Details

analyze1.4s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
9.4%	90.4%	0.2%	6
17.2%	82.7%	0.2%	7
19.5%	80.3%	0.2%	8
30.8%	69%	0.2%	9
35.5%	64.3%	0.2%	10
42.4%	57.4%	0.2%	11
47.1%	52.7%	0.2%	12
49%	50.8%	0.2%	13
50.1%	49.7%	0.2%	14

sample137.0ms

Algorithm

intervals

Results

48.0ms	61×	body	1280	invalid
34.0ms	245×	body	80	valid
23.0ms	44×	body	640	invalid
5.0ms	14×	body	320	invalid
2.0ms	3×	body	1280	valid
2.0ms	4×	body	640	valid
1.0ms	5×	body	160	invalid
1.0ms	6×	body	80	invalid
1.0ms	2×	body	320	valid
1.0ms	2×	body	160	valid

simplify497.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4934	36
1	4934	36

prune16.0ms

Filtered

1 candidates to 1 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: 32.5b

Counts

2 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

1.6b	(*.f64 (atan2.f64 x.im x.re) y.re)
28.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
28.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.7b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `sin-sum_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

4.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
17.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
9.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

series86.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
64.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

simplify57.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4956	685
1	4956	685

prune114.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	59	9	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	60	10	70

Merged error: 19.5b

Counts

70 → 10

localize30.0ms

Local error

Found 4 expressions with local error:

28.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
28.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
28.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.7b	(sin.f64 (+.f64 (.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`sqrt-div_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`sin-sum_binary64`

Counts

4 → 53

Calls

4 calls:

5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
26.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
54.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

simplify87.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4831	684
1	4831	684

prune99.0ms

Filtered

50 candidates to 65 candidates (-30.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	65	10	75

Merged error: 19.2b

Counts

75 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

28.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.7b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
32.7b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
32.7b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`sin-sum_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 39

Calls

4 calls:

5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
8.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
8.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
8.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

series158.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
51.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
49.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
51.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

simplify56.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4871	839
1	4871	839

prune94.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	51	10	61

Merged error: 19.2b

Counts

61 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b	(*.f64 y.re (atan2.f64 x.im x.re))
28.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
28.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.7b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `sin-sum_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

4.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))

series71.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
52.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))

simplify50.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4964	685
1	4964	685

prune68.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	68	10	78

Merged error: 19.2b

Counts

78 → 10

regimes429.0ms

Accuracy

76.3% (3.4b remaining)

Error of 22.1b against oracle of 18.7b and baseline of 33.1b

bsearch51.0ms

Steps

Iters	Range		Point
6	-4.387572817025468e-299	-1.0382332020571772e-299	-1.0480241195093906e-299

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	65
1	70	65

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.6s	2116×	body	1280	invalid
879.0ms	7574×	body	80	valid
635.0ms	1236×	body	640	invalid
164.0ms	459×	body	320	invalid
105.0ms	135×	body	1280	valid
68.0ms	137×	body	640	valid
53.0ms	31×	body	2560	invalid
48.0ms	195×	body	160	invalid
44.0ms	373×	body	80	invalid
35.0ms	98×	body	320	valid
14.0ms	56×	body	160	valid

Details

analyze1.4s

sample137.0ms

simplify497.0ms

prune16.0ms

localize23.0ms

rewrite37.0ms

series86.0ms

simplify57.0ms

prune114.0ms

localize30.0ms

rewrite40.0ms

series74.0ms

simplify87.0ms

prune99.0ms

localize28.0ms

rewrite29.0ms

series158.0ms

simplify56.0ms

prune94.0ms

localize24.0ms

rewrite22.0ms

series71.0ms

simplify50.0ms

prune68.0ms

regimes429.0ms

bsearch51.0ms

simplify3.0ms

end0.0ms

sample4.0s

Profiling