Details

sample34.0ms

Algorithm

intervals

Results

10.0ms	200×	body	80	valid
6.0ms	21×	body	2560	valid
3.0ms	15×	body	1280	valid
2.0ms	6×	body	5120	valid
1.0ms	7×	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: 39.9b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.7b	(- (sqrt (+ (* re re) (* im im))) re)
31.1b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`pow1`
6×	`*-un-lft-identity`
5×	`sqrt-prod` `add-log-exp`
4×	`add-cube-cbrt` `sqrt-div`
3×	`add-exp-log` `sqrt-pow1` `add-cbrt-cube`
2×	`flip3--` `pow1/2` `associate-*r/` `flip--` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `diff-log` `pow-prod-down` `flip-+` `distribute-lft-out--`

Counts

3 → 43

Calls

3 calls:

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)))

series41.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
11.0ms	(- (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify90.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	234	381
1	812	362
2	3077	355
3	5001	353

prune105.0ms

Filtered

42 candidates to 52 candidates (-23.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	46	6	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	6	53

Merged error: 16.2b

Counts

53 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
8.0b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
31.1b	(sqrt (+ (* re re) (* im im)))
31.1b	(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
51×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `difference-of-squares`

Counts

4 → 126

Calls

4 calls:

16.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
15.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series28.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify48.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	261	1112
1	935	975
2	5001	951

prune147.0ms

Filtered

74 candidates to 138 candidates (-86.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	134	4	138
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	136	8	144

Merged error: 16.2b

Counts

144 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

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:

6.0ms	(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)))

series23.0ms

Counts

4 → 12

Calls

4 calls:

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

prune135.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	72	8	80

Merged error: 16.2b

Counts

80 → 8

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(sqrt (* 2.0 (- im re)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 13

Calls

1 calls:

5.0ms

(sqrt (* 2.0 (- im re)))

series15.0ms

Counts

1 → 3

Calls

1 calls:

15.0ms

(sqrt (* 2.0 (- im re)))

simplify51.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	131	101
1	423	99
2	1795	96
3	5001	94

prune26.0ms

Filtered

13 candidates to 16 candidates (-23.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	15	1	16
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	15	9	24

Merged error: 16.1b

Counts

24 → 9

regimes442.0ms

Accuracy

52.8% (10.1b remaining)

Error of 28.1b against oracle of 17.9b and baseline of 39.4b

bsearch53.0ms

Steps

Iters	Range	Point
9	1.972701127919696e-154	3.1184930501819124e-149	4.333641892284193e-154
5	-6.202696328941585e-191	-2.0501294423053805e-191	-2.7347411849077974e-191
8	-1.4361419947092225e+116	-4.701282719128794e+112	-1.4182869934259443e+116

Iters

Range

Point

1.972701127919696e-154

3.1184930501819124e-149

4.333641892284193e-154

-6.202696328941585e-191

-2.0501294423053805e-191

-2.7347411849077974e-191

-1.4361419947092225e+116

-4.701282719128794e+112

-1.4182869934259443e+116

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	36
1	54	36

end0.0ms

sample1.0s

Algorithm

intervals

Results

304.0ms	6044×	body	80	valid
200.0ms	704×	body	2560	valid
115.0ms	485×	body	1280	valid
85.0ms	248×	body	5120	valid
56.0ms	313×	body	640	valid
19.0ms	138×	body	320	valid
6.0ms	68×	body	160	valid

Details

sample34.0ms

simplify7.0ms

prune3.0ms

localize10.0ms

rewrite20.0ms

series41.0ms

simplify90.0ms

prune105.0ms

localize13.0ms

rewrite44.0ms

series28.0ms

simplify48.0ms

prune147.0ms

localize19.0ms

rewrite20.0ms

series23.0ms

simplify144.0ms

prune135.0ms

localize6.0ms

rewrite5.0ms

series15.0ms

simplify51.0ms

prune26.0ms

regimes442.0ms

bsearch53.0ms

simplify2.0ms

end0.0ms

sample1.0s

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