Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 22 to 12 computations (45.5% saved)

sample1.3s (30.8%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 65 to 35 computations (46.2% saved)

simplify174.0ms (4.2%)

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

prune5.0ms (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

5.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	5.9b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
	10.9b	(-.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)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x.im x.im) -3)
✓	2.8b	(fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))
✓	3.1b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))

series38.0ms (0.9%)

Counts

3 → 60

Calls

3 calls:

24.0ms	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
9.0ms	(fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))
5.0ms	(.f64 (.f64 x.im x.im) -3)

rewrite10.0ms (0.2%)

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:

5.0ms	(.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))

simplify59.0ms (1.4%)

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

prune183.0ms (4.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	87	6	93
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	87	8	95

Error

3.0b

Counts

95 → 8

Alt Table

Status	Error	Program
✓	5.9b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
▶	5.9b	(.f64 x.re (fma.f64 x.re x.re (.f64 x.im (*.f64 x.im -3))))
	10.9b	(-.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))
	6.0b	(.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 (cbrt.f64 (.f64 (.f64 x.im x.im) -3)) (cbrt.f64 (.f64 (.f64 x.im x.im) -3))) (cbrt.f64 (.f64 (*.f64 x.im x.im) -3)))))
	15.4b	(.f64 x.re (fma.f64 x.re x.re (cbrt.f64 (.f64 (.f64 (.f64 (.f64 x.im x.im) (.f64 x.im x.im)) (.f64 x.im x.im)) (.f64 (*.f64 -3 -3) -3)))))
	34.0b	(.f64 (sqrt.f64 x.re) (.f64 (sqrt.f64 x.re) (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))))
	21.1b	(cbrt.f64 (.f64 (.f64 (.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))) (.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3)))) (.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))))
	22.5b	(pow.f64 x.re 3)

Compiler

Compiled 1719 to 846 computations (50.8% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x.im (.f64 x.im -3))
✓	2.8b	(fma.f64 x.re x.re (.f64 x.im (.f64 x.im -3)))
✓	3.1b	(.f64 x.re (fma.f64 x.re x.re (.f64 x.im (*.f64 x.im -3))))

series47.0ms (1.1%)

Counts

3 → 60

Calls

3 calls:

25.0ms	(.f64 x.re (fma.f64 x.re x.re (.f64 x.im (*.f64 x.im -3))))
17.0ms	(fma.f64 x.re x.re (.f64 x.im (.f64 x.im -3)))
4.0ms	(.f64 x.im (.f64 x.im -3))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

3 → 52

Calls

3 calls:

7.0ms	(.f64 x.im (.f64 x.im -3))
5.0ms	(.f64 x.re (fma.f64 x.re x.re (.f64 x.im (*.f64 x.im -3))))
1.0ms	(fma.f64 x.re x.re (.f64 x.im (.f64 x.im -3)))

simplify134.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

653×	`distribute-rgt-in_binary64`
648×	`distribute-lft-in_binary64`
419×	`fma-def_binary64`
196×	`*-commutative_binary64`
155×	`distribute-rgt-neg-out_binary64`

Counts

112 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	1445
1	184	1288
2	546	1279
3	1109	1277
4	4981	1277
5	4947	1277

prune181.0ms (4.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	92	8	100

Error

3.0b

Counts

100 → 8

Alt Table

Status	Error	Program
✓	5.9b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
✓	5.9b	(.f64 x.re (fma.f64 x.re x.re (.f64 x.im (*.f64 x.im -3))))
	10.9b	(-.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))
▶	6.0b	(.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 (cbrt.f64 (.f64 (.f64 x.im x.im) -3)) (cbrt.f64 (.f64 (.f64 x.im x.im) -3))) (cbrt.f64 (.f64 (*.f64 x.im x.im) -3)))))
	15.4b	(.f64 x.re (fma.f64 x.re x.re (cbrt.f64 (.f64 (.f64 (.f64 (.f64 x.im x.im) (.f64 x.im x.im)) (.f64 x.im x.im)) (.f64 (*.f64 -3 -3) -3)))))
	34.0b	(.f64 (sqrt.f64 x.re) (.f64 (sqrt.f64 x.re) (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))))
	21.1b	(cbrt.f64 (.f64 (.f64 (.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))) (.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3)))) (.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))))
	22.5b	(pow.f64 x.re 3)

Compiler

Compiled 1699 to 889 computations (47.7% saved)

localize23.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (cbrt.f64 (.f64 (.f64 x.im x.im) -3)) (cbrt.f64 (.f64 (*.f64 x.im x.im) -3)))
✓	2.8b	(fma.f64 x.re x.re (.f64 (.f64 (cbrt.f64 (.f64 (.f64 x.im x.im) -3)) (cbrt.f64 (.f64 (.f64 x.im x.im) -3))) (cbrt.f64 (.f64 (.f64 x.im x.im) -3))))
✓	3.1b	(.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 (cbrt.f64 (.f64 (.f64 x.im x.im) -3)) (cbrt.f64 (.f64 (.f64 x.im x.im) -3))) (cbrt.f64 (.f64 (*.f64 x.im x.im) -3)))))
✓	29.5b	(cbrt.f64 (.f64 (.f64 x.im x.im) -3))

series387.0ms (9.4%)

Counts

4 → 72

Calls

4 calls:

105.0ms	(.f64 (cbrt.f64 (.f64 (.f64 x.im x.im) -3)) (cbrt.f64 (.f64 (*.f64 x.im x.im) -3)))
103.0ms	(cbrt.f64 (.f64 (.f64 x.im x.im) -3))
95.0ms	(.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 (cbrt.f64 (.f64 (.f64 x.im x.im) -3)) (cbrt.f64 (.f64 (.f64 x.im x.im) -3))) (cbrt.f64 (.f64 (*.f64 x.im x.im) -3)))))
84.0ms	(fma.f64 x.re x.re (.f64 (.f64 (cbrt.f64 (.f64 (.f64 x.im x.im) -3)) (cbrt.f64 (.f64 (.f64 x.im x.im) -3))) (cbrt.f64 (.f64 (.f64 x.im x.im) -3))))

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`pow1_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
8×	`add-exp-log_binary64`

Counts

4 → 76

Calls

4 calls:

9.0ms	(.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 (cbrt.f64 (.f64 (.f64 x.im x.im) -3)) (cbrt.f64 (.f64 (.f64 x.im x.im) -3))) (cbrt.f64 (.f64 (*.f64 x.im x.im) -3)))))
5.0ms	(cbrt.f64 (.f64 (.f64 x.im x.im) -3))
5.0ms	(.f64 (cbrt.f64 (.f64 (.f64 x.im x.im) -3)) (cbrt.f64 (.f64 (*.f64 x.im x.im) -3)))
0.0ms	(fma.f64 x.re x.re (.f64 (.f64 (cbrt.f64 (.f64 (.f64 x.im x.im) -3)) (cbrt.f64 (.f64 (.f64 x.im x.im) -3))) (cbrt.f64 (.f64 (.f64 x.im x.im) -3))))

simplify97.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

656×	`distribute-rgt-in_binary64`
651×	`distribute-lft-in_binary64`
459×	`fma-def_binary64`
313×	`unswap-sqr_binary64`
184×	`*-commutative_binary64`

Counts

148 → 135

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	2148
1	200	1934
2	590	1856
3	1277	1843
4	5017	1843

prune345.0ms (8.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	175	8	183

Error

3.0b

Counts

183 → 8

Alt Table

Status	Error	Program
✓	5.9b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
✓	5.9b	(.f64 x.re (fma.f64 x.re x.re (.f64 x.im (*.f64 x.im -3))))
▶	10.9b	(-.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))
✓	6.0b	(.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 (cbrt.f64 (.f64 (.f64 x.im x.im) -3)) (cbrt.f64 (.f64 (.f64 x.im x.im) -3))) (cbrt.f64 (.f64 (*.f64 x.im x.im) -3)))))
	15.4b	(.f64 x.re (fma.f64 x.re x.re (cbrt.f64 (.f64 (.f64 (.f64 (.f64 x.im x.im) (.f64 x.im x.im)) (.f64 x.im x.im)) (.f64 (*.f64 -3 -3) -3)))))
	34.0b	(.f64 (sqrt.f64 x.re) (.f64 (sqrt.f64 x.re) (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))))
	21.1b	(cbrt.f64 (.f64 (.f64 (.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))) (.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3)))) (.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))))
	22.5b	(pow.f64 x.re 3)

Compiler

Compiled 5240 to 2868 computations (45.3% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
✓	3.2b	(-.f64 (.f64 x.re x.re) (.f64 x.im x.im))
✓	3.3b	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
✓	6.0b	(-.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))

series59.0ms (1.4%)

Counts

4 → 96

Calls

4 calls:

18.0ms	(-.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))
17.0ms	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
15.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
8.0ms	(-.f64 (.f64 x.re x.re) (.f64 x.im x.im))

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 → 82

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

simplify178.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

343×	`unswap-sqr_binary64`
222×	`associate-l_binary64`
210×	`distribute-rgt-out_binary64`
207×	`fma-neg_binary64`
202×	`cancel-sign-sub-inv_binary64`

Counts

178 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	163	3003
1	452	2674
2	1764	2513
3	3592	2504
4	4795	2504

prune222.0ms (5.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	2	2	4
Picked	1	0	1
Done	0	3	3
Total	146	8	154

Error

0.0b

Counts

154 → 8

Alt Table

Status	Error	Program
✓	5.9b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
✓	5.9b	(.f64 x.re (fma.f64 x.re x.re (.f64 x.im (*.f64 x.im -3))))
✓	6.0b	(.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 (cbrt.f64 (.f64 (.f64 x.im x.im) -3)) (cbrt.f64 (.f64 (.f64 x.im x.im) -3))) (cbrt.f64 (.f64 (*.f64 x.im x.im) -3)))))
	34.0b	(.f64 (sqrt.f64 x.re) (.f64 (sqrt.f64 x.re) (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))))
	10.9b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (.f64 2 (.f64 x.re x.im)) x.im))
	6.9b	(-.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))
	10.9b	(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))
	22.5b	(pow.f64 x.re 3)

Compiler

Compiled 4242 to 814 computations (80.8% saved)

regimes448.0ms (10.8%)

Accuracy

Total 2.1b remaining (98.6%)

Threshold costs 0b (0%)

Counts

53 → 2

Compiler

Compiled 2739 to 1710 computations (37.6% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 21 to 11 computations (47.6% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
12×	`*-commutative_binary64`
10×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	68
1	41	68
2	58	68
3	74	68
4	82	68
5	85	68
6	86	68
7	86	68

end159.0ms (3.9%)

Compiler: Compiled 226 to 112 computations (50.4% saved)

Details

analyze3.0ms (0.1%)

sample1.3s (30.8%)

simplify174.0ms (4.2%)

prune5.0ms (0.1%)

localize10.0ms (0.2%)

series38.0ms (0.9%)

rewrite10.0ms (0.2%)

simplify59.0ms (1.4%)

prune183.0ms (4.4%)

localize12.0ms (0.3%)

series47.0ms (1.1%)

rewrite17.0ms (0.4%)

simplify134.0ms (3.2%)

prune181.0ms (4.4%)

localize23.0ms (0.5%)

series387.0ms (9.4%)

rewrite24.0ms (0.6%)

simplify97.0ms (2.4%)

prune345.0ms (8.3%)

localize11.0ms (0.3%)

series59.0ms (1.4%)

rewrite25.0ms (0.6%)

simplify178.0ms (4.3%)

prune222.0ms (5.4%)

regimes448.0ms (10.8%)

bsearch3.0ms (0.1%)

simplify8.0ms (0.2%)

end159.0ms (3.9%)

Profiling