

prune3.0ms

localize10.0ms

rewrite23.0ms

series282.0ms

simplify97.0ms

prune172.0ms

localize11.0ms

rewrite31.0ms

series287.0ms

simplify139.0ms

prune205.0ms

localize17.0ms

rewrite26.0ms

series379.0ms

simplify147.0ms

prune274.0ms

localize19.0ms

rewrite19.0ms

series371.0ms

simplify51.0ms

prune284.0ms

regimes291.0ms

bsearch3.0ms

simplify2.0ms

end0.0ms

sample872.0ms

Profiling