Details

analyze16.0ms (0.7%)

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
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
93.7%	6.2%	0.1%	7
96.8%	3.1%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 22 to 13 computations (40.9% saved)

sample1.3s (54.7%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 65 to 38 computations (41.5% saved)

simplify106.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
549×	`sub-neg_binary64`
460×	`distribute-neg-frac_binary64`
455×	`cancel-sign-sub-inv_binary64`
430×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	23	24
2	52	24
3	105	24
4	199	24
5	330	24
6	442	24
7	603	24
8	901	24
9	2304	24
10	3386	24
11	3956	24
12	4454	24
13	4735	24
14	5238	24

prune3.0ms (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

34.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	34.0b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

Compiler

Compiled 76 to 42 computations (44.7% saved)

localize9.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.8b	(fma.f64 -4 (.f64 y y) (.f64 x x))
✓	33.3b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

series89.0ms (3.8%)

Counts

2 → 48

Calls

2 calls:

79.0ms	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))
8.0ms	(fma.f64 -4 (.f64 y y) (.f64 x x))

rewrite60.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

560×	`log-prod_binary64`
377×	`prod-diff_binary64`
205×	`expm1-udef_binary64`
205×	`log1p-udef_binary64`
186×	`log-pow_binary64`

Counts

2 → 67

Calls

2 calls:

58.0ms	(fma.f64 -4 (.f64 y y) (.f64 x x))
58.0ms	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	246	34
2	2736	34
3	5359	34

simplify80.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

557×	`fma-neg_binary64`
502×	`associate-*l/_binary64`
472×	`associate-*r/_binary64`
368×	`fma-def_binary64`
322×	`associate-/r/_binary64`

Counts

115 → 87

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	46	807
1	121	753
2	326	741
3	1272	723
4	4300	669
5	4942	669
6	4998	669
7	4958	669

prune65.0ms (2.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	82	5	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	5	88

Error

0.5b

Counts

88 → 5

Alt Table

Status	Error	Program
	49.0b	(pow.f64 (/.f64 (hypot.f64 x (sqrt.f64 (.f64 -4 (.f64 y y)))) (hypot.f64 x (*.f64 y 2))) 2)
	34.0b	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))
	37.0b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
	33.2b	-1
▶	30.5b	1

Compiler

Compiled 2030 to 1151 computations (43.3% saved)

localize0.0ms (0%)

prune4.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	0	0
Total	5	5

Error

0.5b

Counts

5 → 5

Alt Table

Status	Error	Program
	49.0b	(pow.f64 (/.f64 (hypot.f64 x (sqrt.f64 (.f64 -4 (.f64 y y)))) (hypot.f64 x (*.f64 y 2))) 2)
	34.0b	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))
	37.0b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
▶	33.2b	-1
✓	30.5b	1

Compiler

Compiled 107 to 73 computations (31.8% saved)

localize0.0ms (0%)

prune4.0ms (0.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	1	1
Total	5	5

Error

0.5b

Counts

5 → 5

Alt Table

Status	Error	Program
	49.0b	(pow.f64 (/.f64 (hypot.f64 x (sqrt.f64 (.f64 -4 (.f64 y y)))) (hypot.f64 x (*.f64 y 2))) 2)
▶	34.0b	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))
	37.0b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
✓	33.2b	-1
✓	30.5b	1

Compiler

Compiled 104 to 70 computations (32.7% saved)

localize12.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.0b	(fma.f64 y (.f64 y -4) (.f64 x x))
✓	33.3b	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

series31.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

17.0ms	(fma.f64 y (.f64 y -4) (.f64 x x))
14.0ms	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

rewrite62.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

868×	`log1p-expm1-u_binary64`
868×	`expm1-log1p-u_binary64`
565×	`prod-diff_binary64`
118×	`add-sqr-sqrt_binary64`
112×	`add-log-exp_binary64`

Counts

2 → 57

Calls

2 calls:

61.0ms	(fma.f64 y (.f64 y -4) (.f64 x x))
61.0ms	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	247	29
2	2345	29
3	6256	29

simplify80.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

557×	`fma-neg_binary64`
502×	`associate-*l/_binary64`
472×	`associate-*r/_binary64`
368×	`fma-def_binary64`
322×	`associate-/r/_binary64`

Counts

105 → 77

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	46	807
1	121	753
2	326	741
3	1272	723
4	4300	669
5	4942	669
6	4998	669
7	4958	669

prune54.0ms (2.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	77	5	82

Error

0.5b

Counts

82 → 5

Alt Table

Status	Error	Program
	49.0b	(pow.f64 (/.f64 (hypot.f64 x (sqrt.f64 (.f64 -4 (.f64 y y)))) (hypot.f64 x (*.f64 y 2))) 2)
✓	34.0b	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))
	37.0b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
✓	33.2b	-1
✓	30.5b	1

Compiler

Compiled 1585 to 1093 computations (31% saved)

regimes194.0ms (8.3%)

Accuracy

Total 13.5b remaining (97.2%)

Threshold costs 0b (0%)

Counts

9 → 6

Compiler

Compiled 932 to 610 computations (34.5% saved)

bsearch98.0ms (4.2%)

Steps

Iters	Range		Point
9	2.2099826107732652e+123	9.410521888160938e+128	6.846130813274231e+127
9	5.208539296316691e-62	5.63823929317062e-56	2.961072780439151e-61
8	-3.241224646668368e-68	-4.4975924051654415e-72	-4.611780839164092e-70
5	-2.2845188462257706e+61	-1.056963011895567e+61	-2.2617666078219922e+61
8	-4.393143762401554e+98	-1.6540362943667853e+96	-1.7380791032682012e+96

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	95
1	39	95
2	38	95

end92.0ms (3.9%)

Compiler: Compiled 193 to 122 computations (36.8% saved)

Details

analyze16.0ms (0.7%)

sample1.3s (54.7%)

simplify106.0ms (4.5%)

prune3.0ms (0.1%)

localize9.0ms (0.4%)

series89.0ms (3.8%)

rewrite60.0ms (2.5%)

simplify80.0ms (3.4%)

prune65.0ms (2.8%)

localize0.0ms (0%)

prune4.0ms (0.2%)

localize0.0ms (0%)

prune4.0ms (0.2%)

localize12.0ms (0.5%)

series31.0ms (1.3%)

rewrite62.0ms (2.6%)

simplify80.0ms (3.4%)

prune54.0ms (2.3%)

regimes194.0ms (8.3%)

bsearch98.0ms (4.2%)

simplify3.0ms (0.1%)

end92.0ms (3.9%)

Profiling