Details

sample436.0ms

Algorithm

intervals

Results

63.0ms	63×	body	1280	valid
30.0ms	262×	body	80	valid
17.0ms	34×	body	640	valid
5.0ms	15×	body	320	valid
5.0ms	2×	body	2560	valid
1.0ms	6×	body	160	valid

simplify38.0ms

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

prune18.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 32.8b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

2.3b	(* (atan2 x.im x.re) y.im)
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite31.0ms

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×	`sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms	(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)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
66.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify88.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	206	434
1	539	395
2	1201	392
3	2732	392
4	5002	392

prune453.0ms

Filtered

68 candidates to 54 candidates (20.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	60	8	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	8	69

Merged error: 19.2b

Counts

69 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.7b	(sin (+ (* (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

6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`sin-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	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series173.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
54.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
58.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify61.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (55.0ms)

Iter	Nodes	Cost
0	152	580
1	321	508
2	672	505
3	1724	505
4	5001	504

prune418.0ms

Filtered

51 candidates to 48 candidates (5.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	50	9	59

Merged error: 19.2b

Counts

59 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

3.5b	(log (exp (* (atan2 x.im x.re) y.im)))
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

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

series74.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(log (exp (* (atan2 x.im x.re) y.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
56.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify65.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 4 (59.0ms)

Iter	Nodes	Cost
0	174	444
1	380	400
2	818	399
3	2053	399
4	5002	397

prune424.0ms

Filtered

64 candidates to 53 candidates (17.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	64	9	73

Merged error: 19.2b

Counts

73 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

12.2b	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down` `cube-prod`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cube-mult` `sin-sum` `pow1/3` `unpow3` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 59

Calls

4 calls:

5.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series122.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
57.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify49.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	201	743
1	526	731
2	1327	729
3	5001	729

prune418.0ms

Filtered

71 candidates to 54 candidates (23.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	71	9	80

Merged error: 19.2b

Counts

80 → 9

regimes506.0ms

Accuracy

76.9% (3.3b remaining)

Error of 22.7b against oracle of 19.4b and baseline of 33.5b

bsearch400.0ms

Steps

Iters	Range	Point
10	-5.561573377002615e-304	3.0877076910478216e-302	4.6617580803001e-311
4	-4.3940009064737685e-150	-2.250718756727284e-150	-4.1749528611157483e-150
9	-1.2147220719604092e-68	-1.0646474794999867e-75	-1.498168830979673e-74

Iters

Range

Point

-5.561573377002615e-304

3.0877076910478216e-302

4.6617580803001e-311

-4.3940009064737685e-150

-2.250718756727284e-150

-4.1749528611157483e-150

-1.2147220719604092e-68

-1.0646474794999867e-75

-1.498168830979673e-74

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	76
1	59	76

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.6s	2216×	body	1280	valid
855.0ms	7985×	body	80	valid
677.0ms	1396×	body	640	valid
181.0ms	524×	body	320	valid
81.0ms	47×	body	2560	valid
51.0ms	230×	body	160	valid

Details

sample436.0ms

simplify38.0ms

prune18.0ms

localize24.0ms

rewrite31.0ms

series84.0ms

simplify88.0ms

prune453.0ms

localize30.0ms

rewrite23.0ms

series173.0ms

simplify61.0ms

prune418.0ms

localize24.0ms

rewrite16.0ms

series74.0ms

simplify65.0ms

prune424.0ms

localize27.0ms

rewrite20.0ms

series122.0ms

simplify49.0ms

prune418.0ms

regimes506.0ms

bsearch400.0ms

simplify2.0ms

end0.0ms

sample4.1s

Profiling