Details

analyze194.0ms (5.1%)

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)

sample1.1s (28.3%)

Results

950.0ms	8256×	body	128	valid
73.0ms	630×	body	128	invalid

Compiler

Compiled 65 to 35 computations (46.2% saved)

simplify21.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

578×	`fma-neg_binary64`
351×	`distribute-rgt-in_binary64`
280×	`fma-def_binary64`
251×	`cancel-sign-sub-inv_binary64`
244×	`associate-+l-_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	27	23
2	63	23
3	148	16
4	416	16
5	1205	16
6	2159	16

Stop Event

1×	node limit

Counts

1 → 2

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (.f64 x.re (.f64 x.im (*.f64 x.re 3))) (pow.f64 x.im 3))
	8.7b	(+.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 58 computations (42% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x.re (.f64 x.im (*.f64 x.re 3))) (pow.f64 x.im 3))
✓	0.1b	(.f64 x.re (.f64 x.im (*.f64 x.re 3)))
✓	0.2b	(.f64 x.im (.f64 x.re 3))

series27.0ms (0.7%)

Counts

3 → 72

Calls

3 calls:

12.0ms	(.f64 x.re (.f64 x.im (*.f64 x.re 3)))
11.0ms	(-.f64 (.f64 x.re (.f64 x.im (*.f64 x.re 3))) (pow.f64 x.im 3))
4.0ms	(.f64 x.im (.f64 x.re 3))

rewrite54.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

524×	`log-prod_binary64`
305×	`fma-def_binary64`
174×	`pow1/3_binary64`
172×	`expm1-udef_binary64`
172×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	199	33
2	2642	33

Stop Event

1×	node limit

Counts

3 → 158

Calls

3 calls:

51.0ms	(-.f64 (.f64 x.re (.f64 x.im (*.f64 x.re 3))) (pow.f64 x.im 3))
51.0ms	(.f64 x.re (.f64 x.im (*.f64 x.re 3)))
51.0ms	(.f64 x.im (.f64 x.re 3))

simplify50.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

453×	`fma-neg_binary64`
450×	`unswap-sqr_binary64`
436×	`distribute-rgt-neg-in_binary64`
394×	`associate-l_binary64`
390×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	744
1	38	744
2	95	744
3	200	744
4	491	744
5	1825	744
6	3955	744

Stop Event

1×	node limit

Counts

230 → 166

prune167.0ms (4.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	160	6	166
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	160	8	168

Error

Counts

168 → 8

Alt Table

Status	Error	Program
	33.9b	(fma.f64 (.f64 (.f64 x.im x.re) (sqrt.f64 (.f64 x.re 3))) (sqrt.f64 (.f64 x.re 3)) (neg.f64 (pow.f64 x.im 3)))
▶	0.2b	(fma.f64 (.f64 x.re 3) (.f64 x.im x.re) (neg.f64 (pow.f64 x.im 3)))
	41.1b	(/.f64 1 (/.f64 (fma.f64 x.re (.f64 x.im (.f64 x.re 3)) (pow.f64 x.im 3)) (-.f64 (pow.f64 (.f64 x.im (.f64 (*.f64 x.re 3) x.re)) 2) (pow.f64 x.im 6))))
	8.7b	(+.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))
	33.8b	(fma.f64 (sqrt.f64 x.re) (.f64 (sqrt.f64 x.re) (.f64 x.im (*.f64 x.re 3))) (neg.f64 (pow.f64 x.im 3)))
	0.6b	(fma.f64 (pow.f64 (cbrt.f64 x.re) 2) (.f64 (cbrt.f64 x.re) (.f64 x.im (*.f64 x.re 3))) (neg.f64 (pow.f64 x.im 3)))
	8.7b	(.f64 (neg.f64 x.im) (fma.f64 x.im x.im (.f64 (*.f64 x.re x.re) -3)))
✓	0.2b	(-.f64 (.f64 x.re (.f64 x.im (*.f64 x.re 3))) (pow.f64 x.im 3))

Compiler

Compiled 3418 to 2351 computations (31.2% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (.f64 x.re 3) (.f64 x.im x.re) (neg.f64 (pow.f64 x.im 3)))

series10.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

10.0ms

(fma.f64 (*.f64 x.re 3) (*.f64 x.im x.re) (neg.f64 (pow.f64 x.im 3)))

rewrite88.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

717×	`log1p-expm1-u_binary64`
717×	`expm1-log1p-u_binary64`
333×	`egg-rr`
330×	`prod-diff_binary64`
92×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	187	14
2	2252	14

Stop Event

1×	node limit

Counts

1 → 333

Calls

1 calls:

78.0ms

(fma.f64 (*.f64 x.re 3) (*.f64 x.im x.re) (neg.f64 (pow.f64 x.im 3)))

simplify43.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

450×	`unswap-sqr_binary64`
428×	`fma-neg_binary64`
404×	`distribute-rgt-neg-in_binary64`
376×	`fma-def_binary64`
361×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	336
1	32	336
2	87	336
3	197	336
4	488	336
5	1724	336
6	3726	336

Stop Event

1×	node limit

Counts

357 → 339

prune286.0ms (7.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	339	0	339
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	339	8	347

Error

Counts

347 → 8

Alt Table

Status	Error	Program
	33.9b	(fma.f64 (.f64 (.f64 x.im x.re) (sqrt.f64 (.f64 x.re 3))) (sqrt.f64 (.f64 x.re 3)) (neg.f64 (pow.f64 x.im 3)))
✓	0.2b	(fma.f64 (.f64 x.re 3) (.f64 x.im x.re) (neg.f64 (pow.f64 x.im 3)))
	41.1b	(/.f64 1 (/.f64 (fma.f64 x.re (.f64 x.im (.f64 x.re 3)) (pow.f64 x.im 3)) (-.f64 (pow.f64 (.f64 x.im (.f64 (*.f64 x.re 3) x.re)) 2) (pow.f64 x.im 6))))
	8.7b	(+.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))
	33.8b	(fma.f64 (sqrt.f64 x.re) (.f64 (sqrt.f64 x.re) (.f64 x.im (*.f64 x.re 3))) (neg.f64 (pow.f64 x.im 3)))
▶	0.6b	(fma.f64 (pow.f64 (cbrt.f64 x.re) 2) (.f64 (cbrt.f64 x.re) (.f64 x.im (*.f64 x.re 3))) (neg.f64 (pow.f64 x.im 3)))
	8.7b	(.f64 (neg.f64 x.im) (fma.f64 x.im x.im (.f64 (*.f64 x.re x.re) -3)))
✓	0.2b	(-.f64 (.f64 x.re (.f64 x.im (*.f64 x.re 3))) (pow.f64 x.im 3))

Compiler

Compiled 10460 to 5182 computations (50.5% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 x.im (.f64 x.re 3))
✓	0.2b	(.f64 (cbrt.f64 x.re) (.f64 x.im (*.f64 x.re 3)))
✓	0.5b	(pow.f64 (cbrt.f64 x.re) 2)
✓	0.6b	(cbrt.f64 x.re)

series358.0ms (9.5%)

Counts

3 → 48

Calls

3 calls:

285.0ms	(.f64 (cbrt.f64 x.re) (.f64 x.im (*.f64 x.re 3)))
39.0ms	(pow.f64 (cbrt.f64 x.re) 2)
34.0ms	(cbrt.f64 x.re)

rewrite43.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

809×	`log1p-expm1-u_binary64`
809×	`expm1-log1p-u_binary64`
95×	`add-sqr-sqrt_binary64`
94×	`associate-r_binary64`
89×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	204	21
2	2311	21

Stop Event

1×	node limit

Counts

3 → 56

Calls

3 calls:

43.0ms	(.f64 (cbrt.f64 x.re) (.f64 x.im (*.f64 x.re 3)))
43.0ms	(pow.f64 (cbrt.f64 x.re) 2)
43.0ms	(cbrt.f64 x.re)

simplify70.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

520×	`unswap-sqr_binary64`
460×	`associate-l_binary64`
453×	`fma-def_binary64`
415×	`sqr-pow_binary64`
360×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	476
1	64	476
2	145	476
3	434	476
4	1683	476
5	2631	476
6	2810	476
7	3101	476
8	3696	476
9	4281	476

Stop Event

1×	node limit

Counts

104 → 66

prune109.0ms (2.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	114	8	122

Error

Counts

122 → 8

Alt Table

Status	Error	Program
	33.9b	(fma.f64 (.f64 (.f64 x.im x.re) (sqrt.f64 (.f64 x.re 3))) (sqrt.f64 (.f64 x.re 3)) (neg.f64 (pow.f64 x.im 3)))
✓	0.2b	(fma.f64 (.f64 x.re 3) (.f64 x.im x.re) (neg.f64 (pow.f64 x.im 3)))
▶	0.8b	(fma.f64 (pow.f64 (cbrt.f64 x.re) 2) (.f64 (cbrt.f64 x.re) (pow.f64 (cbrt.f64 (.f64 x.im (*.f64 x.re 3))) 3)) (neg.f64 (pow.f64 x.im 3)))
	33.8b	(fma.f64 (sqrt.f64 x.re) (.f64 (sqrt.f64 x.re) (.f64 x.im (*.f64 x.re 3))) (neg.f64 (pow.f64 x.im 3)))
✓	0.6b	(fma.f64 (pow.f64 (cbrt.f64 x.re) 2) (.f64 (cbrt.f64 x.re) (.f64 x.im (*.f64 x.re 3))) (neg.f64 (pow.f64 x.im 3)))
	8.7b	(.f64 (neg.f64 x.im) (fma.f64 x.im x.im (.f64 (*.f64 x.re x.re) -3)))
✓	0.2b	(-.f64 (.f64 x.re (.f64 x.im (*.f64 x.re 3))) (pow.f64 x.im 3))
	8.7b	(+.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 2579 to 1629 computations (36.8% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(pow.f64 (cbrt.f64 x.re) 2)
✓	0.6b	(pow.f64 (cbrt.f64 (.f64 x.im (.f64 x.re 3))) 3)
	0.6b	(cbrt.f64 x.re)
✓	12.7b	(cbrt.f64 (.f64 x.im (.f64 x.re 3)))

series654.0ms (17.3%)

Counts

2 → 48

Calls

2 calls:

348.0ms	(pow.f64 (cbrt.f64 (.f64 x.im (.f64 x.re 3))) 3)
306.0ms	(cbrt.f64 (.f64 x.im (.f64 x.re 3)))

rewrite40.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

620×	`log1p-expm1-u_binary64`
620×	`expm1-log1p-u_binary64`
357×	`log-prod_binary64`
123×	`expm1-udef_binary64`
123×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	162	16
2	1751	16

Stop Event

1×	node limit

Counts

2 → 71

Calls

2 calls:

38.0ms	(pow.f64 (cbrt.f64 (.f64 x.im (.f64 x.re 3))) 3)
38.0ms	(cbrt.f64 (.f64 x.im (.f64 x.re 3)))

simplify38.0ms (1%)

Algorithm

1×	egg-herbie

Rules

865×	`fma-def_binary64`
422×	`unswap-sqr_binary64`
264×	`associate-l_binary64`
228×	`unsub-neg_binary64`
218×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	936
1	124	936
2	304	888
3	862	480
4	2729	480

Stop Event

1×	node limit

Counts

119 → 83

prune156.0ms (4.1%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	156	8	164

Error

Counts

164 → 8

Alt Table

Status	Error	Program
	33.9b	(fma.f64 (.f64 (.f64 x.im x.re) (sqrt.f64 (.f64 x.re 3))) (sqrt.f64 (.f64 x.re 3)) (neg.f64 (pow.f64 x.im 3)))
✓	0.2b	(fma.f64 (.f64 x.re 3) (.f64 x.im x.re) (neg.f64 (pow.f64 x.im 3)))
✓	0.8b	(fma.f64 (pow.f64 (cbrt.f64 x.re) 2) (.f64 (cbrt.f64 x.re) (pow.f64 (cbrt.f64 (.f64 x.im (*.f64 x.re 3))) 3)) (neg.f64 (pow.f64 x.im 3)))
	33.8b	(fma.f64 (sqrt.f64 x.re) (.f64 (sqrt.f64 x.re) (.f64 x.im (*.f64 x.re 3))) (neg.f64 (pow.f64 x.im 3)))
✓	0.6b	(fma.f64 (pow.f64 (cbrt.f64 x.re) 2) (.f64 (cbrt.f64 x.re) (.f64 x.im (*.f64 x.re 3))) (neg.f64 (pow.f64 x.im 3)))
	8.7b	(.f64 (neg.f64 x.im) (fma.f64 x.im x.im (.f64 (*.f64 x.re x.re) -3)))
✓	0.2b	(-.f64 (.f64 x.re (.f64 x.im (*.f64 x.re 3))) (pow.f64 x.im 3))
	8.7b	(+.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 3904 to 2519 computations (35.5% saved)

regimes152.0ms (4%)

Accuracy

Total 0.1b remaining (87.8%)

Threshold costs 0.1b (87.8%)

Counts

56 → 1

Compiler

Compiled 2631 to 1854 computations (29.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-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	9	16
1	14	16
2	19	16
3	21	16
4	22	16

Stop Event

1×

saturated

end110.0ms (2.9%)

Compiler: Compiled 163 to 109 computations (33.1% saved)

Details

analyze194.0ms (5.1%)

sample1.1s (28.3%)

simplify21.0ms (0.5%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series27.0ms (0.7%)

rewrite54.0ms (1.4%)

simplify50.0ms (1.3%)

prune167.0ms (4.4%)

localize7.0ms (0.2%)

series10.0ms (0.3%)

rewrite88.0ms (2.3%)

simplify43.0ms (1.1%)

prune286.0ms (7.6%)

localize10.0ms (0.3%)

series358.0ms (9.5%)

rewrite43.0ms (1.2%)

simplify70.0ms (1.8%)

prune109.0ms (2.9%)

localize13.0ms (0.4%)

series654.0ms (17.3%)

rewrite40.0ms (1%)

simplify38.0ms (1%)

prune156.0ms (4.1%)

regimes152.0ms (4%)

simplify2.0ms (0.1%)

end110.0ms (2.9%)

Profiling