Details

analyze477.0ms (10.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample1.8s (40.8%)

Results

795.0ms	6317×	body	128	valid
357.0ms	660×	body	2048	valid
307.0ms	503×	body	4096	valid
184.0ms	408×	body	1024	valid
80.0ms	245×	body	512	valid
26.0ms	123×	body	256	valid

Compiler

Compiled 57 to 40 computations (29.8% saved)

simplify22.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

201×	`fma-def_binary64`
142×	`fma-neg_binary64`
51×	`distribute-rgt-in_binary64`
43×	`cancel-sign-sub-inv_binary64`
27×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	53	15
4	80	15
5	109	15
6	180	15
7	286	15
8	410	15
9	493	15
10	610	15
11	682	15
12	705	15
13	744	15
14	793	15
15	856	15
16	892	15
17	901	15

Stop Event

1×

saturated

Counts

1 → 2

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

12.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 51 to 37 computations (27.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
✓	0.5b	(-.f64 (hypot.f64 re im) re)

series39.0ms (0.9%)

Counts

2 → 32

Calls

2 calls:

29.0ms	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
10.0ms	(-.f64 (hypot.f64 re im) re)

rewrite45.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

811×	`log1p-expm1-u_binary64`
811×	`expm1-log1p-u_binary64`
410×	`prod-diff_binary64`
86×	`add-sqr-sqrt_binary64`
82×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	173	19
2	2186	19

Stop Event

1×	node limit

Counts

2 → 74

Calls

2 calls:

44.0ms	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
44.0ms	(-.f64 (hypot.f64 re im) re)

simplify30.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

527×	`fma-def_binary64`
371×	`associate-l_binary64`
337×	`associate-/l*_binary64`
311×	`times-frac_binary64`
236×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	140	1017
1	421	994
2	1460	945

Stop Event

1×	node limit

Counts

106 → 119

prune79.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	113	6	119
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	113	7	120

Error

0.1b

Counts

120 → 7

Alt Table

Status	Error	Program
	52.1b	(.f64 1/2 (fma.f64 (sqrt.f64 1/2) (.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (.f64 (.f64 (/.f64 (pow.f64 im 3) (sqrt.f64 1/2)) (sqrt.f64 2)) -1/16))))
	47.9b	(.f64 1/2 (.f64 (.f64 im (sqrt.f64 2)) (.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re)))))
	47.9b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
▶	31.1b	(.f64 1/2 (.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (.f64 (sqrt.f64 (/.f64 1 im)) (.f64 re 1/2)))))
✓	12.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	56.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/2 (.f64 (/.f64 im re) im) (.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8)))))
	56.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 1/2 re) (.f64 im im)))))

Compiler

Compiled 2797 to 1912 computations (31.6% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (sqrt.f64 im) (.f64 (sqrt.f64 (/.f64 1 im)) (.f64 re 1/2)))
✓	0.2b	(sqrt.f64 (/.f64 1 im))
✓	0.3b	(.f64 (sqrt.f64 (/.f64 1 im)) (.f64 re 1/2))
✓	0.4b	(.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (.f64 (sqrt.f64 (/.f64 1 im)) (*.f64 re 1/2))))

series54.0ms (1.2%)

Counts

4 → 36

Calls

4 calls:

22.0ms	(.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (.f64 (sqrt.f64 (/.f64 1 im)) (*.f64 re 1/2))))
14.0ms	(-.f64 (sqrt.f64 im) (.f64 (sqrt.f64 (/.f64 1 im)) (.f64 re 1/2)))
13.0ms	(.f64 (sqrt.f64 (/.f64 1 im)) (.f64 re 1/2))
5.0ms	(sqrt.f64 (/.f64 1 im))

rewrite86.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

915×	`prod-diff_binary64`
234×	`egg-rr`
136×	`add-sqr-sqrt_binary64`
131×	`log1p-expm1-u_binary64`
131×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	57
1	294	46
2	3560	46

Stop Event

1×	node limit

Counts

4 → 234

Calls

4 calls:

80.0ms	(-.f64 (sqrt.f64 im) (.f64 (sqrt.f64 (/.f64 1 im)) (.f64 re 1/2)))
80.0ms	(sqrt.f64 (/.f64 1 im))
80.0ms	(.f64 (sqrt.f64 (/.f64 1 im)) (.f64 re 1/2))
80.0ms	(.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (.f64 (sqrt.f64 (/.f64 1 im)) (*.f64 re 1/2))))

simplify59.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

401×	`fma-def_binary64`
385×	`fma-neg_binary64`
154×	`cancel-sign-sub-inv_binary64`
138×	`associate-l_binary64`
127×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	609
1	48	591
2	115	528
3	319	528
4	558	528
5	761	528
6	1051	528
7	1320	528
8	1822	528
9	2015	528
10	2123	528
11	2123	528

Stop Event

1×

saturated

Counts

270 → 246

prune196.0ms (4.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	246	0	246
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	246	7	253

Error

0.1b

Counts

253 → 7

Alt Table

Status	Error	Program
	52.1b	(.f64 1/2 (fma.f64 (sqrt.f64 1/2) (.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (.f64 (.f64 (/.f64 (pow.f64 im 3) (sqrt.f64 1/2)) (sqrt.f64 2)) -1/16))))
▶	47.9b	(.f64 1/2 (.f64 (.f64 im (sqrt.f64 2)) (.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re)))))
	47.9b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
✓	31.1b	(.f64 1/2 (.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (.f64 (sqrt.f64 (/.f64 1 im)) (.f64 re 1/2)))))
✓	12.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	56.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/2 (.f64 (/.f64 im re) im) (.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8)))))
	56.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 1/2 re) (.f64 im im)))))

Compiler

Compiled 8388 to 5555 computations (33.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 re))
✓	0.2b	(.f64 (.f64 im (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re))))
✓	0.2b	(*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re)))
✓	0.4b	(*.f64 im (sqrt.f64 2))

series35.0ms (0.8%)

Counts

4 → 24

Calls

4 calls:

21.0ms	(.f64 (.f64 im (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re))))
7.0ms	(*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re)))
4.0ms	(sqrt.f64 (/.f64 1 re))
3.0ms	(*.f64 im (sqrt.f64 2))

rewrite45.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

574×	`log-prod_binary64`
203×	`expm1-udef_binary64`
203×	`log1p-udef_binary64`
191×	`log-pow_binary64`
189×	`pow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	38
1	263	28
2	2918	28

Stop Event

1×	node limit

Counts

4 → 91

Calls

4 calls:

44.0ms	(sqrt.f64 (/.f64 1 re))
44.0ms	(.f64 (.f64 im (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re))))
44.0ms	(*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re)))
44.0ms	(*.f64 im (sqrt.f64 2))

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

26×	`associate-l_binary64`
16×	`associate-r_binary64`
14×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	300
1	22	300
2	43	300
3	82	300
4	86	300

Stop Event

1×

saturated

Counts

115 → 94

prune88.0ms (2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	87	7	94
Fresh	4	0	4
Picked	1	0	1
Done	0	2	2
Total	92	9	101

Error

Counts

101 → 9

Alt Table

Status	Error	Program
▶	47.8b	(.f64 1/2 (+.f64 0 (.f64 im (sqrt.f64 (*.f64 2 (/.f64 1/2 re))))))
✓	12.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	47.9b	(.f64 1/2 (.f64 (.f64 im (sqrt.f64 2)) (.f64 (sqrt.f64 1/2) (pow.f64 (sqrt.f64 (pow.f64 re -1/2)) 2))))
	51.3b	(.f64 1/2 (.f64 (*.f64 im (sqrt.f64 2)) (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 1/2 re)) 3))))
	47.9b	(.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 im (sqrt.f64 1/2)) (sqrt.f64 (/.f64 1 re)))))
	47.8b	(.f64 1/2 (pow.f64 (sqrt.f64 (.f64 im (sqrt.f64 (*.f64 2 (/.f64 1/2 re))))) 2))
	48.0b	(.f64 1/2 (pow.f64 (cbrt.f64 (.f64 im (sqrt.f64 (*.f64 2 (/.f64 1/2 re))))) 3))
✓	31.1b	(.f64 1/2 (.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (.f64 (sqrt.f64 (/.f64 1 im)) (.f64 re 1/2)))))
	47.9b	(.f64 1/2 (.f64 (.f64 im (sqrt.f64 2)) (.f64 (sqrt.f64 1/2) (pow.f64 re -1/2))))

Compiler

Compiled 1777 to 1511 computations (15% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 1/2 (+.f64 0 (.f64 im (sqrt.f64 (*.f64 2 (/.f64 1/2 re))))))
✓	0.0b	(*.f64 2 (/.f64 1/2 re))
✓	0.1b	(sqrt.f64 (*.f64 2 (/.f64 1/2 re)))
✓	0.1b	(.f64 im (sqrt.f64 (.f64 2 (/.f64 1/2 re))))

series39.0ms (0.9%)

Counts

4 → 36

Calls

4 calls:

15.0ms	(.f64 1/2 (+.f64 0 (.f64 im (sqrt.f64 (*.f64 2 (/.f64 1/2 re))))))
12.0ms	(.f64 im (sqrt.f64 (.f64 2 (/.f64 1/2 re))))
11.0ms	(sqrt.f64 (*.f64 2 (/.f64 1/2 re)))
1.0ms	(*.f64 2 (/.f64 1/2 re))

rewrite57.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

494×	`log-prod_binary64`
182×	`expm1-udef_binary64`
182×	`log1p-udef_binary64`
165×	`pow3_binary64`
160×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	31
1	263	31
2	2872	31

Stop Event

1×	node limit

Counts

4 → 141

Calls

4 calls:

51.0ms	(.f64 1/2 (+.f64 0 (.f64 im (sqrt.f64 (*.f64 2 (/.f64 1/2 re))))))
51.0ms	(*.f64 2 (/.f64 1/2 re))
51.0ms	(sqrt.f64 (*.f64 2 (/.f64 1/2 re)))
51.0ms	(.f64 im (sqrt.f64 (.f64 2 (/.f64 1/2 re))))

simplify13.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	300
1	15	300
2	22	300
3	24	300

Stop Event

1×

saturated

Counts

177 → 144

prune93.0ms (2.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	141	3	144
Fresh	5	1	6
Picked	1	0	1
Done	0	2	2
Total	147	6	153

Error

Counts

153 → 6

Alt Table

Status	Error	Program
	47.8b	(.f64 (sqrt.f64 (/.f64 1 re)) (.f64 im 1/2))
	48.0b	(.f64 1/2 (pow.f64 (cbrt.f64 (.f64 im (sqrt.f64 (*.f64 2 (/.f64 1/2 re))))) 3))
✓	31.1b	(.f64 1/2 (.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 im) (.f64 (sqrt.f64 (/.f64 1 im)) (.f64 re 1/2)))))
✓	12.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	47.8b	(.f64 1/2 (+.f64 0 (fma.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1/2 re)) 0)))
	47.8b	(.f64 1/2 (+.f64 0 (fma.f64 (sqrt.f64 im) (.f64 (sqrt.f64 im) (/.f64 1 (sqrt.f64 re))) 0)))

Compiler

Compiled 2238 to 1644 computations (26.5% saved)

regimes993.0ms (22.5%)

Accuracy

Total 5.7b remaining (98.2%)

Threshold costs 0b (0%)

Counts

100 → 2

Compiler

Compiled 10652 to 8954 computations (15.9% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 12 to 7 computations (41.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	47
1	33	47
2	38	47
3	40	47
4	41	47

Stop Event

1×

saturated

end97.0ms (2.2%)

Compiler: Compiled 154 to 118 computations (23.4% saved)

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	53	15
4	80	15
5	109	15
6	180	15
7	286	15
8	410	15
9	493	15
10	610	15
11	682	15
12	705	15
13	744	15
14	793	15
15	856	15
16	892	15
17	901	15

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	53	15
4	80	15
5	109	15
6	180	15
7	286	15
8	410	15
9	493	15
10	610	15
11	682	15
12	705	15
13	744	15
14	793	15
15	856	15
16	892	15
17	901	15

Details

analyze477.0ms (10.8%)

sample1.8s (40.8%)

simplify22.0ms (0.5%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series39.0ms (0.9%)

rewrite45.0ms (1%)

simplify30.0ms (0.7%)

prune79.0ms (1.8%)

localize12.0ms (0.3%)

series54.0ms (1.2%)

rewrite86.0ms (1.9%)

simplify59.0ms (1.3%)

prune196.0ms (4.5%)

localize9.0ms (0.2%)

series35.0ms (0.8%)

rewrite45.0ms (1%)

simplify14.0ms (0.3%)

prune88.0ms (2%)

localize8.0ms (0.2%)

series39.0ms (0.9%)

rewrite57.0ms (1.3%)

simplify13.0ms (0.3%)

prune93.0ms (2.1%)

regimes993.0ms (22.5%)

bsearch3.0ms (0.1%)

simplify3.0ms (0.1%)

end97.0ms (2.2%)

Profiling

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	53	15
4	80	15
5	109	15
6	180	15
7	286	15
8	410	15
9	493	15
10	610	15
11	682	15
12	705	15
13	744	15
14	793	15
15	856	15
16	892	15
17	901	15