Details

sample382.0ms

Algorithm

intervals

Results

50.0ms	78×	body	1280	valid
25.0ms	256×	body	80	valid
18.0ms	42×	body	640	valid
4.0ms	15×	body	320	valid
2.0ms	8×	body	160	valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	35	21
1	63	17
2	98	17
3	217	17
4	895	17
5	5001	17

prune15.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 33.7b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (atan2 x.im x.re) y.re)
30.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`hypot-def`
9×	`*-commutative`
4×	`sqrt-div`
3×	`+-commutative`
2×	`flip3-+` `pow1/2` `sin-sum` `flip-+`

Counts

4 → 19

Calls

4 calls:

2.0ms	(* (atan2 x.im x.re) y.re)
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.re)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
161.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify132.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	120	130
1	262	128
2	583	124
3	1402	124
4	4460	124
5	5001	124

prune147.0ms

Filtered

31 candidates to 23 candidates (74.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	27	4	31
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	28	5	33

Merged error: 19.5b

Counts

33 → 5

localize30.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (atan2 x.im x.re) y.im)
1.4b	(* (atan2 x.im x.re) y.re)
30.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-commutative`
5×	`hypot-def`
2×	`+-commutative` `sin-sum` `sqrt-div`
1×	`flip3-+` `pow1/2` `flip-+`

Counts

4 → 12

Calls

4 calls:

2.0ms	(* (atan2 x.im x.re) y.im)
2.0ms	(* (atan2 x.im x.re) y.re)
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(* (atan2 x.im x.re) y.re)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
152.0ms	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify129.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	119	93
1	261	92
2	583	90
3	1402	90
4	4460	90
5	5001	90

prune104.0ms

Filtered

24 candidates to 15 candidates (62.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	22	2	24
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	24	5	29

Merged error: 3.4b

Counts

29 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (hypot x.im x.re)) y.re)
1.1b	(* (atan2 x.im x.re) y.im)
1.4b	(* (atan2 x.im x.re) y.re)
34.4b	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

3×	`*-commutative`
2×	`sin-sum`
1×	`+-commutative`

Counts

4 → 5

Calls

4 calls:

2.0ms	(* (log (hypot x.im x.re)) y.re)
2.0ms	(* (atan2 x.im x.re) y.im)
2.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (log (hypot x.im x.re)) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(* (atan2 x.im x.re) y.re)
146.0ms	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify306.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	78	72
1	128	72
2	221	70
3	696	70
4	3536	70
5	5001	70

prune72.0ms

Filtered

17 candidates to 11 candidates (64.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	16	1	17
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	17	5	22

Merged error: 3.4b

Counts

22 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (hypot x.re x.im)) y.im)
1.1b	(* (atan2 x.im x.re) y.im)
1.4b	(* (atan2 x.im x.re) y.re)
34.4b	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

3×	`*-commutative`
2×	`sin-sum`
1×	`+-commutative`

Counts

4 → 5

Calls

4 calls:

2.0ms	(* (log (hypot x.re x.im)) y.im)
2.0ms	(* (atan2 x.im x.re) y.im)
2.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (log (hypot x.re x.im)) y.im)
16.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(* (atan2 x.im x.re) y.re)
149.0ms	(sin (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify166.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	62	72
1	99	72
2	175	70
3	510	70
4	1538	70
5	5001	70

prune54.0ms

Filtered

17 candidates to 12 candidates (70.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	16	1	17
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	17	5	22

Merged error: 3.4b

Counts

22 → 5

regimes139.0ms

Accuracy

0% (0.1b remaining)

Error of 3.3b against oracle of 3.2b and baseline of 3.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	15
1	24	15

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	2246×	body	1280	valid
712.0ms	7980×	body	80	valid
578.0ms	1367×	body	640	valid
156.0ms	546×	body	320	valid
59.0ms	39×	body	2560	valid
40.0ms	215×	body	160	valid