Metrics for arccos

analyze5.0ms (0.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	75%	0%	0%	25%	0%	3
40%	25%	37.5%	0%	0%	37.5%	0%	4
66.7%	37.5%	18.7%	0%	0%	43.7%	0%	5
82.4%	43.7%	9.4%	0%	0%	46.9%	0%	6
90.9%	46.9%	4.7%	0%	0%	48.4%	0%	7
95.4%	48.4%	2.3%	0%	0%	49.2%	0%	8
97.7%	49.2%	1.2%	0%	0%	49.6%	0%	9
98.8%	49.6%	0.6%	0%	0%	49.8%	0%	10
99.4%	49.8%	0.3%	0%	0%	49.9%	0%	11
99.7%	49.9%	0.1%	0%	0%	49.9%	0%	12

Compiler

Compiled 13 to 11 computations (15.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

Operation ival-atan, time spent: 1.0ms, 33.0% of total-time

Operation ival-sqrt, time spent: 1.0ms, 33.0% 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-add, time spent: 0.0ms, 0.0% of total-time

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

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

sample1.4s (32%)

Results

1.3s	8255×	valid
1.0ms	10×	invalid
0.0ms	1×	valid

Precisions

Click to see histograms. Total time spent on operations: 714.0ms

Operation ival-sub, time spent: 182.0ms, 25.0% of total-time

Operation ival-add, time spent: 141.0ms, 20.0% of total-time

Operation ival-div, time spent: 131.0ms, 18.0% of total-time

Operation ival-sqrt, time spent: 111.0ms, 16.0% of total-time

Operation ival-mult, time spent: 65.0ms, 9.0% of total-time

Operation ival-atan, time spent: 55.0ms, 8.0% of total-time

Operation const, time spent: 30.0ms, 4.0% of total-time

Bogosity

preprocess2.1s (47.4%)

Algorithm

1×	egg-herbie

Rules

1506×	`fma-def`
390×	`div-sub`
250×	`times-frac`
192×	`associate-/r*`
174×	`distribute-lft-in`

FPErrors

Click to see full error table

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	164
1	50	156
2	82	156
3	159	156
4	388	156
5	983	156
6	1777	156
7	2174	156
8	2494	156

Stop Event

1×

saturated

Calls

Call 1

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

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

Compiler

Compiled 104 to 80 computations (23.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.8s

Operation ival-atan, time spent: 507.0ms, 29.0% of total-time

Operation ival-sqrt, time spent: 401.0ms, 23.0% of total-time

Operation ival-add, time spent: 306.0ms, 17.0% of total-time

Operation ival-sub, time spent: 303.0ms, 17.0% of total-time

Operation ival-div, time spent: 163.0ms, 9.0% of total-time

Operation const, time spent: 38.0ms, 2.0% of total-time

Operation ival-mult, time spent: 38.0ms, 2.0% of total-time

eval0.0ms (0%)

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

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))

Compiler

Compiled 12 to 10 computations (16.7% saved)

localize879.0ms (19.8%)

Compiler: Compiled 46 to 35 computations (23.9% saved)
Precisions: Click to see histograms. Total time spent on operations: 729.0ms
Operation ival-atan, time spent: 228.0ms, 31.0% of total-time
Operation ival-sub, time spent: 154.0ms, 21.0% of total-time
Operation ival-add, time spent: 142.0ms, 19.0% of total-time
Operation ival-div, time spent: 85.0ms, 12.0% of total-time
Operation ival-sqrt, time spent: 84.0ms, 12.0% of total-time
Operation const, time spent: 19.0ms, 3.0% of total-time
Operation ival-mult, time spent: 17.0ms, 2.0% of total-time

eval0.0ms (0%)

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

prune1.0ms (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

100.0%

Counts

1 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))

Compiler

Compiled 24 to 20 computations (16.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	39
1	23	39
2	27	39
3	29	39
4	30	39

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 12 to 10 computations (16.7% saved)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess26.0ms (0.6%)

Compiler: Compiled 48 to 40 computations (16.7% saved)

analyze5.0ms (0.1%)

sample1.4s (32%)

preprocess2.1s (47.4%)

eval0.0ms (0%)

prune1.0ms (0%)

localize879.0ms (19.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess26.0ms (0.6%)

Profiling