Metrics for Given's Rotation SVD example, simplified

analyze5.0ms (0.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 14 to 13 computations (7.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

Operation ival-sub, time spent: 0.0ms, 0.0% of total-time

Operation ival-sqrt, time spent: 0.0ms, 0.0% of total-time

Operation ival-mult, time spent: 0.0ms, 0.0% of total-time

Operation ival-add, time spent: 0.0ms, 0.0% of total-time

Operation ival-div, time spent: 0.0ms, 0.0% of total-time

Operation ival-hypot, time spent: 0.0ms, 0.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

sample1.4s (38%)

Results

1.3s	8125×	0	valid
38.0ms	130×	1	valid
0.0ms	1×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 751.0ms

Operation ival-add, time spent: 172.0ms, 23.0% of total-time

Operation ival-sub, time spent: 157.0ms, 21.0% of total-time

Operation ival-hypot, time spent: 129.0ms, 17.0% of total-time

Operation ival-sqrt, time spent: 120.0ms, 16.0% of total-time

Operation ival-div, time spent: 69.0ms, 9.0% of total-time

Operation ival-mult, time spent: 67.0ms, 9.0% of total-time

Operation const, time spent: 38.0ms, 5.0% of total-time

Bogosity

preprocess1.7s (44%)

Algorithm

1×	egg-herbie

Rules

72×	`fma-def`
34×	`sub-neg`
22×	`+-commutative`
20×	`associate--r+`
18×	`associate-+l-`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(hypot.f64 1 x)`
-	-	`(/.f64 1 (hypot.f64 1 x))`
-	-	`1/2`
-	-	`(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))`
-	-	`(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))`
-	-	`(+.f64 1 (/.f64 1 (hypot.f64 1 x)))`
-	-	`1`
-	-	`(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	164
1	50	136
2	78	136
3	109	136
4	154	136
5	187	136
6	204	136
7	213	136
8	214	136

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 (neg.f64 x)))))))
(neg.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 (neg.f64 x))))))))

Outputs
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 (/.f64 1 (hypot.f64 1 x)) 1/2))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 (/.f64 1 (hypot.f64 1 x)) 1/2))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 (neg.f64 x)))))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 (/.f64 1 (hypot.f64 1 (neg.f64 x))) 1/2))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 (neg.f64 x))))))
(neg.f64 (-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 (neg.f64 x))))))))
(neg.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 (/.f64 1 (hypot.f64 1 (neg.f64 x))) 1/2)))))
(+.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 (neg.f64 x))))))
(+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 (neg.f64 x))))) -1)

Compiler

Compiled 115 to 100 computations (13% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.3s

Operation ival-hypot, time spent: 429.0ms, 32.0% of total-time

Operation ival-div, time spent: 282.0ms, 21.0% of total-time

Operation ival-add, time spent: 273.0ms, 20.0% of total-time

Operation ival-sqrt, time spent: 117.0ms, 9.0% of total-time

Operation ival-mult, time spent: 112.0ms, 8.0% of total-time

Operation ival-sub, time spent: 68.0ms, 5.0% of total-time

Operation const, time spent: 53.0ms, 4.0% of total-time

eval1.0ms (0%)

Compiler: Compiled 23 to 21 computations (8.7% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	96.7%	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 11 to 10 computations (9.1% saved)

localize578.0ms (15.4%)

Compiler: Compiled 38 to 32 computations (15.8% saved)
Precisions: Click to see histograms. Total time spent on operations: 455.0ms
Operation ival-hypot, time spent: 179.0ms, 39.0% of total-time
Operation ival-add, time spent: 94.0ms, 21.0% of total-time
Operation ival-div, time spent: 76.0ms, 17.0% of total-time
Operation ival-sqrt, time spent: 51.0ms, 11.0% of total-time
Operation ival-sub, time spent: 35.0ms, 8.0% of total-time
Operation const, time spent: 20.0ms, 4.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune2.0ms (0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

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

Accuracy

96.7%

Counts

1 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	96.7%	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 34 to 31 computations (8.8% saved)

regimes39.0ms (1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))

Outputs
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Calls

7 calls:

25.0ms	(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
3.0ms	x
3.0ms	(/.f64 1 (hypot.f64 1 x))
2.0ms	(hypot.f64 1 x)
2.0ms	(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))

Results

Accuracy	Segments	Branch
96.7%	1	`x`
96.7%	1	`(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))`
96.7%	1	`(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))`
96.7%	1	`(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))`
96.7%	1	`(+.f64 1 (/.f64 1 (hypot.f64 1 x)))`
96.7%	1	`(/.f64 1 (hypot.f64 1 x))`
96.7%	1	`(hypot.f64 1 x)`

Compiler

Compiled 54 to 47 computations (13% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative`
4×	`sub-neg`
3×	`1-exp`
2×	`neg-mul-1`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	32
1	21	32
2	25	32
3	27	32
4	28	32

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Outputs
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 11 to 10 computations (9.1% saved)

soundness23.0ms (0.6%)

Rules

72×	`fma-def`
34×	`sub-neg`
22×	`+-commutative`
20×	`associate--r+`
18×	`associate-+l-`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	164
1	50	136
2	78	136
3	109	136
4	154	136
5	187	136
6	204	136
7	213	136
8	214	136

Stop Event

1×

saturated

Compiler

Compiled 61 to 56 computations (8.2% saved)

end0.0ms (0%)

preprocess27.0ms (0.7%)

Compiler: Compiled 48 to 44 computations (8.3% saved)

Iter	Nodes	Cost
0	22	164
1	50	136
2	78	136
3	109	136
4	154	136
5	187	136
6	204	136
7	213	136
8	214	136

Iter	Nodes	Cost
0	22	164
1	50	136
2	78	136
3	109	136
4	154	136
5	187	136
6	204	136
7	213	136
8	214	136

Iter	Nodes	Cost
0	22	164
1	50	136
2	78	136
3	109	136
4	154	136
5	187	136
6	204	136
7	213	136
8	214	136

Iter	Nodes	Cost
0	22	164
1	50	136
2	78	136
3	109	136
4	154	136
5	187	136
6	204	136
7	213	136
8	214	136

analyze5.0ms (0.1%)

sample1.4s (38%)

preprocess1.7s (44%)

eval1.0ms (0%)

prune1.0ms (0%)

localize578.0ms (15.4%)

eval0.0ms (0%)

prune2.0ms (0%)

regimes39.0ms (1%)

simplify3.0ms (0.1%)

soundness23.0ms (0.6%)

end0.0ms (0%)

preprocess27.0ms (0.7%)

Profiling

Iter	Nodes	Cost
0	22	164
1	50	136
2	78	136
3	109	136
4	154	136
5	187	136
6	204	136
7	213	136
8	214	136

Iter	Nodes	Cost
0	22	164
1	50	136
2	78	136
3	109	136
4	154	136
5	187	136
6	204	136
7	213	136
8	214	136