Details

analyze754.0ms (32.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
12.5%	87.3%	0.2%	10
25%	74.9%	0.2%	11
31.2%	63.9%	4.9%	12
39%	50.9%	10.1%	13
44.8%	44.4%	10.7%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.0s (45.1%)

Results

876.0ms	8256×	body	128	valid
140.0ms	1456×	body	128	invalid

Compiler

Compiled 24 to 16 computations (33.3% saved)

preprocess40.0ms (1.8%)

Algorithm

2×	egg-herbie

Rules

427×	`fma-def_binary64`
190×	`fma-neg_binary64`
94×	`cancel-sign-sub-inv_binary64`
57×	`unsub-neg_binary64`
52×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	70
1	65	70
2	124	70
3	193	70
4	291	70
5	551	70
6	866	70
7	1235	70
8	1290	70
9	1298	70
10	1299	70
0	4	4
1	4	4

Stop Event

1×	unsound
1×	saturated

Symmetry

(sort x.re y.re)

(sort x.im y.im)

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify26.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

171×	`fma-def_binary64`
87×	`fma-neg_binary64`
37×	`cancel-sign-sub-inv_binary64`
23×	`distribute-rgt-neg-in_binary64`
20×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	16	10
2	31	10
3	48	10
4	75	10
5	123	10
6	204	10
7	305	10
8	407	10
9	523	10
10	581	10
11	587	10

Stop Event

1×

saturated

Counts

1 → 1

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series9.0ms (0.4%)

Counts

1 → 48

Calls

12 calls:

1.0ms	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))	x.re	0
1.0ms	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))	x.re	inf
1.0ms	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))	x.re	-inf
1.0ms	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))	y.im	inf
1.0ms	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))	y.re	inf

rewrite44.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

890×	`log1p-expm1-u_binary64`
890×	`expm1-log1p-u_binary64`
94×	`add-sqr-sqrt_binary64`
93×	`*-un-lft-identity_binary64`
93×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	179	10
2	2433	10

Stop Event

1×	node limit

Counts

1 → 50

simplify30.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

172×	`fma-def_binary64`
87×	`fma-neg_binary64`
37×	`cancel-sign-sub-inv_binary64`
23×	`distribute-rgt-neg-in_binary64`
20×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	420
1	21	420
2	39	420
3	55	420
4	79	420
5	127	420
6	208	420
7	309	420
8	411	420
9	527	420
10	585	420
11	591	420

Stop Event

1×

saturated

Counts

98 → 55

prune28.0ms (1.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	53	2	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	2	56

Error

Counts

56 → 2

Alt Table

Status	Error	Program
	0.0b	(fma.f64 x.im (neg.f64 y.im) (*.f64 x.re y.re))
▶	0.0b	(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))

Compiler

Compiled 948 to 244 computations (74.3% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))

series9.0ms (0.4%)

Counts

1 → 48

Calls

12 calls:

1.0ms	(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))	x.re	-inf
1.0ms	(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))	y.re	-inf
1.0ms	(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))	y.re	inf
1.0ms	(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))	x.re	0
1.0ms	(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))	x.re	inf

rewrite35.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

727×	`pow1_binary64`
664×	`log1p-expm1-u_binary64`
664×	`expm1-log1p-u_binary64`
85×	`add-sqr-sqrt_binary64`
83×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	164	8
2	2058	8

Stop Event

1×	node limit

Counts

1 → 25

simplify31.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

172×	`fma-def_binary64`
87×	`fma-neg_binary64`
37×	`cancel-sign-sub-inv_binary64`
23×	`distribute-rgt-neg-in_binary64`
20×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	420
1	21	420
2	39	420
3	55	420
4	79	420
5	127	420
6	208	420
7	309	420
8	411	420
9	527	420
10	585	420
11	591	420

Stop Event

1×

saturated

Counts

73 → 30

prune11.0ms (0.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	30	0	30
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	30	2	32

Error

Counts

32 → 2

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 x.im (neg.f64 y.im) (*.f64 x.re y.re))
✓	0.0b	(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))

Compiler

Compiled 336 to 106 computations (68.5% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x.im (neg.f64 y.im) (*.f64 x.re y.re))

series11.0ms (0.5%)

Counts

1 → 48

Calls

12 calls:

2.0ms	(fma.f64 x.im (neg.f64 y.im) (*.f64 x.re y.re))	y.re	-inf
1.0ms	(fma.f64 x.im (neg.f64 y.im) (*.f64 x.re y.re))	x.re	-inf
1.0ms	(fma.f64 x.im (neg.f64 y.im) (*.f64 x.re y.re))	x.im	inf
1.0ms	(fma.f64 x.im (neg.f64 y.im) (*.f64 x.re y.re))	x.im	-inf
1.0ms	(fma.f64 x.im (neg.f64 y.im) (*.f64 x.re y.re))	x.im	0

rewrite33.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

692×	`pow1_binary64`
632×	`add-log-exp_binary64`
631×	`log1p-expm1-u_binary64`
631×	`expm1-log1p-u_binary64`
83×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	160	8
2	1959	8

Stop Event

1×	node limit

Counts

1 → 22

simplify29.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

172×	`fma-def_binary64`
87×	`fma-neg_binary64`
37×	`cancel-sign-sub-inv_binary64`
23×	`distribute-rgt-neg-in_binary64`
20×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	420
1	21	420
2	39	420
3	55	420
4	79	420
5	127	420
6	208	420
7	309	420
8	411	420
9	527	420
10	585	420
11	591	420

Stop Event

1×

saturated

Counts

70 → 26

prune10.0ms (0.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	26	2	28

Error

Counts

28 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 x.im (neg.f64 y.im) (*.f64 x.re y.re))
✓	0.0b	(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))

Compiler

Compiled 293 to 92 computations (68.6% saved)

regimes85.0ms (3.7%)

Accuracy

Total 0.0b remaining (94.6%)

Threshold costs 0.0b (94.6%)

Counts

9 → 1

Compiler

Compiled 996 to 659 computations (33.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	17	10
2	26	10
3	31	10
4	33	10

Stop Event

1×

saturated

end55.0ms (2.4%)

Stop Event

1×

done

Remove

(sort x.im y.im)

(sort x.re y.re)

Compiler

Compiled 88 to 56 computations (36.4% saved)

Iter	Nodes	Cost
0	8	10
1	16	10
2	31	10
3	48	10
4	75	10
5	123	10
6	204	10
7	305	10
8	407	10
9	523	10
10	581	10
11	587	10

Iter	Nodes	Cost
0	10	420
1	21	420
2	39	420
3	55	420
4	79	420
5	127	420
6	208	420
7	309	420
8	411	420
9	527	420
10	585	420
11	591	420

Iter	Nodes	Cost
0	10	420
1	21	420
2	39	420
3	55	420
4	79	420
5	127	420
6	208	420
7	309	420
8	411	420
9	527	420
10	585	420
11	591	420

Iter	Nodes	Cost
0	10	420
1	21	420
2	39	420
3	55	420
4	79	420
5	127	420
6	208	420
7	309	420
8	411	420
9	527	420
10	585	420
11	591	420

Iter	Nodes	Cost
0	8	10
1	16	10
2	31	10
3	48	10
4	75	10
5	123	10
6	204	10
7	305	10
8	407	10
9	523	10
10	581	10
11	587	10

Iter	Nodes	Cost
0	10	420
1	21	420
2	39	420
3	55	420
4	79	420
5	127	420
6	208	420
7	309	420
8	411	420
9	527	420
10	585	420
11	591	420

Iter	Nodes	Cost
0	10	420
1	21	420
2	39	420
3	55	420
4	79	420
5	127	420
6	208	420
7	309	420
8	411	420
9	527	420
10	585	420
11	591	420

Iter	Nodes	Cost
0	10	420
1	21	420
2	39	420
3	55	420
4	79	420
5	127	420
6	208	420
7	309	420
8	411	420
9	527	420
10	585	420
11	591	420

Details

analyze754.0ms (32.9%)

sample1.0s (45.1%)

preprocess40.0ms (1.8%)

simplify26.0ms (1.1%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series9.0ms (0.4%)

rewrite44.0ms (1.9%)

simplify30.0ms (1.3%)

prune28.0ms (1.2%)

localize5.0ms (0.2%)

series9.0ms (0.4%)

rewrite35.0ms (1.5%)

simplify31.0ms (1.4%)

prune11.0ms (0.5%)

localize5.0ms (0.2%)

series11.0ms (0.5%)

rewrite33.0ms (1.4%)

simplify29.0ms (1.3%)

prune10.0ms (0.4%)

regimes85.0ms (3.7%)

simplify2.0ms (0.1%)

end55.0ms (2.4%)

Profiling

Iter	Nodes	Cost
0	8	10
1	16	10
2	31	10
3	48	10
4	75	10
5	123	10
6	204	10
7	305	10
8	407	10
9	523	10
10	581	10
11	587	10

Iter	Nodes	Cost
0	10	420
1	21	420
2	39	420
3	55	420
4	79	420
5	127	420
6	208	420
7	309	420
8	411	420
9	527	420
10	585	420
11	591	420

Iter	Nodes	Cost
0	10	420
1	21	420
2	39	420
3	55	420
4	79	420
5	127	420
6	208	420
7	309	420
8	411	420
9	527	420
10	585	420
11	591	420

Iter	Nodes	Cost
0	10	420
1	21	420
2	39	420
3	55	420
4	79	420
5	127	420
6	208	420
7	309	420
8	411	420
9	527	420
10	585	420
11	591	420