Details

analyze190.0ms (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%	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 (31.6%)

Results

942.0ms	8256×	body	128	valid
71.0ms	605×	body	128	invalid

Compiler

Compiled 65 to 35 computations (46.2% saved)

simplify133.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

613×	`sub-neg_binary64`
578×	`fma-neg_binary64`
529×	`neg-mul-1_binary64`
501×	`neg-sub0_binary64`
455×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	26	23
2	60	23
3	130	16
4	335	16
5	881	16
6	1496	16
7	3511	16
8	4061	16
9	3977	16
10	4614	16
11	4771	16
12	4918	16
13	4914	16

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

7.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	7.9b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
▶	7.9b	(+.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 54 computations (46% 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.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
✓	0.1b	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
✓	7.4b	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.im)

series45.0ms (1.3%)

Counts

4 → 96

Calls

4 calls:

14.0ms	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.im)
13.0ms	(+.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))
11.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
6.0ms	(+.f64 (.f64 x.re x.im) (.f64 x.im x.re))

rewrite23.0ms (0.7%)

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 → 77

Calls

4 calls:

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

simplify70.0ms (2%)

Algorithm

1×	egg-herbie

Rules

727×	`distribute-rgt-in_binary64`
685×	`distribute-lft-in_binary64`
245×	`associate-l_binary64`
206×	`associate-r_binary64`
181×	`distribute-rgt-out_binary64`

Counts

173 → 139

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	2758
1	427	2398
2	1675	2360
3	4822	2360

prune96.0ms (2.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	135	4	139
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	136	5	141

Error

0.0b

Counts

141 → 5

Alt Table

Status	Error	Program
	7.9b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
▶	0.2b	(+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
	19.9b	(+.f64 (neg.f64 (pow.f64 x.im 3)) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
	7.9b	(fma.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))
	8.1b	(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x.im x.re))) (cbrt.f64 (.f64 2 (.f64 x.im x.re)))) (cbrt.f64 (.f64 2 (.f64 x.im x.re)))) x.re))

Compiler

Compiled 4205 to 911 computations (78.3% saved)

localize13.0ms (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.im)) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
	0.1b	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
✓	0.2b	(.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im))

series27.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

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

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`associate-*l/_binary64`
18×	`flip-+_binary64`
18×	`flip3-+_binary64`
16×	`frac-add_binary64`
12×	`frac-times_binary64`

Counts

2 → 59

Calls

2 calls:

10.0ms	(+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
7.0ms	(.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im))

simplify100.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

535×	`associate-l_binary64`
483×	`associate-r_binary64`
427×	`fma-neg_binary64`
304×	`distribute-rgt-out_binary64`
299×	`distribute-rgt-in_binary64`

Counts

107 → 103

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	173	3975
1	667	3223
2	3176	2270
3	4304	2268
4	4675	2268

prune148.0ms (4.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	160	6	166
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	164	7	171

Error

0.0b

Counts

171 → 7

Alt Table

Status	Error	Program
	24.0b	(.f64 (sqrt.f64 (+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))) (sqrt.f64 (+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re))))
▶	0.2b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
	7.9b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
	7.8b	(+.f64 (.f64 1 (-.f64 (.f64 x.im (.f64 x.re x.re)) (pow.f64 x.im 3))) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
	0.5b	(+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.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.re (cbrt.f64 (.f64 2 (*.f64 x.im x.re))))))
	0.7b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
	9.6b	(+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.f64 (cbrt.f64 (pow.f64 (.f64 2 (*.f64 x.im x.re)) 3)) x.re))

Compiler

Compiled 6105 to 1342 computations (78% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series23.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

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

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
5×	`associate-l_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 34

Calls

2 calls:

4.0ms	(*.f64 (-.f64 x.re x.im) x.im)
0.0ms	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))

simplify83.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

834×	`fma-def_binary64`
381×	`*-commutative_binary64`
379×	`exp-prod_binary64`
293×	`fma-neg_binary64`
252×	`associate-l_binary64`

Counts

82 → 65

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	1147
1	144	995
2	409	995
3	1394	925
4	3300	925
5	4985	925
6	4958	925

prune134.0ms (3.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	123	5	128
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	127	8	135

Error

Counts

135 → 8

Alt Table

Status	Error	Program
	7.9b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
	0.7b	(fma.f64 (+.f64 x.re x.im) (.f64 (.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im))) (.f64 (cbrt.f64 (-.f64 x.re x.im)) x.im)) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
	7.8b	(+.f64 (-.f64 (.f64 x.im (.f64 x.re x.re)) (pow.f64 x.im 3)) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
	0.8b	(fma.f64 (+.f64 x.re x.im) (.f64 (.f64 (-.f64 x.re x.im) (.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im)) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
✓	0.2b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
	9.6b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im) (.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 x.im x.re)) 3)) x.re))
	0.5b	(+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.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.re (cbrt.f64 (.f64 2 (*.f64 x.im x.re))))))
▶	0.5b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im) (.f64 (.f64 (.f64 2 (.f64 x.im x.re)) (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re)))

Compiler

Compiled 3359 to 805 computations (76% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 2 (.f64 x.im x.re)) (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)))
✓	0.2b	(.f64 (.f64 (.f64 2 (.f64 x.im x.re)) (*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re))
✓	0.4b	(*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))
✓	0.6b	(cbrt.f64 x.re)

series445.0ms (12.7%)

Counts

4 → 72

Calls

4 calls:

350.0ms	(.f64 (.f64 2 (.f64 x.im x.re)) (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)))
36.0ms	(cbrt.f64 x.re)
35.0ms	(*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))
24.0ms	(.f64 (.f64 (.f64 2 (.f64 x.im x.re)) (*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re))

rewrite35.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`pow1_binary64`
56×	`add-exp-log_binary64`
39×	`pow-prod-down_binary64`
38×	`cbrt-unprod_binary64`
38×	`prod-exp_binary64`

Counts

4 → 123

Calls

4 calls:

12.0ms	(.f64 (.f64 (.f64 2 (.f64 x.im x.re)) (*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re))
9.0ms	(.f64 (.f64 2 (.f64 x.im x.re)) (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)))
4.0ms	(*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))
1.0ms	(cbrt.f64 x.re)

simplify146.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

464×	`sqr-pow_binary64`
363×	`associate-l_binary64`
349×	`log-prod_binary64`
337×	`exp-prod_binary64`
332×	`associate-r_binary64`

Counts

195 → 158

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	149	2554
1	321	2048
2	1346	1905
3	2117	1877
4	3628	1781
5	4625	1781
6	4982	1781
7	4877	1781

prune192.0ms (5.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	194	8	202

Error

Counts

202 → 8

Alt Table

Status	Error	Program
	7.9b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
	0.7b	(fma.f64 (+.f64 x.re x.im) (.f64 (.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im))) (.f64 (cbrt.f64 (-.f64 x.re x.im)) x.im)) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
	7.8b	(+.f64 (-.f64 (.f64 x.im (.f64 x.re x.re)) (pow.f64 x.im 3)) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
	0.8b	(fma.f64 (+.f64 x.re x.im) (.f64 (.f64 (-.f64 x.re x.im) (.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im)) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
✓	0.2b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
	9.6b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im) (.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 x.im x.re)) 3)) x.re))
	0.5b	(+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.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.re (cbrt.f64 (.f64 2 (*.f64 x.im x.re))))))
✓	0.5b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im) (.f64 (.f64 (.f64 2 (.f64 x.im x.re)) (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re)))

Compiler

Compiled 5575 to 1681 computations (69.8% saved)

regimes310.0ms (8.8%)

Accuracy

Total 0.2b remaining (90.5%)

Threshold costs 0.2b (90.5%)

Counts

102 → 1

Compiler

Compiled 7449 to 3897 computations (47.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-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	11	23
1	18	23
2	23	23
3	25	23
4	26	23
5	26	23

end118.0ms (3.3%)

Compiler: Compiled 232 to 119 computations (48.7% saved)

Details

analyze190.0ms (5.4%)

sample1.1s (31.6%)

simplify133.0ms (3.8%)

prune3.0ms (0.1%)

localize10.0ms (0.3%)

series45.0ms (1.3%)

rewrite23.0ms (0.7%)

simplify70.0ms (2%)

prune96.0ms (2.7%)

localize13.0ms (0.4%)

series27.0ms (0.8%)

rewrite26.0ms (0.7%)

simplify100.0ms (2.8%)

prune148.0ms (4.2%)

localize12.0ms (0.3%)

series23.0ms (0.7%)

rewrite6.0ms (0.2%)

simplify83.0ms (2.4%)

prune134.0ms (3.8%)

localize12.0ms (0.4%)

series445.0ms (12.7%)

rewrite35.0ms (1%)

simplify146.0ms (4.1%)

prune192.0ms (5.5%)

regimes310.0ms (8.8%)

simplify3.0ms (0.1%)

end118.0ms (3.3%)

Profiling