Details

analyze208.0ms (5.5%)

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%	74.9%	0.1%	6
31.2%	50%	18.8%	7
34.3%	43.7%	22%	8
45.3%	26.5%	28.2%	9
46.8%	23.4%	29.8%	10
48.8%	14%	37.2%	11
49.8%	12.1%	38.1%	12
52.8%	7.1%	40.1%	13
53.3%	6.1%	40.6%	14

Compiler

Compiled 22 to 12 computations (45.5% saved)

sample1.2s (31.6%)

Results

1.0s	8256×	body	128	valid
74.0ms	591×	body	128	invalid

Compiler

Compiled 65 to 35 computations (46.2% saved)

simplify132.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

613×	`sub-neg_binary64`
578×	`fma-neg_binary64`
529×	`neg-mul-1_binary64`
501×	`neg-sub0_binary64`
455×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	26	23
2	60	23
3	130	16
4	335	16
5	881	16
6	1496	16
7	3511	16
8	4061	16
9	3977	16
10	4614	16
11	4771	16
12	4918	16
13	4914	16

prune3.0ms (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

6.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	6.2b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
▶	6.1b	(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))

Compiler

Compiled 100 to 54 computations (46% saved)

localize12.0ms (0.3%)

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.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
✓	0.2b	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
✓	5.7b	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.im)

series48.0ms (1.3%)

Counts

4 → 96

Calls

4 calls:

14.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
14.0ms	(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
13.0ms	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.im)
7.0ms	(+.f64 (.f64 x.re x.im) (.f64 x.im x.re))

rewrite23.0ms (0.6%)

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 → 77

Calls

4 calls:

6.0ms	(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
5.0ms	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.im)
5.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
3.0ms	(+.f64 (.f64 x.re x.im) (.f64 x.im x.re))

simplify79.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

727×	`distribute-rgt-in_binary64`
685×	`distribute-lft-in_binary64`
245×	`associate-l_binary64`
206×	`associate-r_binary64`
181×	`distribute-rgt-out_binary64`

Counts

173 → 139

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	2758
1	427	2398
2	1675	2360
3	4822	2360

prune108.0ms (2.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	135	4	139
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	136	5	141

Error

0.0b

Counts

141 → 5

Alt Table

Status	Error	Program
	6.2b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
	6.6b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im)) (cbrt.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im))) (cbrt.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im))) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
▶	0.2b	(+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
	15.0b	(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im) (.f64 (cbrt.f64 (.f64 (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) (+.f64 (.f64 x.re x.im) (.f64 x.im x.re))) (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)))) x.re))
	6.1b	(+.f64 (-.f64 (.f64 (pow.f64 x.re 2) x.im) (pow.f64 x.im 3)) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))

Compiler

Compiled 4271 to 913 computations (78.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series34.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

16.0ms

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

12.0ms

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

6.0ms

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

rewrite32.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`associate-*l/_binary64`
18×	`flip-+_binary64`
18×	`flip3-+_binary64`
16×	`frac-add_binary64`
12×	`frac-times_binary64`

Counts

3 → 83

Calls

3 calls:

11.0ms

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

7.0ms

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

5.0ms

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

simplify125.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

602×	`associate-l_binary64`
526×	`associate-r_binary64`
306×	`distribute-rgt-out_binary64`
303×	`distribute-rgt-in_binary64`
291×	`distribute-lft-in_binary64`

Counts

155 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	197	4461
1	710	3616
2	3393	2663
3	4379	2663
4	4644	2663

prune162.0ms (4.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	177	6	183
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	180	8	188

Error

0.0b

Counts

188 → 8

Alt Table

Status	Error	Program
	20.3b	(+.f64 (.f64 (+.f64 x.re x.im) (cbrt.f64 (.f64 (.f64 (.f64 (-.f64 x.re x.im) x.im) (.f64 (-.f64 x.re x.im) x.im)) (.f64 (-.f64 x.re x.im) x.im)))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
	0.6b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
	21.6b	(+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.f64 (sqrt.f64 (.f64 x.re (.f64 2 (.f64 x.im x.re)))) (sqrt.f64 (.f64 x.re (.f64 2 (*.f64 x.im x.re))))))
	6.1b	(+.f64 (-.f64 (.f64 (pow.f64 x.re 2) x.im) (pow.f64 x.im 3)) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
	0.5b	(+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.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.re (cbrt.f64 (.f64 2 (*.f64 x.im x.re))))))
	34.8b	(+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.f64 (.f64 (.f64 2 (.f64 x.im x.re)) (sqrt.f64 x.re)) (sqrt.f64 x.re)))
	6.2b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
▶	0.2b	(+.f64 (.f64 (+.f64 x.re x.im) (-.f64 (.f64 x.re x.im) (pow.f64 x.im 2))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re))

Compiler

Compiled 6565 to 1437 computations (78.1% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series34.0ms (0.9%)

Counts

3 → 54

Calls

3 calls:

16.0ms

(+.f64 (*.f64 (+.f64 x.re x.im) (-.f64 (*.f64 x.re x.im) (pow.f64 x.im 2))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))

12.0ms

(*.f64 (+.f64 x.re x.im) (-.f64 (*.f64 x.re x.im) (pow.f64 x.im 2)))

6.0ms

(-.f64 (*.f64 x.re x.im) (pow.f64 x.im 2))

rewrite48.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`cancel-sign-sub-inv_binary64`
40×	`prod-diff_binary64`
34×	`associate-+l+_binary64`
34×	`distribute-lft-in_binary64`
34×	`distribute-rgt-in_binary64`

Counts

3 → 159

Calls

3 calls:

14.0ms

(+.f64 (*.f64 (+.f64 x.re x.im) (-.f64 (*.f64 x.re x.im) (pow.f64 x.im 2))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))

9.0ms

(*.f64 (+.f64 x.re x.im) (-.f64 (*.f64 x.re x.im) (pow.f64 x.im 2)))

4.0ms

(-.f64 (*.f64 x.re x.im) (pow.f64 x.im 2))

simplify211.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

594×	`associate-l_binary64`
549×	`associate-r_binary64`
480×	`fma-neg_binary64`
445×	`exp-prod_binary64`
355×	`fma-def_binary64`

Counts

213 → 244

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	314	7089
1	882	5007
2	3896	3948
3	4007	3932
4	4634	3932
5	4848	3932
6	4563	3932

prune306.0ms (8.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	281	2	283
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	285	6	291

Error

0.0b

Counts

291 → 6

Alt Table

Status	Error	Program
	20.3b	(+.f64 (.f64 (+.f64 x.re x.im) (cbrt.f64 (.f64 (.f64 (.f64 (-.f64 x.re x.im) x.im) (.f64 (-.f64 x.re x.im) x.im)) (.f64 (-.f64 x.re x.im) x.im)))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
	0.6b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
	21.6b	(+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.f64 (sqrt.f64 (.f64 x.re (.f64 2 (.f64 x.im x.re)))) (sqrt.f64 (.f64 x.re (.f64 2 (*.f64 x.im x.re))))))
	6.1b	(+.f64 (-.f64 (.f64 (pow.f64 x.re 2) x.im) (pow.f64 x.im 3)) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
	0.5b	(+.f64 (.f64 (+.f64 x.re x.im) (-.f64 (.f64 x.re x.im) (pow.f64 x.im 2))) (.f64 (.f64 (cbrt.f64 (.f64 x.re (.f64 2 (.f64 x.im x.re)))) (cbrt.f64 (.f64 x.re (.f64 2 (.f64 x.im x.re))))) (cbrt.f64 (.f64 x.re (.f64 2 (*.f64 x.im x.re))))))
▶	0.2b	(fma.f64 (+.f64 x.re x.im) (-.f64 (.f64 x.re x.im) (pow.f64 x.im 2)) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))

Compiler

Compiled 10882 to 3671 computations (66.3% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series18.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

18.0ms

(fma.f64 (+.f64 x.re x.im) (-.f64 (*.f64 x.re x.im) (pow.f64 x.im 2)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (+.f64 x.re x.im) (-.f64 (*.f64 x.re x.im) (pow.f64 x.im 2)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))

simplify59.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

575×	`associate-l_binary64`
493×	`associate-r_binary64`
401×	`exp-prod_binary64`
366×	`fma-def_binary64`
351×	`distribute-rgt-in_binary64`

Counts

34 → 24

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	700
1	61	602
2	155	602
3	542	592
4	3427	592
5	4987	592

prune147.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	134	6	140

Error

Counts

140 → 6

Alt Table

Status	Error	Program
	21.6b	(+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.f64 (sqrt.f64 (.f64 x.re (.f64 2 (.f64 x.im x.re)))) (sqrt.f64 (.f64 x.re (.f64 2 (*.f64 x.im x.re))))))
	6.1b	(+.f64 (-.f64 (.f64 (pow.f64 x.re 2) x.im) (pow.f64 x.im 3)) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
	0.6b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
✓	0.2b	(fma.f64 (+.f64 x.re x.im) (-.f64 (.f64 x.re x.im) (pow.f64 x.im 2)) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
	0.5b	(fma.f64 (+.f64 x.re x.im) (-.f64 (.f64 x.re x.im) (pow.f64 x.im 2)) (.f64 (.f64 (cbrt.f64 (.f64 x.re (.f64 2 (.f64 x.im x.re)))) (cbrt.f64 (.f64 x.re (.f64 2 (.f64 x.im x.re))))) (cbrt.f64 (.f64 x.re (.f64 2 (.f64 x.im x.re))))))
	9.6b	(fma.f64 (+.f64 x.re x.im) (-.f64 (.f64 x.re x.im) (pow.f64 x.im 2)) (.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 x.im x.re)) 3)) x.re))

Compiler

Compiled 3737 to 1190 computations (68.2% saved)

regimes661.0ms (17.4%)

Accuracy

Total 0.2b remaining (78.1%)

Threshold costs 0.2b (78.1%)

Counts

192 → 1

Compiler

Compiled 15360 to 8169 computations (46.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	17	26
2	22	26
3	24	26
4	25	26
5	25	26

end112.0ms (3%)

Compiler: Compiled 218 to 115 computations (47.2% saved)

Details

analyze208.0ms (5.5%)

sample1.2s (31.6%)

simplify132.0ms (3.5%)

prune3.0ms (0.1%)

localize12.0ms (0.3%)

series48.0ms (1.3%)

rewrite23.0ms (0.6%)

simplify79.0ms (2.1%)

prune108.0ms (2.9%)

localize11.0ms (0.3%)

series34.0ms (0.9%)

rewrite32.0ms (0.9%)

simplify125.0ms (3.3%)

prune162.0ms (4.3%)

localize11.0ms (0.3%)

series34.0ms (0.9%)

rewrite48.0ms (1.3%)

simplify211.0ms (5.6%)

prune306.0ms (8.1%)

localize11.0ms (0.3%)

series18.0ms (0.5%)

rewrite1.0ms (0%)

simplify59.0ms (1.5%)

prune147.0ms (3.9%)

regimes661.0ms (17.4%)

simplify3.0ms (0.1%)

end112.0ms (3%)

Profiling