Details

analyze1.6s (15%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5006	504
0	4	4
1	4	4

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
48.9%	50.8%	0.3%	13
50%	49.7%	0.4%	14

Compiler

Compiled 38 to 20 computations (47.4% saved)

sample123.0ms (1.2%)

Algorithm

1×

intervals

Results

44.0ms	87×	body	1024	invalid
32.0ms	248×	body	128	valid
12.0ms	34×	body	512	invalid
4.0ms	18×	body	256	invalid
2.0ms	15×	body	128	invalid
2.0ms	2×	body	2048	invalid
1.0ms	3×	body	1024	valid
1.0ms	2×	body	512	valid
1.0ms	3×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify65.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune9.0ms (0.1%)

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

Error

32.8b

Counts

2 → 2

Compiler

Compiled 109 to 57 computations (47.7% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.0b	(*.f64 (atan2.f64 x.im x.re) y.im)
29.9b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
29.9b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
35.3b	(cos.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)))

rewrite104.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

32.8b

Rules

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

Counts

4 → 56

Calls

4 calls:

8.0ms	(cos.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)))
4.0ms	(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)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2594 to 353 computations (86.4% saved)

series652.0ms (6.3%)

Error

18.2b

Counts

4 → 52

Calls

4 calls:

278.0ms	(cos.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)))
139.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
98.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
74.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 5417 to 2754 computations (49.2% saved)

simplify75.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5198	2086

prune157.0ms (1.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	105	5	110

Error

18.2b

Counts

110 → 5

Compiler

Compiled 4551 to 1202 computations (73.6% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.8b	(*.f64 y.re (atan2.f64 x.im x.re))
2.0b	(*.f64 (atan2.f64 x.im x.re) y.im)
19.0b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
29.9b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite75.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

18.2b

Rules

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

Counts

4 → 58

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
2.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 1851 to 341 computations (81.6% saved)

series429.0ms (4.2%)

Error

2.7b

Counts

4 → 45

Calls

4 calls:

129.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
122.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
71.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
68.0ms	(*.f64 y.re (atan2.f64 x.im x.re))

Compiler

Compiled 3270 to 1723 computations (47.3% saved)

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5145	1447

prune112.0ms (1.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	101	7	108

Error

2.7b

Counts

108 → 7

Compiler

Compiled 3112 to 754 computations (75.8% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.8b	(*.f64 (atan2.f64 x.im x.re) y.re)
29.9b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
29.9b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
35.3b	(cos.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)))

rewrite98.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

Rules

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

Counts

4 → 56

Calls

4 calls:

7.0ms	(cos.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)))
7.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
4.0ms	(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)))

Compiler

Compiled 2986 to 356 computations (88.1% saved)

series633.0ms (6.1%)

Error

2.7b

Counts

4 → 52

Calls

4 calls:

240.0ms	(cos.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)))
151.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
96.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
77.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)

Compiler

Compiled 6376 to 3011 computations (52.8% saved)

simplify73.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5177	2086

prune157.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	108	7	115

Error

2.7b

Counts

115 → 7

Compiler

Compiled 5360 to 1246 computations (76.8% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.0b	(*.f64 (atan2.f64 x.im x.re) y.im)
29.9b	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))
29.9b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
35.3b	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))

rewrite140.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

Rules

12×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-l_binary64` `associate-r_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64` `unpow-prod-down_binary64` `distribute-lft-out_binary64`
1×	`cos-sum_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 58

Calls

4 calls:

11.0ms	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))
6.0ms	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2850 to 1225 computations (57% saved)

series634.0ms (6.1%)

Error

2.7b

Counts

4 → 52

Calls

4 calls:

242.0ms	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
142.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
92.0ms	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))
79.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 5828 to 3615 computations (38% saved)

simplify87.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4946	2116
1	4946	2116

prune187.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	111	6	117

Error

2.7b

Counts

117 → 6

Compiler

Compiled 4756 to 2089 computations (56.1% saved)

regimes599.0ms (5.8%)

Accuracy

Total 5.7b remaining (62.6%)

Threshold costs 0b (0%)

Compiler

Compiled 6602 to 4045 computations (38.7% saved)

bsearch89.0ms (0.9%)

Steps

Iters	Range		Point
9	-1.543447434715671e-295	-1.483581797470141e-300	-1.4981339154053327e-300

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	65	81
1	65	81

end0.0ms (0%)

sample4.1s (39.8%)

Algorithm

1×

intervals

Results

1.1s	2268×	body	1024	invalid
821.0ms	7600×	body	128	valid
342.0ms	980×	body	512	invalid
90.0ms	171×	body	1024	valid
88.0ms	391×	body	256	invalid
60.0ms	513×	body	128	invalid
41.0ms	125×	body	512	valid
24.0ms	32×	body	2048	invalid
20.0ms	89×	body	256	valid
12.0ms	15×	body	2048	valid

Compiler

Compiled 1383 to 841 computations (39.2% saved)

Details

analyze1.6s (15%)

sample123.0ms (1.2%)

simplify65.0ms (0.6%)

prune9.0ms (0.1%)

localize23.0ms (0.2%)

rewrite104.0ms (1%)

series652.0ms (6.3%)

simplify75.0ms (0.7%)

prune157.0ms (1.5%)

localize18.0ms (0.2%)

rewrite75.0ms (0.7%)

series429.0ms (4.2%)

simplify66.0ms (0.6%)

prune112.0ms (1.1%)

localize25.0ms (0.2%)

rewrite98.0ms (0.9%)

series633.0ms (6.1%)

simplify73.0ms (0.7%)

prune157.0ms (1.5%)

localize30.0ms (0.3%)

rewrite140.0ms (1.4%)

series634.0ms (6.1%)

simplify87.0ms (0.8%)

prune187.0ms (1.8%)

regimes599.0ms (5.8%)

bsearch89.0ms (0.9%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.1s (39.8%)

Profiling