Details

analyze866.0ms (29.2%)

Algorithm

1×

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
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
12.5%	87.3%	0.2%	10
25%	74.9%	0.2%	11
31.2%	63.9%	4.9%	12
39%	50.9%	10.1%	13
44.8%	44.4%	10.7%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample31.0ms (1%)

Algorithm

1×

intervals

Results

6.0ms	256×	body	128	valid
1.0ms	46×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify14.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

36×	`cancel-sign-sub-inv_binary64`
23×	`sub-neg_binary64` `distribute-rgt-neg-in_binary64`
19×	`unsub-neg_binary64`
17×	`neg-mul-1_binary64`
16×	`distribute-rgt-in_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	17	14
2	27	14
3	39	14
4	56	14
5	80	14
6	115	14
7	164	14
8	191	14
9	193	14
10	191	14
11	160	14

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

Compiler

Compiled 22 to 14 computations (36.4% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

rewrite17.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

3×	`add-log-exp_binary64`
1×	`diff-log_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `flip3--_binary64` `*-un-lft-identity_binary64` `sub-neg_binary64` `flip--_binary64` `cancel-sign-sub-inv_binary64`

Counts

1 → 12

Calls

1 calls:

4.0ms

(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

Compiler

Compiled 191 to 46 computations (75.9% saved)

series40.0ms (1.4%)

Error

0.0b

Counts

1 → 24

Calls

1 calls:

36.0ms

(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

Compiler

Compiled 379 to 249 computations (34.3% saved)

simplify85.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

438×	`times-frac_binary64`
434×	`unsub-neg_binary64`
376×	`sub-neg_binary64`
364×	`unswap-sqr_binary64`
233×	`distribute-rgt-neg-in_binary64`

Counts

36 → 16

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	39	546
1	106	517
2	298	517
3	786	517
4	1717	517
5	2904	517
6	4571	517
7	4948	517

prune10.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	14	2	16
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	14	3	17

Error

Counts

17 → 3

Alt Table

Status	Error	Program
▶	28.9b	(/.f64 (-.f64 (.f64 (.f64 y.re x.re) (.f64 y.re x.re)) (.f64 (.f64 y.im x.im) (.f64 y.im x.im))) (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)))
	36.9b	(cbrt.f64 (pow.f64 (-.f64 (.f64 y.re x.re) (.f64 y.im x.im)) 3))
✓	0.0b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

Compiler

Compiled 234 to 85 computations (63.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 y.im x.im) (*.f64 y.im x.im))
0.3b	(.f64 (.f64 y.re x.re) (*.f64 y.re x.re))
2.8b	(-.f64 (.f64 (.f64 y.re x.re) (.f64 y.re x.re)) (.f64 (.f64 y.im x.im) (.f64 y.im x.im)))
27.6b	(/.f64 (-.f64 (.f64 (.f64 y.re x.re) (.f64 y.re x.re)) (.f64 (.f64 y.im x.im) (.f64 y.im x.im))) (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)))

rewrite99.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

82×	`pow1_binary64`
34×	`pow-prod-down_binary64`
30×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`prod-exp_binary64` `cbrt-unprod_binary64`
13×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`

Counts

4 → 117

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (.f64 (.f64 y.re x.re) (.f64 y.re x.re)) (.f64 (.f64 y.im x.im) (.f64 y.im x.im))) (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)))
8.0ms	(-.f64 (.f64 (.f64 y.re x.re) (.f64 y.re x.re)) (.f64 (.f64 y.im x.im) (.f64 y.im x.im)))
6.0ms	(.f64 (.f64 y.im x.im) (*.f64 y.im x.im))
6.0ms	(.f64 (.f64 y.re x.re) (*.f64 y.re x.re))

Compiler

Compiled 3253 to 374 computations (88.5% saved)

series223.0ms (7.5%)

Error

Counts

4 → 60

Calls

4 calls:

91.0ms	(/.f64 (-.f64 (.f64 (.f64 y.re x.re) (.f64 y.re x.re)) (.f64 (.f64 y.im x.im) (.f64 y.im x.im))) (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)))
88.0ms	(-.f64 (.f64 (.f64 y.re x.re) (.f64 y.re x.re)) (.f64 (.f64 y.im x.im) (.f64 y.im x.im)))
20.0ms	(.f64 (.f64 y.im x.im) (*.f64 y.im x.im))
18.0ms	(.f64 (.f64 y.re x.re) (*.f64 y.re x.re))

Compiler

Compiled 2016 to 1276 computations (36.7% saved)

simplify178.0ms (6%)

Algorithm

1×	egg-herbie

Rules

324×	`times-frac_binary64`
260×	`associate-l_binary64`
239×	`distribute-rgt-in_binary64`
230×	`distribute-lft-in_binary64`
218×	`cancel-sign-sub-inv_binary64`

Counts

177 → 145

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	4260
1	418	3921
2	1754	3604
3	4595	3178
4	4988	3178
5	4970	3178

prune49.0ms (1.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	145	3	148

Error

Counts

148 → 3

Alt Table

Status	Error	Program
✓	28.9b	(/.f64 (-.f64 (.f64 (.f64 y.re x.re) (.f64 y.re x.re)) (.f64 (.f64 y.im x.im) (.f64 y.im x.im))) (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)))
▶	36.9b	(cbrt.f64 (pow.f64 (-.f64 (.f64 y.re x.re) (.f64 y.im x.im)) 3))
✓	0.0b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

Compiler

Compiled 1809 to 569 computations (68.5% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 y.re x.re) (.f64 y.im x.im))
0.3b	(pow.f64 (-.f64 (.f64 y.re x.re) (.f64 y.im x.im)) 3)
35.0b	(cbrt.f64 (pow.f64 (-.f64 (.f64 y.re x.re) (.f64 y.im x.im)) 3))

rewrite49.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

12×	`cbrt-prod_binary64`
9×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
6×	`unpow-prod-down_binary64` `cube-prod_binary64`
5×	`add-log-exp_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `cube-div_binary64`

Counts

3 → 60

Calls

3 calls:

7.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 y.re x.re) (.f64 y.im x.im)) 3))
4.0ms	(pow.f64 (-.f64 (.f64 y.re x.re) (.f64 y.im x.im)) 3)
3.0ms	(-.f64 (.f64 y.re x.re) (.f64 y.im x.im))

Compiler

Compiled 1032 to 336 computations (67.4% saved)

series206.0ms (6.9%)

Error

Counts

3 → 96

Calls

3 calls:

103.0ms	(pow.f64 (-.f64 (.f64 y.re x.re) (.f64 y.im x.im)) 3)
47.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 y.re x.re) (.f64 y.im x.im)) 3))
44.0ms	(-.f64 (.f64 y.re x.re) (.f64 y.im x.im))

Compiler

Compiled 2628 to 1951 computations (25.8% saved)

simplify180.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

332×	`*-commutative_binary64`
313×	`cancel-sign-sub-inv_binary64`
312×	`exp-prod_binary64`
280×	`unswap-sqr_binary64`
247×	`distribute-rgt-neg-in_binary64`

Counts

156 → 108

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	116	4167
1	306	3913
2	989	3825
3	2660	3825
4	4751	3822
5	5034	3822

prune24.0ms (0.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	108	3	111

Error

Counts

111 → 3

Alt Table

Status	Error	Program
	28.9b	(/.f64 (-.f64 (.f64 (.f64 y.re x.re) (.f64 y.re x.re)) (.f64 (.f64 y.im x.im) (.f64 y.im x.im))) (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)))
	36.9b	(cbrt.f64 (pow.f64 (-.f64 (.f64 y.re x.re) (.f64 y.im x.im)) 3))
	0.0b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

Compiler

Compiled 652 to 296 computations (54.6% saved)

regimes193.0ms (6.5%)

Accuracy

Total 0.0b remaining (14.1%)

Threshold costs 0.0b (14.1%)

Compiler

Compiled 2799 to 1487 computations (46.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`sub-neg_binary64` `+-commutative_binary64`
3×	`neg-mul-1_binary64` `neg-sub0_binary64`
2×	`cancel-sign-sub-inv_binary64` `distribute-rgt-neg-in_binary64`
1×	`distribute-lft-neg-out_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	17	14
2	27	14
3	33	14
4	37	14
5	38	14
6	38	14

end23.0ms (0.8%)

Remove

(sort x.im y.im)

(sort x.re y.re)

Compiler

Compiled 55 to 35 computations (36.4% saved)

sample654.0ms (22%)

Algorithm

1×

intervals

Results

212.0ms	8000×	body	128	valid
36.0ms	1371×	body	128	invalid

Compiler

Compiled 79 to 47 computations (40.5% saved)

Iter	Nodes	Cost
0	10	14
1	17	14
2	27	14
3	39	14
4	56	14
5	80	14
6	115	14
7	164	14
8	191	14
9	193	14
10	191	14
11	160	14

Iter	Nodes	Cost
0	10	14
1	17	14
2	27	14
3	39	14
4	56	14
5	80	14
6	115	14
7	164	14
8	191	14
9	193	14
10	191	14
11	160	14

Details

analyze866.0ms (29.2%)

sample31.0ms (1%)

simplify14.0ms (0.5%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite17.0ms (0.6%)

series40.0ms (1.4%)

simplify85.0ms (2.9%)

prune10.0ms (0.3%)

localize10.0ms (0.3%)

rewrite99.0ms (3.3%)

series223.0ms (7.5%)

simplify178.0ms (6%)

prune49.0ms (1.7%)

localize8.0ms (0.3%)

rewrite49.0ms (1.6%)

series206.0ms (6.9%)

simplify180.0ms (6.1%)

prune24.0ms (0.8%)

regimes193.0ms (6.5%)

simplify3.0ms (0.1%)

end23.0ms (0.8%)

sample654.0ms (22%)

Profiling

Iter	Nodes	Cost
0	10	14
1	17	14
2	27	14
3	39	14
4	56	14
5	80	14
6	115	14
7	164	14
8	191	14
9	193	14
10	191	14
11	160	14