Details

analyze192.0ms (6.6%)

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 (36.8%)

Results

950.0ms	8256×	body	128	valid
70.0ms	630×	body	128	invalid

Compiler

Compiled 65 to 35 computations (46.2% saved)

simplify22.0ms (0.8%)

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

prune4.0ms (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))

series28.0ms (1%)

Counts

3 → 72

Calls

3 calls:

12.0ms	(-.f64 (.f64 x.re (.f64 x.im (*.f64 x.re 3))) (pow.f64 x.im 3))
9.0ms	(.f64 x.re (.f64 x.im (*.f64 x.re 3)))
7.0ms	(.f64 x.im (.f64 x.re 3))

rewrite53.0ms (1.8%)

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:

50.0ms	(-.f64 (.f64 x.re (.f64 x.im (*.f64 x.re 3))) (pow.f64 x.im 3))
50.0ms	(.f64 x.re (.f64 x.im (*.f64 x.re 3)))
50.0ms	(.f64 x.im (.f64 x.re 3))

simplify47.0ms (1.6%)

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 (5.8%)

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
	33.8b	(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)))
	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))
	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))
	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)))
	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)))

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)))

series13.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

12.0ms

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

rewrite83.0ms (2.9%)

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:

73.0ms

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

simplify43.0ms (1.5%)

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

prune290.0ms (10%)

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
	33.8b	(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)))
	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))
	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))
▶	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)))
	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)))

Compiler

Compiled 10460 to 5182 computations (50.5% saved)

localize11.0ms (0.4%)

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)

series89.0ms (3.1%)

Counts

3 → 12

Calls

3 calls:

58.0ms	(.f64 (cbrt.f64 x.re) (.f64 x.im (*.f64 x.re 3)))
22.0ms	(pow.f64 (cbrt.f64 x.re) 2)
10.0ms	(cbrt.f64 x.re)

rewrite41.0ms (1.4%)

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:

40.0ms	(.f64 (cbrt.f64 x.re) (.f64 x.im (*.f64 x.re 3)))
40.0ms	(pow.f64 (cbrt.f64 x.re) 2)
40.0ms	(cbrt.f64 x.re)

simplify62.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

621×	`sqr-pow_binary64`
412×	`unswap-sqr_binary64`
373×	`pow-sqr_binary64`
345×	`cube-prod_binary64`
306×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	144
1	23	144
2	47	144
3	102	144
4	259	144
5	817	144
6	1172	144
7	1830	144
8	1958	144
9	2138	144
10	2368	144
11	2712	144
12	3169	144
13	3756	144
14	4490	144

Stop Event

1×	node limit

Counts

68 → 58

prune100.0ms (3.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	103	8	111

Error

Counts

111 → 8

Alt Table

Status	Error	Program
	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)))
	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))
▶	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)))
	33.9b	(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)))
	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))
✓	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)))
✓	0.2b	(fma.f64 (.f64 x.re 3) (.f64 x.im x.re) (neg.f64 (pow.f64 x.im 3)))

Compiler

Compiled 2353 to 1474 computations (37.4% saved)

localize12.0ms (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)))

series88.0ms (3%)

Counts

2 → 0

Calls

2 calls:

62.0ms	(pow.f64 (cbrt.f64 (.f64 x.im (.f64 x.re 3))) 3)
26.0ms	(cbrt.f64 (.f64 x.im (.f64 x.re 3)))

rewrite37.0ms (1.3%)

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:

36.0ms	(pow.f64 (cbrt.f64 (.f64 x.im (.f64 x.re 3))) 3)
36.0ms	(cbrt.f64 (.f64 x.im (.f64 x.re 3)))

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

71 → 71

prune140.0ms (4.8%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	135	8	143

Error

Counts

143 → 8

Alt Table

Status	Error	Program
	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)))
	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))
✓	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)))
	33.9b	(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)))
	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))
✓	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)))
✓	0.2b	(fma.f64 (.f64 x.re 3) (.f64 x.im x.re) (neg.f64 (pow.f64 x.im 3)))

Compiler

Compiled 3389 to 2161 computations (36.2% saved)

regimes164.0ms (5.7%)

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)

simplify3.0ms (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

end121.0ms (4.2%)

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

Details

analyze192.0ms (6.6%)

sample1.1s (36.8%)

simplify22.0ms (0.8%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series28.0ms (1%)

rewrite53.0ms (1.8%)

simplify47.0ms (1.6%)

prune167.0ms (5.8%)

localize7.0ms (0.2%)

series13.0ms (0.4%)

rewrite83.0ms (2.9%)

simplify43.0ms (1.5%)

prune290.0ms (10%)

localize11.0ms (0.4%)

series89.0ms (3.1%)

rewrite41.0ms (1.4%)

simplify62.0ms (2.1%)

prune100.0ms (3.5%)

localize12.0ms (0.4%)

series88.0ms (3%)

rewrite37.0ms (1.3%)

simplify6.0ms (0.2%)

prune140.0ms (4.8%)

regimes164.0ms (5.7%)

simplify3.0ms (0.1%)

end121.0ms (4.2%)

Profiling