Details

analyze168.0ms (5.8%)

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)

sample1.2s (40.7%)

Results

1.0s	8256×	body	128	valid
47.0ms	421×	body	128	invalid

Compiler

Compiled 65 to 35 computations (46.2% saved)

simplify125.0ms (4.3%)

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

6.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	6.4b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
	6.4b	(-.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))

Compiler

Compiled 97 to 51 computations (47.4% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))
✓	0.2b	(.f64 (.f64 x.im x.im) -3)
✓	6.0b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))

series26.0ms (0.9%)

Counts

3 → 60

Calls

3 calls:

16.0ms	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
7.0ms	(fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))
2.0ms	(.f64 (.f64 x.im x.im) -3)

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
9×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`

Counts

3 → 53

Calls

3 calls:

6.0ms	(.f64 (.f64 x.im x.im) -3)
3.0ms	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
0.0ms	(fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))

simplify52.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

652×	`distribute-rgt-in_binary64`
645×	`distribute-lft-in_binary64`
429×	`fma-def_binary64`
175×	`*-commutative_binary64`
160×	`associate-+l+_binary64`

Counts

113 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	88	1459
1	181	1302
2	525	1293
3	1135	1293
4	4953	1293

prune101.0ms (3.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	87	6	93
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	88	7	95

Error

6.1b

Counts

95 → 7

Alt Table

Status	Error	Program
	6.4b	(.f64 x.re (fma.f64 x.re x.re (.f64 x.im (*.f64 x.im -3))))
	6.4b	(-.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))
	30.1b	(cbrt.f64 (pow.f64 (fma.f64 -3 (.f64 x.re (.f64 x.im x.im)) (pow.f64 x.re 3)) 3))
	26.5b	(.f64 (sqrt.f64 (.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3)))) (sqrt.f64 (.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))))
	6.5b	(.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 (.f64 x.im x.im) (*.f64 (cbrt.f64 -3) (cbrt.f64 -3))) (cbrt.f64 -3))))
▶	6.4b	(.f64 x.re (fma.f64 -3 (.f64 x.im x.im) (*.f64 x.re x.re)))
	27.5b	(pow.f64 x.re 3)

Compiler

Compiled 1649 to 819 computations (50.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 -3 (.f64 x.im x.im) (.f64 x.re x.re))
✓	6.0b	(.f64 x.re (fma.f64 -3 (.f64 x.im x.im) (*.f64 x.re x.re)))

series21.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

14.0ms	(.f64 x.re (fma.f64 -3 (.f64 x.im x.im) (*.f64 x.re x.re)))
7.0ms	(fma.f64 -3 (.f64 x.im x.im) (.f64 x.re x.re))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

3.0ms	(.f64 x.re (fma.f64 -3 (.f64 x.im x.im) (*.f64 x.re x.re)))
0.0ms	(fma.f64 -3 (.f64 x.im x.im) (.f64 x.re x.re))

simplify48.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

869×	`distribute-rgt-in_binary64`
865×	`distribute-lft-in_binary64`
516×	`fma-def_binary64`
267×	`associate-l_binary64`
210×	`associate-r_binary64`

Counts

80 → 55

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	55	1190
1	112	1033
2	318	1033
3	1135	1033
4	5164	1033

prune49.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	55	7	62

Error

6.1b

Counts

62 → 7

Alt Table

Status	Error	Program
	6.4b	(.f64 x.re (fma.f64 x.re x.re (.f64 x.im (*.f64 x.im -3))))
▶	6.4b	(-.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))
	30.1b	(cbrt.f64 (pow.f64 (fma.f64 -3 (.f64 x.re (.f64 x.im x.im)) (pow.f64 x.re 3)) 3))
	26.5b	(.f64 (sqrt.f64 (.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3)))) (sqrt.f64 (.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))))
	6.5b	(.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 (.f64 x.im x.im) (*.f64 (cbrt.f64 -3) (cbrt.f64 -3))) (cbrt.f64 -3))))
✓	6.4b	(.f64 x.re (fma.f64 -3 (.f64 x.im x.im) (*.f64 x.re x.re)))
	27.5b	(pow.f64 x.re 3)

Compiler

Compiled 1028 to 473 computations (54% saved)

localize10.0ms (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.re) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))
✓	0.2b	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
✓	6.0b	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)

series42.0ms (1.5%)

Counts

4 → 96

Calls

4 calls:

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

rewrite24.0ms (0.8%)

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:

7.0ms	(-.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)
3.0ms	(+.f64 (.f64 x.re x.im) (.f64 x.im x.re))

simplify117.0ms (4.1%)

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

prune113.0ms (3.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	138	4	142
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	139	10	149

Error

0.0b

Counts

149 → 10

Alt Table

Status	Error	Program
	27.4b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 x.re x.im))) (sqrt.f64 (.f64 2 (*.f64 x.re x.im)))) x.im))
	6.5b	(.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 (.f64 x.im x.im) (*.f64 (cbrt.f64 -3) (cbrt.f64 -3))) (cbrt.f64 -3))))
	6.4b	(.f64 x.re (fma.f64 x.re x.re (.f64 x.im (*.f64 x.im -3))))
✓	6.4b	(-.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))
	30.1b	(cbrt.f64 (pow.f64 (fma.f64 -3 (.f64 x.re (.f64 x.im x.im)) (pow.f64 x.re 3)) 3))
▶	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))
	22.7b	(-.f64 (pow.f64 x.re 3) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
	26.5b	(.f64 (sqrt.f64 (.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3)))) (sqrt.f64 (.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))))
✓	6.4b	(.f64 x.re (fma.f64 -3 (.f64 x.im x.im) (*.f64 x.re x.re)))
	6.4b	(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 4383 to 943 computations (78.5% saved)

localize12.0ms (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))
	0.2b	(.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))

series24.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

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

rewrite28.0ms (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:

12.0ms	(-.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))
7.0ms	(.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re))

simplify101.0ms (3.5%)

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

prune160.0ms (5.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	161	8	169
Fresh	5	2	7
Picked	1	0	1
Done	2	0	2
Total	169	10	179

Error

Counts

179 → 10

Alt Table

Status	Error	Program
	25.4b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 x.re x.im))) (sqrt.f64 (.f64 2 (.f64 x.re x.im)))) 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))
	16.9b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (cbrt.f64 (.f64 (.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 x.re x.im) (*.f64 x.im x.re)) x.im))))
	6.5b	(.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 (.f64 x.im x.im) (*.f64 (cbrt.f64 -3) (cbrt.f64 -3))) (cbrt.f64 -3))))
	0.7b	(-.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))
	23.0b	(.f64 (sqrt.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))) (sqrt.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))))
	39.5b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (/.f64 (.f64 x.im (.f64 2 (pow.f64 (.f64 x.re x.im) 3))) (+.f64 (.f64 (.f64 x.re x.im) (.f64 x.re x.im)) (-.f64 (.f64 (.f64 x.im x.re) (.f64 x.im x.re)) (.f64 (.f64 x.re x.im) (.f64 x.im x.re))))))
	0.5b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (.f64 (.f64 (.f64 2 (.f64 x.re x.im)) (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im)))
	6.4b	(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))
	6.4b	(+.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)

Compiler

Compiled 6131 to 1346 computations (78% saved)

regimes312.0ms (10.8%)

Accuracy

Total 0.2b remaining (87.3%)

Threshold costs 0.2b (87.3%)

Counts

107 → 1

Compiler

Compiled 7260 to 3765 computations (48.1% saved)

simplify3.0ms (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

end142.0ms (4.9%)

Compiler: Compiled 353 to 162 computations (54.1% saved)

Details

analyze168.0ms (5.8%)

sample1.2s (40.7%)

simplify125.0ms (4.3%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series26.0ms (0.9%)

rewrite11.0ms (0.4%)

simplify52.0ms (1.8%)

prune101.0ms (3.5%)

localize6.0ms (0.2%)

series21.0ms (0.7%)

rewrite4.0ms (0.1%)

simplify48.0ms (1.7%)

prune49.0ms (1.7%)

localize10.0ms (0.3%)

series42.0ms (1.5%)

rewrite24.0ms (0.8%)

simplify117.0ms (4.1%)

prune113.0ms (3.9%)

localize12.0ms (0.4%)

series24.0ms (0.8%)

rewrite28.0ms (1%)

simplify101.0ms (3.5%)

prune160.0ms (5.6%)

regimes312.0ms (10.8%)

simplify3.0ms (0.1%)

end142.0ms (4.9%)

Profiling