Details

sample25.0ms

Algorithm

intervals

Results

7.0ms	198×	body	80	valid
4.0ms	21×	body	2560	valid
1.0ms	10×	body	1280	valid
1.0ms	12×	body	640	valid
1.0ms	6×	body	5120	valid
0.0ms	6×	body	160	valid
0.0ms	3×	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: 37.7b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
1.3b	(- (sqrt (+ (* re re) (* im im))) re)
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 17

Calls

3 calls:

5.0ms	(+ (* re re) (* im im))
5.0ms	(- (sqrt (+ (* re re) (* im im))) re)
5.0ms	(sqrt (+ (* re re) (* im im)))

series109.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* re re) (* im im))
44.0ms	(- (sqrt (+ (* re re) (* im im))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify157.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	119	84
1	443	76
2	1215	70
3	4612	66
4	5001	66

prune57.0ms

Filtered

26 candidates to 17 candidates (65.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	24	2	26
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	24	3	27

Merged error: 8.0b

Counts

27 → 3

localize10.0ms

Local error

Found 1 expressions with local error:

1.3b	(- (hypot im re) re)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

1×	`sub-neg` `flip3--` `flip--`

Counts

1 → 4

Calls

1 calls:

2.0ms

(- (hypot im re) re)

series51.0ms

Counts

1 → 3

Calls

1 calls:

51.0ms

(- (hypot im re) re)

simplify190.0ms

Algorithm

egg-herbie

Counts

7 → 7

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	47	22
1	89	22
2	167	22
3	331	21
4	1203	21
5	4958	21
6	5001	21

prune20.0ms

Filtered

7 candidates to 6 candidates (85.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	7	0	7
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	7	3	10

Merged error: 8.0b

Counts

10 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (/ (pow im 2) (+ re (hypot re im))))
0.6b	(+ re (hypot re im))
6.3b	(sqrt (* 2.0 (/ (pow im 2) (+ re (hypot re im)))))
24.1b	(/ (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)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* 2.0 (/ (pow im 2) (+ re (hypot re im))))
58.0ms	(+ re (hypot re im))
208.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ re (hypot re im)))))
77.0ms	(/ (pow im 2) (+ re (hypot re im)))

simplify112.0ms

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

prune132.0ms

Filtered

44 candidates to 39 candidates (88.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	39	5	44
Fresh	0	0	0
Picked	1	0	1
Done	1	1	2
Total	41	6	47

Merged error: 2.3b

Counts

47 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ re (hypot re im)) (pow im (/ 2 2)))
0.0b	(/ (* im 2.0) (/ (+ re (hypot re im)) (pow im (/ 2 2))))
0.6b	(+ re (hypot re im))
6.3b	(sqrt (/ (* im 2.0) (/ (+ re (hypot re im)) (pow im (/ 2 2)))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 39

Calls

4 calls:

4.0ms	(/ (+ re (hypot re im)) (pow im (/ 2 2)))
6.0ms	(/ (* im 2.0) (/ (+ re (hypot re im)) (pow im (/ 2 2))))
2.0ms	(+ re (hypot re im))
6.0ms	(sqrt (/ (* im 2.0) (/ (+ re (hypot re im)) (pow im (/ 2 2)))))

series427.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (+ re (hypot re im)) (pow im (/ 2 2)))
81.0ms	(/ (* im 2.0) (/ (+ re (hypot re im)) (pow im (/ 2 2))))
51.0ms	(+ re (hypot re im))
208.0ms	(sqrt (/ (* im 2.0) (/ (+ re (hypot re im)) (pow im (/ 2 2)))))

simplify40.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	307	303
1	966	288
2	5001	277

prune153.0ms

Filtered

51 candidates to 49 candidates (96.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	52	5	57

Merged error: 0.0b

Counts

57 → 5

regimes66.0ms

Accuracy

98.2% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 13.0b

bsearch44.0ms

Steps

Iters	Range		Point
10	1.6481460862435214e-262	2.3921132320884054e-244	2.1159026106570812e-251

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	12
1	24	12

end0.0ms

sample658.0ms

Algorithm

intervals

Results

203.0ms	6088×	body	80	valid
130.0ms	674×	body	2560	valid
68.0ms	453×	body	1280	valid
65.0ms	277×	body	5120	valid
38.0ms	294×	body	640	valid
13.0ms	148×	body	320	valid
4.0ms	66×	body	160	valid