Details

sample406.0ms

Algorithm

intervals

Results

48.0ms	68×	body	1280	valid
36.0ms	54×	body	640	valid
29.0ms	257×	body	80	valid
8.0ms	23×	body	320	valid
2.0ms	11×	body	160	valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	31	21
1	53	20
2	84	20
3	203	20
4	879	20
5	5001	20

prune13.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 31.7b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

2.3b	(* (atan2 x.im x.re) y.im)
28.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.8b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

4.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
155.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify78.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	191	420
1	501	383
2	1134	381
3	2494	381
4	5002	381

prune276.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	3	69

Merged error: 17.2b

Counts

69 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.3b	(* (atan2 x.im x.re) y.im)
28.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`pow1`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `add-log-exp`
3×	`sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

4 → 66

Calls

4 calls:

4.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
5.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
4.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
89.0ms	(* (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)))

simplify80.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	290	540
1	897	500
2	2715	491
3	5001	491

prune224.0ms

Filtered

78 candidates to 56 candidates (71.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	76	5	81

Merged error: 3.3b

Counts

81 → 5

localize28.0ms

Local error

Found 4 expressions with local error:

28.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.8b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.8b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.8b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cos-sum` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 39

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
133.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
133.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
136.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify166.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (54.0ms)

Iter	Nodes	Cost
0	137	538
1	283	472
2	606	472
3	1507	472
4	4743	471
5	5002	471

prune299.0ms

Filtered

51 candidates to 48 candidates (94.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	51	5	56

Merged error: 3.3b

Counts

56 → 5

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im))
0.1b	(* (log (* -1 x.re)) y.re)
2.3b	(* (atan2 x.im x.re) y.im)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
8×	`associate-l`
7×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r`
5×	`add-log-exp`
3×	`pow-prod-down`
2×	`prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 50

Calls

3 calls:

4.0ms	(- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im))
5.0ms	(* (log (* -1 x.re)) y.re)
4.0ms	(* (atan2 x.im x.re) y.im)

series188.0ms

Counts

3 → 9

Calls

3 calls:

105.0ms	(- (* (log (* -1 x.re)) y.re) (* (atan2 x.im x.re) y.im))
67.0ms	(* (log (* -1 x.re)) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)

simplify102.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	225	318
1	816	291
2	4191	287
3	5001	287

prune133.0ms

Filtered

59 candidates to 38 candidates (64.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	59	5	64

Merged error: 3.3b

Counts

64 → 5

regimes203.0ms

Accuracy

62.4% (6.0b remaining)

Error of 9.6b against oracle of 3.6b and baseline of 19.4b

bsearch183.0ms

Steps

Iters	Range		Point
8	3.601699856001094e-106	3.818707587865065e-102	6.526698771006735e-105
6	-2.5194563738095413e-276	-3.9706152788232444e-277	-1.6604473415741906e-276

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	26
1	52	26
2	52	26

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.4s	2045×	body	1280	valid
826.0ms	7963×	body	80	valid
682.0ms	1452×	body	640	valid
222.0ms	671×	body	320	valid
74.0ms	321×	body	160	valid

Details

sample406.0ms

simplify41.0ms

prune13.0ms

localize26.0ms

rewrite23.0ms

series244.0ms

simplify78.0ms

prune276.0ms

localize16.0ms

rewrite19.0ms

series264.0ms

simplify80.0ms

prune224.0ms

localize28.0ms

rewrite24.0ms

series436.0ms

simplify166.0ms

prune299.0ms

localize16.0ms

rewrite15.0ms

series188.0ms

simplify102.0ms

prune133.0ms

regimes203.0ms

bsearch183.0ms

simplify2.0ms

end0.0ms

sample3.6s

Profiling