Details

analyze428.0ms (7.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	62.4%	12.6%	6
31.2%	50%	18.8%	7
40.6%	37.5%	22%	8
45.3%	26.5%	28.2%	9
46.8%	19.5%	33.7%	10
48.8%	14%	37.2%	11
51.7%	10.1%	38.1%	12
52.8%	7.1%	40.1%	13
53.3%	5.1%	41.6%	14

Compiler

Compiled 22 to 12 computations (45.5% saved)

sample49.0ms (0.9%)

Algorithm

1×

intervals

Results

32.0ms	256×	body	128	valid
2.0ms	17×	body	128	invalid

Compiler

Compiled 45 to 25 computations (44.4% saved)

simplify170.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

680×	`unsub-neg_binary64`
594×	`fma-neg_binary64`
560×	`sub-neg_binary64`
520×	`fma-def_binary64`
399×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	30	25
2	71	23
3	194	16
4	573	14
5	1779	14
6	3048	14
7	4137	14
8	4615	14
9	4749	14
10	4784	14
11	4907	14
12	4998	14

prune6.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

7.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	8.0b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))
	8.0b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))

Compiler

Compiled 97 to 51 computations (47.4% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x.re x.im) (.f64 x.im x.re))
✓	0.1b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))
✓	0.1b	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
✓	7.4b	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)

series83.0ms (1.5%)

Counts

4 → 96

Calls

4 calls:

28.0ms	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))
25.0ms	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
20.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
10.0ms	(+.f64 (.f64 x.re x.im) (.f64 x.im x.re))

rewrite56.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-*l/_binary64`
12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 79

Calls

4 calls:

14.0ms	(+.f64 (.f64 x.re x.im) (.f64 x.im x.re))
12.0ms	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))
10.0ms	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
10.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)

simplify208.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

245×	`times-frac_binary64`
240×	`associate-l_binary64`
214×	`associate-r_binary64`
204×	`fma-neg_binary64`
200×	`distribute-rgt-out_binary64`

Counts

175 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	2858
1	447	2479
2	1756	2377
3	3539	2365
4	4775	2365
5	5089	2365

prune199.0ms (3.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	137	5	142
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	139	5	144

Error

0.0b

Counts

144 → 5

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
	8.4b	(-.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im))) (cbrt.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) (.f64 (cbrt.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im))) x.re)) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))
	8.0b	(+.f64 (.f64 x.re (-.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) (.f64 x.im (+.f64 x.im x.im)))) 0)
	21.7b	(-.f64 (pow.f64 x.re 3) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
	8.3b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re))) (cbrt.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)))) (.f64 x.im (cbrt.f64 (.f64 2 (.f64 x.re x.im))))))

Compiler

Compiled 4312 to 867 computations (79.9% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (.f64 x.re x.im) (.f64 x.im x.re))
✓	0.1b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
	0.1b	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
✓	0.2b	(.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re))

series50.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

28.0ms	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
22.0ms	(.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re))

rewrite60.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`associate-*l/_binary64`
17×	`flip-+_binary64`
17×	`flip3-+_binary64`
16×	`frac-sub_binary64`
12×	`frac-times_binary64`

Counts

2 → 61

Calls

2 calls:

21.0ms	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
15.0ms	(.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re))

simplify169.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

567×	`fma-neg_binary64`
525×	`associate-l_binary64`
507×	`associate-r_binary64`
326×	`neg-sub0_binary64`
325×	`neg-mul-1_binary64`

Counts

109 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	3168
1	732	2601
2	3424	2376
3	4095	2376
4	4702	2376

prune308.0ms (5.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	164	5	169
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	167	7	174

Error

0.0b

Counts

174 → 7

Alt Table

Status	Error	Program
	25.0b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (.f64 (sqrt.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re))) (.f64 x.im (sqrt.f64 (.f64 2 (.f64 x.re x.im))))))
	8.0b	(+.f64 (.f64 x.re (-.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) (.f64 x.im (+.f64 x.im x.im)))) 0)
	0.8b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
▶	0.2b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (neg.f64 (.f64 x.im (.f64 2 (.f64 x.re x.im)))))
	7.9b	(+.f64 (-.f64 (-.f64 (pow.f64 x.re 3) (.f64 x.re (.f64 x.im x.im))) (.f64 x.im (.f64 2 (*.f64 x.re x.im)))) 0)
	8.3b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re))) (cbrt.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)))) (.f64 x.im (cbrt.f64 (.f64 2 (.f64 x.re x.im))))))
	22.8b	(-.f64 (.f64 (sqrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re))) (sqrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)))) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))

Compiler

Compiled 6220 to 1396 computations (77.6% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 x.re x.im) x.re)
✓	0.0b	(.f64 2 (.f64 x.re x.im))
✓	0.1b	(.f64 x.im (.f64 2 (*.f64 x.re x.im)))
✓	0.2b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (neg.f64 (.f64 x.im (.f64 2 (.f64 x.re x.im)))))

series81.0ms (1.5%)

Counts

4 → 72

Calls

4 calls:

34.0ms	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (neg.f64 (.f64 x.im (.f64 2 (.f64 x.re x.im)))))
20.0ms	(.f64 x.im (.f64 2 (*.f64 x.re x.im)))
17.0ms	(*.f64 (-.f64 x.re x.im) x.re)
9.0ms	(.f64 2 (.f64 x.re x.im))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
20×	`pow1_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`associate-l_binary64`

Counts

4 → 77

Calls

4 calls:

12.0ms	(*.f64 (-.f64 x.re x.im) x.re)
10.0ms	(.f64 x.im (.f64 2 (*.f64 x.re x.im)))
8.0ms	(.f64 2 (.f64 x.re x.im))
1.0ms	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (neg.f64 (.f64 x.im (.f64 2 (.f64 x.re x.im)))))

simplify145.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

798×	`fma-def_binary64`
590×	`fma-neg_binary64`
401×	`*-commutative_binary64`
288×	`unswap-sqr_binary64`
263×	`associate-+l+_binary64`

Counts

149 → 117

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	122	1941
1	284	1669
2	944	1623
3	1958	1541
4	4786	1541
5	5251	1541

prune247.0ms (4.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	117	7	124

Error

Counts

124 → 7

Alt Table

Status	Error	Program
	25.0b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (.f64 (sqrt.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re))) (.f64 x.im (sqrt.f64 (.f64 2 (.f64 x.re x.im))))))
	8.0b	(+.f64 (.f64 x.re (-.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) (.f64 x.im (+.f64 x.im x.im)))) 0)
	0.8b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
✓	0.2b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (neg.f64 (.f64 x.im (.f64 2 (.f64 x.re x.im)))))
	14.5b	(fma.f64 (+.f64 x.re x.im) (.f64 (sqrt.f64 (.f64 (-.f64 x.re x.im) x.re)) (sqrt.f64 (.f64 (-.f64 x.re x.im) x.re))) (neg.f64 (.f64 x.im (.f64 2 (.f64 x.re x.im)))))
	7.9b	(+.f64 (-.f64 (pow.f64 x.re 3) (.f64 x.re (.f64 x.im x.im))) (neg.f64 (.f64 x.im (.f64 2 (*.f64 x.re x.im)))))
▶	0.4b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (neg.f64 (.f64 x.im (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (*.f64 x.re x.im))))))

Compiler

Compiled 2909 to 1124 computations (61.4% saved)

localize26.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x.im (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 x.re x.im))))
✓	0.2b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (neg.f64 (.f64 x.im (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (*.f64 x.re x.im))))))
✓	0.3b	(.f64 (sqrt.f64 2) (.f64 x.re x.im))
✓	0.4b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (*.f64 x.re x.im)))

series185.0ms (3.3%)

Counts

4 → 96

Calls

4 calls:

66.0ms	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (neg.f64 (.f64 x.im (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (*.f64 x.re x.im))))))
54.0ms	(.f64 x.im (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 x.re x.im))))
46.0ms	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (*.f64 x.re x.im)))
18.0ms	(.f64 (sqrt.f64 2) (.f64 x.re x.im))

rewrite56.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary64`
32×	`add-exp-log_binary64`
32×	`pow1_binary64`
19×	`cbrt-unprod_binary64`
19×	`prod-exp_binary64`

Counts

4 → 85

Calls

4 calls:

20.0ms	(.f64 x.im (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 x.re x.im))))
15.0ms	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (*.f64 x.re x.im)))
10.0ms	(.f64 (sqrt.f64 2) (.f64 x.re x.im))
1.0ms	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (neg.f64 (.f64 x.im (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (*.f64 x.re x.im))))))

simplify170.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

544×	`fma-neg_binary64`
541×	`fma-def_binary64`
502×	`*-commutative_binary64`
302×	`distribute-rgt-in_binary64`
284×	`associate-r_binary64`

Counts

181 → 130

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	2296
1	294	2018
2	1047	1972
3	2026	1884
4	4825	1884
5	5208	1884

prune292.0ms (5.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	130	7	137

Error

Counts

137 → 7

Alt Table

Status	Error	Program
	0.3b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (neg.f64 (.f64 x.im (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x.re (*.f64 x.im (pow.f64 (sqrt.f64 2) 3/2)))))))
	14.5b	(fma.f64 (+.f64 x.re x.im) (.f64 (sqrt.f64 (.f64 (-.f64 x.re x.im) x.re)) (sqrt.f64 (.f64 (-.f64 x.re x.im) x.re))) (neg.f64 (.f64 x.im (.f64 2 (.f64 x.re x.im)))))
	0.8b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
✓	0.2b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (neg.f64 (.f64 x.im (.f64 2 (.f64 x.re x.im)))))
	8.0b	(+.f64 (.f64 x.re (-.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) (.f64 x.im (+.f64 x.im x.im)))) 0)
	7.9b	(+.f64 (-.f64 (pow.f64 x.re 3) (.f64 x.re (.f64 x.im x.im))) (neg.f64 (.f64 x.im (.f64 2 (*.f64 x.re x.im)))))
✓	0.4b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (neg.f64 (.f64 x.im (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (*.f64 x.re x.im))))))

Compiler

Compiled 3530 to 1767 computations (49.9% saved)

regimes666.0ms (12.1%)

Accuracy

Total 0.2b remaining (90.5%)

Threshold costs 0.2b (90.5%)

Counts

118 → 1

Compiler

Compiled 8586 to 4704 computations (45.2% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
7×	`+-commutative_binary64`
6×	`distribute-lft-neg-in_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	26	23
2	42	23
3	54	23
4	60	23
5	63	23
6	64	23
7	63	23

end1.0ms (0%)

Compiler: Compiled 18 to 10 computations (44.4% saved)

sample1.8s (31.7%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
50.0ms	432×	body	128	invalid

Compiler

Compiled 220 to 119 computations (45.9% saved)

Details

analyze428.0ms (7.8%)

sample49.0ms (0.9%)

simplify170.0ms (3.1%)

prune6.0ms (0.1%)

localize21.0ms (0.4%)

series83.0ms (1.5%)

rewrite56.0ms (1%)

simplify208.0ms (3.8%)

prune199.0ms (3.6%)

localize23.0ms (0.4%)

series50.0ms (0.9%)

rewrite60.0ms (1.1%)

simplify169.0ms (3.1%)

prune308.0ms (5.6%)

localize21.0ms (0.4%)

series81.0ms (1.5%)

rewrite39.0ms (0.7%)

simplify145.0ms (2.6%)

prune247.0ms (4.5%)

localize26.0ms (0.5%)

series185.0ms (3.3%)

rewrite56.0ms (1%)

simplify170.0ms (3.1%)

prune292.0ms (5.3%)

regimes666.0ms (12.1%)

simplify7.0ms (0.1%)

end1.0ms (0%)

sample1.8s (31.7%)

Profiling