Metrics for Migdal et al, Equation (64)

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 23 to 16 computations (30.4% saved)

Precisions

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

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

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

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

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

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

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

sample2.4s (45.7%)

Results

1.2s	4670×	valid
1.0s	3585×	infinite
0.0ms	1×	valid

Precisions

Click to see histograms. Total time spent on operations: 1.2s

Operation ival-mult, time spent: 281.0ms, 24.0% of total-time

Operation ival-sqrt, time spent: 255.0ms, 22.0% of total-time

Operation ival-cos, time spent: 243.0ms, 21.0% of total-time

Operation ival-div, time spent: 195.0ms, 17.0% of total-time

Operation ival-add, time spent: 170.0ms, 15.0% of total-time

Operation const, time spent: 27.0ms, 2.0% of total-time

Bogosity

preprocess1.9s (36.3%)

Algorithm

1×	egg-herbie

Rules

3576×	`fma-def`
1010×	`div-sub`
974×	`associate-/l*`
962×	`distribute-lft-in`
814×	`distribute-lft-neg-in`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))`
-	-	`(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))`
-	-	`a2`
-	-	`(cos.f64 th)`
-	-	`(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))`
-	-	`(*.f64 a2 a2)`
-	-	`(sqrt.f64 2)`
-	-	`th`
-	-	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
-	-	`(*.f64 a1 a1)`
-	-	`a1`
-	-	`2`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	606
1	145	562
2	418	562
3	1078	562
4	2438	562
5	4177	562
6	5513	562
7	6050	562
8	6122	562
9	6133	562
10	6139	562
11	7356	562

Stop Event

1×	node limit

Calls

Call 1

Inputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (neg.f64 a1) (neg.f64 a1))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (neg.f64 a2) (neg.f64 a2))))
(+.f64 (.f64 (/.f64 (cos.f64 (neg.f64 th)) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 (neg.f64 th)) (sqrt.f64 2)) (.f64 a2 a2)))
(neg.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (neg.f64 a1) (neg.f64 a1))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))))
(neg.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (neg.f64 a2) (neg.f64 a2)))))
(neg.f64 (+.f64 (.f64 (/.f64 (cos.f64 (neg.f64 th)) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 (neg.f64 th)) (sqrt.f64 2)) (.f64 a2 a2))))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))
(+.f64 (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (.f64 th th)) (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (.f64 a2 a2)))
(+.f64 (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (.f64 th th)))

Outputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (neg.f64 a1) (neg.f64 a1))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (neg.f64 a2) (neg.f64 a2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (/.f64 (cos.f64 (neg.f64 th)) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 (neg.f64 th)) (sqrt.f64 2)) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(neg.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (neg.f64 a1) (neg.f64 a1))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))))
(neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (neg.f64 (fma.f64 a1 a1 (.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 2)))
(.f64 (cos.f64 th) (neg.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 2)))
(neg.f64 (+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (neg.f64 a2) (neg.f64 a2)))))
(neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (neg.f64 (fma.f64 a1 a1 (.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 2)))
(.f64 (cos.f64 th) (neg.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 2)))
(neg.f64 (+.f64 (.f64 (/.f64 (cos.f64 (neg.f64 th)) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 (neg.f64 th)) (sqrt.f64 2)) (.f64 a2 a2))))
(neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (neg.f64 (fma.f64 a1 a1 (.f64 a2 a2))))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 2)))
(.f64 (cos.f64 th) (neg.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (.f64 th th)) (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (+.f64 (.f64 th th) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (fma.f64 th th (.f64 a2 a2)))
(+.f64 (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (.f64 th th)))
(.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 th th)))
(.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 th th)))
(.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (fma.f64 th th (.f64 a1 a1)))
(.f64 (cos.f64 a2) (/.f64 (fma.f64 th th (.f64 a1 a1)) (sqrt.f64 2)))
(/.f64 (cos.f64 a2) (/.f64 (sqrt.f64 2) (fma.f64 th th (*.f64 a1 a1))))

Symmetry

(abs a1)

(abs a2)

(abs th)

(sort a1 a2)

Compiler

Compiled 142 to 75 computations (47.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0s

Operation ival-cos, time spent: 365.0ms, 36.0% of total-time

Operation ival-sqrt, time spent: 299.0ms, 29.0% of total-time

Operation ival-div, time spent: 151.0ms, 15.0% of total-time

Operation ival-mult, time spent: 136.0ms, 13.0% of total-time

Operation ival-add, time spent: 54.0ms, 5.0% of total-time

Operation const, time spent: 21.0ms, 2.0% of total-time

eval1.0ms (0%)

Compiler: Compiled 40 to 21 computations (47.5% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))

Compiler

Compiled 16 to 11 computations (31.3% saved)

localize468.0ms (8.9%)

Compiler: Compiled 43 to 18 computations (58.1% saved)
Precisions: Click to see histograms. Total time spent on operations: 277.0ms
Operation ival-cos, time spent: 121.0ms, 44.0% of total-time
Operation ival-sqrt, time spent: 66.0ms, 24.0% of total-time
Operation ival-mult, time spent: 34.0ms, 12.0% of total-time
Operation ival-add, time spent: 26.0ms, 9.0% of total-time
Operation ival-div, time spent: 23.0ms, 8.0% of total-time
Operation const, time spent: 7.0ms, 3.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

prune4.0ms (0.1%)

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

99.6%

Counts

1 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))

Compiler

Compiled 51 to 31 computations (39.2% saved)

regimes24.0ms (0.5%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Outputs
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))

Calls

8 calls:

4.0ms	a2
3.0ms	a1
3.0ms	th
3.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
3.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Results

Accuracy	Segments	Branch
99.6%	1	`a1`
99.6%	1	`a2`
99.6%	1	`th`
99.6%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))`
99.6%	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
99.6%	1	`(cos.f64 th)`
99.6%	1	`(*.f64 a1 a1)`
99.6%	1	`(*.f64 a2 a2)`

Compiler

Compiled 59 to 43 computations (27.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	54
1	20	54

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))

Outputs
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))

Compiler

Compiled 16 to 11 computations (31.3% saved)

soundness402.0ms (7.7%)

Rules

3576×	`fma-def`
1010×	`div-sub`
974×	`associate-/l*`
962×	`distribute-lft-in`
814×	`distribute-lft-neg-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	606
1	145	562
2	418	562
3	1078	562
4	2438	562
5	4177	562
6	5513	562
7	6050	562
8	6122	562
9	6133	562
10	6139	562
11	7356	562

Stop Event

1×	node limit

Compiler

Compiled 35 to 20 computations (42.9% saved)

end0.0ms (0%)

preprocess41.0ms (0.8%)

Remove

(sort a1 a2)

(abs th)

(abs a2)

(abs a1)

Compiler

Compiled 332 to 228 computations (31.3% saved)

analyze0.0ms (0%)

sample2.4s (45.7%)

preprocess1.9s (36.3%)

eval1.0ms (0%)

prune1.0ms (0%)

localize468.0ms (8.9%)

eval0.0ms (0%)

prune4.0ms (0.1%)

regimes24.0ms (0.5%)

simplify2.0ms (0%)

soundness402.0ms (7.7%)

end0.0ms (0%)

preprocess41.0ms (0.8%)

Profiling