Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	192×	body	80	valid
5.0ms	25×	body	2560	valid
3.0ms	17×	body	1280	valid
2.0ms	8×	body	5120	valid
1.0ms	9×	body	640	valid
0.0ms	3×	body	160	valid
0.0ms	2×	body	320	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	8
1	28	8
2	36	8
3	44	8
4	46	8
5	46	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: 39.9b

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)))
0.7b	(- (sqrt (+ (* re re) (* im im))) re)
31.4b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-commutative`
5×	`hypot-def`
4×	`sqrt-div`
2×	`+-commutative` `flip3--` `fma-def` `flip3-+` `pow1/2` `associate-*r/` `sqrt-prod` `flip--` `flip-+`
1×	`sub-neg`

Counts

4 → 22

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
11.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
5.0ms	(- (sqrt (+ (* re re) (* im im))) re)
5.0ms	(sqrt (+ (* re re) (* im im)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
174.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify73.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	200	174
1	720	158
2	2450	146
3	5001	142

prune80.0ms

Filtered

34 candidates to 25 candidates (73.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	31	3	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	32	3	35

Merged error: 8.6b

Counts

35 → 3

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(sqrt (* 2.0 (- (hypot im re) re)))
0.7b	(- (hypot im re) re)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

2×	`flip3--` `sqrt-div` `associate-*r/` `sqrt-prod` `flip--`
1×	`sub-neg` `pow1/2` `*-commutative`

Counts

2 → 9

Calls

2 calls:

7.0ms	(sqrt (* 2.0 (- (hypot im re) re)))
2.0ms	(- (hypot im re) re)

series249.0ms

Counts

2 → 6

Calls

2 calls:

196.0ms	(sqrt (* 2.0 (- (hypot im re) re)))
52.0ms	(- (hypot im re) re)

simplify70.0ms

Algorithm

egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	185	107
1	552	98
2	2288	92
3	5001	91

prune41.0ms

Filtered

15 candidates to 13 candidates (86.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	14	1	15
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	15	3	18

Merged error: 8.4b

Counts

18 → 3

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (- (hypot im re) re))
0.3b	(* (sqrt (- (hypot im re) re)) (sqrt 2.0))
0.7b	(- (hypot im re) re)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

4×	`sqrt-div`
3×	`flip3--` `pow1/2` `flip--`
2×	`associate-*l/`
1×	`sub-neg` `sqrt-unprod` `pow-prod-down` `*-commutative`

Counts

3 → 12

Calls

3 calls:

2.0ms	(sqrt (- (hypot im re) re))
4.0ms	(* (sqrt (- (hypot im re) re)) (sqrt 2.0))
2.0ms	(- (hypot im re) re)

series375.0ms

Counts

3 → 9

Calls

3 calls:

127.0ms	(sqrt (- (hypot im re) re))
193.0ms	(* (sqrt (- (hypot im re) re)) (sqrt 2.0))
55.0ms	(- (hypot im re) re)

simplify134.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 3 (130.0ms)

Iter	Nodes	Cost
0	272	154
1	842	135
2	4273	125
3	5001	124

prune64.0ms

Filtered

21 candidates to 20 candidates (95.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	21	0	21
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	21	3	24

Merged error: 8.4b

Counts

24 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (/ (pow im 2) (+ re (hypot re im))))
0.7b	(+ re (hypot re im))
7.3b	(sqrt (* 2.0 (/ (pow im 2) (+ re (hypot re im)))))
20.2b	(/ (pow im 2) (+ re (hypot re im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`associate-*r/`
6×	`sqrt-div` `associate-r` `associate-/r/` `associate-/l*`
5×	`clear-num` `sqrt-prod`
4×	`flip3-+` `flip-+`
3×	`frac-2neg` `div-inv` `unpow2` `sqr-pow`
2×	`un-div-inv` `*-commutative`
1×	`+-commutative` `pow1/2`

Counts

4 → 32

Calls

4 calls:

5.0ms	(* 2.0 (/ (pow im 2) (+ re (hypot re im))))
2.0ms	(+ re (hypot re im))
5.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ re (hypot re im)))))
4.0ms	(/ (pow im 2) (+ re (hypot re im)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* 2.0 (/ (pow im 2) (+ re (hypot re im))))
53.0ms	(+ re (hypot re im))
205.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ re (hypot re im)))))
77.0ms	(/ (pow im 2) (+ re (hypot re im)))

simplify107.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	237	218
1	814	207
2	3595	201
3	5001	201

prune117.0ms

Filtered

44 candidates to 39 candidates (88.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	40	4	44
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	41	6	47

Merged error: 2.2b

Counts

47 → 6

regimes89.0ms

Accuracy

65.3% (3.8b remaining)

Error of 6.0b against oracle of 2.2b and baseline of 13.2b

bsearch69.0ms

Steps

Iters	Range		Point
5	3.229871111029786e+177	8.840794207796226e+177	8.651257411630312e+177
7	3.3407704314481424e-278	2.583287639093751e-276	9.987616216396506e-278

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	22
1	38	22

end0.0ms

sample666.0ms

Algorithm

intervals

Results

196.0ms	6020×	body	80	valid
141.0ms	728×	body	2560	valid
74.0ms	475×	body	1280	valid
67.0ms	274×	body	5120	valid
37.0ms	287×	body	640	valid
12.0ms	130×	body	320	valid
5.0ms	86×	body	160	valid