Metrics for Eccentricity of an ellipse

analyze17.0ms (0.8%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	37.5%	62.5%	0%	0%	0%	0
0%	0%	37.5%	62.5%	0%	0%	0%	1
0%	0%	18.7%	81.3%	0%	0%	0%	2
0%	0%	9.4%	90.6%	0%	0%	0%	3
0%	0%	9.4%	90.6%	0%	0%	0%	4
0%	0%	7%	93%	0%	0%	0%	5
20%	1.2%	4.7%	94.1%	0%	0%	0%	6
25%	1.2%	3.5%	95.3%	0%	0%	0%	7
40%	1.8%	2.6%	95.6%	0%	0%	0%	8
51.9%	2%	1.9%	96%	0%	0%	0%	9
64.7%	2.4%	1.3%	96.3%	0%	0%	0%	10
72.9%	2.6%	1%	96.5%	0%	0%	0%	11
80.2%	2.7%	0.7%	96.6%	0%	0%	0%	12

Compiler

Compiled 26 to 15 computations (42.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

Operation ival-sqrt, time spent: 2.0ms, 22.0% of total-time

Operation ival-mult, time spent: 2.0ms, 22.0% of total-time

Operation ival-<=, time spent: 2.0ms, 22.0% of total-time

Operation ival-fabs, time spent: 1.0ms, 11.0% of total-time

Operation ival-div, time spent: 1.0ms, 11.0% of total-time

Operation ival-sub, time spent: 1.0ms, 11.0% of total-time

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

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

sample1.5s (65.7%)

Results

1.2s	8255×	valid
102.0ms	735×	precondition
0.0ms	1×	valid

Precisions

Click to see histograms. Total time spent on operations: 670.0ms

Operation ival-sub, time spent: 158.0ms, 24.0% of total-time

Operation ival-mult, time spent: 133.0ms, 20.0% of total-time

Operation ival-<=, time spent: 128.0ms, 19.0% of total-time

Operation ival-sqrt, time spent: 113.0ms, 17.0% of total-time

Operation ival-div, time spent: 76.0ms, 11.0% of total-time

Operation ival-and, time spent: 26.0ms, 4.0% of total-time

Operation const, time spent: 19.0ms, 3.0% of total-time

Operation ival-fabs, time spent: 18.0ms, 3.0% of total-time

Bogosity

preprocess155.0ms (6.9%)

Algorithm

1×	egg-herbie

Rules

1380×	`div-sub`
942×	`times-frac`
760×	`associate-r`
718×	`associate-*r/`
582×	`associate-/r/`

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
58	-	-	`(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))`
0	-	-	`(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))`
0	-	-	`(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))`
0	-	-	`(-.f64 (.f64 a a) (.f64 b b))`
0	-	-	`(*.f64 b b)`
0	-	-	`b`
0	-	-	`a`
0	-	-	`(*.f64 a a)`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	407
1	106	323
2	376	295
3	2248	295

Stop Event

1×	node limit

Calls

Call 1

Inputs
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 (neg.f64 a) (neg.f64 a)) (.f64 b b)) (*.f64 (neg.f64 a) (neg.f64 a)))))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 (neg.f64 b) (neg.f64 b))) (*.f64 a a))))
(neg.f64 (sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 (neg.f64 a) (neg.f64 a)) (.f64 b b)) (*.f64 (neg.f64 a) (neg.f64 a))))))
(neg.f64 (sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 (neg.f64 b) (neg.f64 b))) (*.f64 a a)))))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 b b) (.f64 a a)) (*.f64 b b))))

Outputs
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 (neg.f64 a) (neg.f64 a)) (.f64 b b)) (*.f64 (neg.f64 a) (neg.f64 a)))))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 (neg.f64 b) (neg.f64 b))) (*.f64 a a))))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))
(neg.f64 (sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 (neg.f64 a) (neg.f64 a)) (.f64 b b)) (*.f64 (neg.f64 a) (neg.f64 a))))))
(neg.f64 (sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))))
(neg.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a))))))
(neg.f64 (sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1))))
(neg.f64 (sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 (neg.f64 b) (neg.f64 b))) (*.f64 a a)))))
(neg.f64 (sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))))
(neg.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a))))))
(neg.f64 (sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1))))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 b b) (.f64 a a)) (*.f64 b b))))
(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 a b) (/.f64 a b)))))
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 a b) (/.f64 a b) -1)))

Symmetry

(abs a)

(abs b)

Compiler

Compiled 123 to 26 computations (78.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

Operation ival-sub, time spent: 9.0ms, 31.0% of total-time

Operation ival-mult, time spent: 8.0ms, 28.0% of total-time

Operation ival-sqrt, time spent: 6.0ms, 21.0% of total-time

Operation ival-div, time spent: 4.0ms, 14.0% of total-time

Operation ival-fabs, time spent: 1.0ms, 3.0% of total-time

Operation const, time spent: 1.0ms, 3.0% of total-time

eval1.0ms (0%)

Compiler: Compiled 23 to 12 computations (47.8% saved)

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))
▶	100.0%	(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))

Compiler

Compiled 25 to 15 computations (40% saved)

localize361.0ms (16.1%)

Compiler: Compiled 79 to 25 computations (68.4% saved)
Precisions: Click to see histograms. Total time spent on operations: 233.0ms
Operation ival-sub, time spent: 72.0ms, 31.0% of total-time
Operation ival-fma, time spent: 62.0ms, 27.0% of total-time
Operation ival-sqrt, time spent: 36.0ms, 15.0% of total-time
Operation ival-fabs, time spent: 24.0ms, 10.0% of total-time
Operation ival-div, time spent: 16.0ms, 7.0% of total-time
Operation ival-mult, time spent: 13.0ms, 6.0% of total-time
Operation const, time spent: 10.0ms, 4.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune2.0ms (0.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Accuracy

100.0%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))
✓	100.0%	(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))

Compiler

Compiled 61 to 33 computations (45.9% saved)

regimes19.0ms (0.8%)

Counts

3 → 1

Calls

Call 1

Inputs
(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))

Outputs
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))

Calls

7 calls:

5.0ms	b
3.0ms	a
3.0ms	(*.f64 a a)
2.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
2.0ms	(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))

Results

Accuracy	Segments	Branch
100.0%	1	`a`
100.0%	1	`b`
100.0%	1	`(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))`
100.0%	1	`(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))`
100.0%	1	`(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))`
100.0%	1	`(*.f64 a a)`
100.0%	1	`(*.f64 b b)`

Compiler

Compiled 58 to 31 computations (46.6% saved)

regimes17.0ms (0.7%)

Accuracy

Total -14.5b remaining (-123666.7%)

Threshold costs -14.5b (-123666.7%)

Counts

2 → 1

Calls

Call 1

Inputs
(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Outputs
(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))

Calls

7 calls:

4.0ms	a
3.0ms	b
2.0ms	(*.f64 a a)
2.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
2.0ms	(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))

Results

Accuracy	Segments	Branch
100.0%	1	`a`
100.0%	1	`b`
100.0%	1	`(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))`
100.0%	1	`(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))`
100.0%	1	`(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))`
100.0%	1	`(*.f64 a a)`
100.0%	1	`(*.f64 b b)`

Compiler

Compiled 58 to 31 computations (46.6% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

12×	`sub-neg`
12×	`+-commutative`
8×	`neg-mul-1`
8×	`*-commutative`
8×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	86
1	31	86
2	41	86
3	50	86
4	59	86
5	60	86

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))
(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))

Outputs
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))
(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))

Compiler

Compiled 25 to 15 computations (40% saved)

soundness163.0ms (7.3%)

Rules

1380×	`div-sub`
1380×	`div-sub`
942×	`times-frac`
942×	`times-frac`
760×	`associate-r`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	407
1	106	323
2	376	295
3	2248	295
0	32	407
1	106	323
2	376	295
3	2248	295

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 249 to 83 computations (66.7% saved)

end0.0ms (0%)

preprocess32.0ms (1.4%)

Remove

(abs b)

(abs a)

Compiler

Compiled 220 to 124 computations (43.6% saved)

analyze17.0ms (0.8%)

sample1.5s (65.7%)

preprocess155.0ms (6.9%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize361.0ms (16.1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes19.0ms (0.8%)

regimes17.0ms (0.7%)

simplify4.0ms (0.2%)

soundness163.0ms (7.3%)

end0.0ms (0%)

preprocess32.0ms (1.4%)

Profiling