Details

sample345.0ms

Algorithm

intervals

Results

35.0ms	58×	body	1280	valid
24.0ms	259×	body	80	valid
15.0ms	37×	body	640	valid
6.0ms	20×	body	320	valid
1.0ms	4×	body	160	valid

simplify37.0ms

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

prune27.0ms

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: 34.8b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.im)
31.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.1b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 19

Calls

4 calls:

2.0ms	(* (atan2 x.im x.re) y.im)
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (atan2 x.im x.re) y.im)
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
156.0ms	(cos (+ (* (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 (8.0ms)

Iter	Nodes	Cost
0	116	126
1	255	124
2	576	120
3	1395	120
4	4453	120
5	5001	120

prune136.0ms

Filtered

31 candidates to 21 candidates (67.7%)

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: 22.6b

Counts

33 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.6b	(* (atan2 x.im x.re) y.im)
31.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-commutative`
8×	`exp-sum`
6×	`prod-diff`
5×	`hypot-def`
4×	`pow1/2`
3×	`associate-l` `log-pow`
2×	`sqrt-div`
1×	`+-commutative` `sub-neg` `flip3-+` `exp-diff` `flip-+`

Counts

4 → 20

Calls

4 calls:

7.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
3.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.0ms	(* (atan2 x.im x.re) y.im)
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
90.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify95.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 4 (92.0ms)

Iter	Nodes	Cost
0	177	185
1	417	171
2	969	127
3	2953	124
4	5002	118

prune99.0ms

Filtered

32 candidates to 19 candidates (59.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	30	2	32
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	30	7	37

Merged error: 3.9b

Counts

37 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
0.0b	(exp (- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im)))
0.3b	(* (log (hypot x.re x.im)) y.re)
1.6b	(* (atan2 x.im x.re) y.im)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-commutative`
8×	`prod-diff`
6×	`exp-sum`
2×	`sub-neg` `fma-neg`
1×	`flip3--` `exp-diff` `flip--`

Counts

4 → 19

Calls

4 calls:

5.0ms	(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
5.0ms	(exp (- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im)))
2.0ms	(* (log (hypot x.re x.im)) y.re)
2.0ms	(* (atan2 x.im x.re) y.im)

series356.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
104.0ms	(exp (- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im)))
100.0ms	(* (log (hypot x.re x.im)) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)

simplify95.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	156	222
1	431	215
2	1093	182
3	2885	164
4	5001	164

prune90.0ms

Filtered

31 candidates to 18 candidates (58.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	31	7	38

Merged error: 3.9b

Counts

38 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (atan2 x.im x.re) y.re)
1.6b	(* (atan2 x.im x.re) y.im)
31.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.1b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 12

Calls

4 calls:

2.0ms	(* (atan2 x.im x.re) y.re)
2.0ms	(* (atan2 x.im x.re) y.im)
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series208.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
138.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify128.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	116	101
1	255	100
2	576	98
3	1395	98
4	4453	98
5	5001	98

prune77.0ms

Filtered

24 candidates to 15 candidates (62.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	22	2	24
Fresh	2	2	4
Picked	1	0	1
Done	1	1	2
Total	26	5	31

Merged error: 2.8b

Counts

31 → 5

regimes173.0ms

Accuracy

70.8% (0.4b remaining)

Error of 3.2b against oracle of 2.9b and baseline of 4.1b

bsearch212.0ms

Steps

Iters	Range		Point
8	0.41440189822893647	357.20278190505735	4.400169083194702
9	-208845680.95928752	-0.0748897710117716	-9.196962954825882

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	22
1	41	22
2	41	22

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	1941×	body	1280	valid
702.0ms	7954×	body	80	valid
567.0ms	1445×	body	640	valid
172.0ms	629×	body	320	valid
51.0ms	285×	body	160	valid