Details

analyze234.0ms (5.4%)

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)

sample24.0ms (0.5%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	15×	body	128	invalid

Compiler

Compiled 45 to 25 computations (44.4% saved)

simplify127.0ms (2.9%)

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

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

8.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	8.5b	(-.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))
	8.5b	(.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)

localize11.0ms (0.2%)

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 x.im x.re)) x.im)
✓	0.2b	(-.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))
✓	7.9b	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)

series47.0ms (1.1%)

Counts

4 → 96

Calls

4 calls:

16.0ms	(-.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))
14.0ms	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
11.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
6.0ms	(+.f64 (.f64 x.re x.im) (.f64 x.im x.re))

rewrite25.0ms (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 → 79

Calls

4 calls:

6.0ms	(-.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))
5.0ms	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
5.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
4.0ms	(+.f64 (.f64 x.re x.im) (.f64 x.im x.re))

simplify119.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

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

Counts

175 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	2898
1	445	2551
2	1755	2377
3	3540	2365
4	4776	2365
5	5089	2365

prune106.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	136	6	142
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	138	6	144

Error

0.0b

Counts

144 → 6

Alt Table

Status	Error	Program
	8.5b	(+.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)
▶	0.3b	(-.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))
	38.4b	(/.f64 (-.f64 (.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re)) (.f64 (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))) (+.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)))
	8.4b	(-.f64 (pow.f64 x.re 3) (.f64 3 (.f64 x.re (pow.f64 x.im 2))))
	8.8b	(-.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))))))
	8.4b	(fma.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re (.f64 (.f64 x.re (*.f64 x.im x.im)) -2))

Compiler

Compiled 4386 to 889 computations (79.7% saved)

localize11.0ms (0.2%)

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

series29.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

16.0ms	(-.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))
13.0ms	(.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re))

rewrite30.0ms (0.7%)

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:

13.0ms	(-.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))
9.0ms	(.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re))

simplify100.0ms (2.3%)

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

prune156.0ms (3.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	164	5	169
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	167	8	175

Error

0.0b

Counts

175 → 8

Alt Table

Status	Error	Program
	0.3b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (.f64 (.f64 2 (*.f64 x.re x.im)) x.im))
	38.4b	(/.f64 (-.f64 (.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re)) (.f64 (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))) (+.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)))
	1.0b	(.f64 (.f64 (cbrt.f64 (-.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))) (cbrt.f64 (-.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)))) (cbrt.f64 (-.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))))
	8.8b	(-.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))))))
	0.7b	(-.f64 (.f64 (.f64 (cbrt.f64 (+.f64 x.re x.im)) (cbrt.f64 (+.f64 x.re x.im))) (.f64 (cbrt.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)))))
	8.4b	(+.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)
	8.4b	(fma.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re (.f64 (.f64 x.re (*.f64 x.im x.im)) -2))

Compiler

Compiled 6358 to 1414 computations (77.8% saved)

localize10.0ms (0.2%)

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)))))

series41.0ms (0.9%)

Counts

4 → 72

Calls

4 calls:

18.0ms	(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)))))
11.0ms	(.f64 x.im (.f64 2 (*.f64 x.re x.im)))
7.0ms	(.f64 2 (.f64 x.re x.im))
5.0ms	(*.f64 (-.f64 x.re x.im) x.re)

rewrite18.0ms (0.4%)

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:

5.0ms	(.f64 x.im (.f64 2 (*.f64 x.re x.im)))
5.0ms	(*.f64 (-.f64 x.re x.im) x.re)
4.0ms	(.f64 2 (.f64 x.re x.im))
0.0ms	(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)))))

simplify90.0ms (2.1%)

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

prune168.0ms (3.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	118	7	125

Error

Counts

125 → 7

Alt Table

Status	Error	Program
	0.7b	(fma.f64 (+.f64 x.re x.im) (.f64 (.f64 (-.f64 x.re x.im) (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re)) (neg.f64 (.f64 x.im (.f64 2 (.f64 x.re x.im)))))
	0.7b	(-.f64 (.f64 (.f64 (cbrt.f64 (+.f64 x.re x.im)) (cbrt.f64 (+.f64 x.re x.im))) (.f64 (cbrt.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))
▶	0.3b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (.f64 (.f64 2 (*.f64 x.re x.im)) x.im))
	38.4b	(/.f64 (-.f64 (.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re)) (.f64 (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))) (+.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)))
	8.4b	(fma.f64 -3 (.f64 x.re (.f64 x.im x.im)) (pow.f64 x.re 3))
✓	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)))))
	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 2931 to 1114 computations (62% saved)

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series49.0ms (1.1%)

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 2 (*.f64 x.re x.im)) x.im))
21.0ms	(.f64 (.f64 2 (*.f64 x.re x.im)) x.im)

rewrite35.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
11×	`pow1_binary64`
6×	`cbrt-unprod_binary64`
6×	`prod-exp_binary64`

Counts

2 → 39

Calls

2 calls:

19.0ms	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (.f64 (.f64 2 (*.f64 x.re x.im)) x.im))
12.0ms	(.f64 (.f64 2 (*.f64 x.re x.im)) x.im)

simplify144.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

465×	`*-commutative_binary64`
394×	`fma-def_binary64`
389×	`fma-neg_binary64`
379×	`cancel-sign-sub-inv_binary64`
215×	`associate-l_binary64`

Counts

87 → 65

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	95	1406
1	258	1348
2	1123	1269
3	3132	1267
4	4851	1267
5	5000	1267
6	4815	1267

prune225.0ms (5.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	136	7	143

Error

Counts

143 → 7

Alt Table

Status	Error	Program
	8.4b	(fma.f64 -3 (.f64 x.re (.f64 x.im x.im)) (pow.f64 x.re 3))
	37.1b	(/.f64 (-.f64 (.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re))) (.f64 (.f64 (.f64 2 (.f64 x.re x.im)) x.im) (.f64 (.f64 2 (.f64 x.re x.im)) x.im))) (+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (.f64 (.f64 2 (*.f64 x.re x.im)) x.im)))
	0.7b	(fma.f64 (+.f64 x.re x.im) (.f64 (.f64 (-.f64 x.re x.im) (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re)) (neg.f64 (.f64 x.im (.f64 2 (.f64 x.re x.im)))))
✓	0.3b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (.f64 (.f64 2 (*.f64 x.re x.im)) 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)))))
	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))))))
	0.7b	(-.f64 (.f64 (.f64 (cbrt.f64 (+.f64 x.re x.im)) (cbrt.f64 (+.f64 x.re x.im))) (.f64 (.f64 x.re (-.f64 x.re x.im)) (cbrt.f64 (+.f64 x.re x.im)))) (.f64 (.f64 2 (*.f64 x.re x.im)) x.im))

Compiler

Compiled 3540 to 1223 computations (65.5% saved)

regimes727.0ms (16.6%)

Accuracy

Total 0.2b remaining (90.3%)

Threshold costs 0.2b (90.3%)

Counts

124 → 1

Compiler

Compiled 10509 to 5265 computations (49.9% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
8×	`*-commutative_binary64`
6×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	58
1	29	58
2	40	58
3	52	58
4	57	58
5	60	58
6	61	58
7	61	58

end1.0ms (0%)

Compiler: Compiled 41 to 13 computations (68.3% saved)

sample1.8s (41.3%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
54.0ms	429×	body	128	invalid

Compiler

Compiled 249 to 121 computations (51.4% saved)

Details

analyze234.0ms (5.4%)

sample24.0ms (0.5%)

simplify127.0ms (2.9%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

series47.0ms (1.1%)

rewrite25.0ms (0.6%)

simplify119.0ms (2.7%)

prune106.0ms (2.4%)

localize11.0ms (0.2%)

series29.0ms (0.7%)

rewrite30.0ms (0.7%)

simplify100.0ms (2.3%)

prune156.0ms (3.6%)

localize10.0ms (0.2%)

series41.0ms (0.9%)

rewrite18.0ms (0.4%)

simplify90.0ms (2.1%)

prune168.0ms (3.9%)

localize21.0ms (0.5%)

series49.0ms (1.1%)

rewrite35.0ms (0.8%)

simplify144.0ms (3.3%)

prune225.0ms (5.2%)

regimes727.0ms (16.6%)

simplify10.0ms (0.2%)

end1.0ms (0%)

sample1.8s (41.3%)

Profiling