Metrics for The quadratic formula (r2)

analyze131.0ms (1.5%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
25%	25%	74.9%	0.1%	0%	0%	0%	4
37.5%	37.4%	62.4%	0.1%	0%	0%	0%	5
37.5%	37.4%	62.4%	0.1%	0%	0%	0%	6
40%	37.4%	56.2%	0.1%	0%	6.2%	0%	7
48.3%	45.2%	48.4%	0.1%	0%	6.2%	0%	8
53%	48.4%	42.9%	0.1%	0%	8.6%	0%	9
58.1%	50.3%	36.3%	0.1%	0%	13.3%	0%	10
66.1%	56.8%	29.1%	0.1%	0%	14%	0%	11
70.4%	58.8%	24.7%	0.1%	0%	16.4%	0%	12

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample7.9s (94.1%)

Results

576.0ms	5468×	0	valid-sollya
529.0ms	5468×	0	valid
553.0ms	1926×	2	valid
348.0ms	1926×	2	valid-sollya
92.0ms	984×	0	invalid
120.0ms	983×	0	invalid-sollya
160.0ms	862×	1	valid
112.0ms	861×	1	valid-sollya
0.0ms	1×	1	exit-sollya
0.0ms	1×	0	exit-sollya

Sollya Eval

Pt	Rival-out	Sollya-interval	Sollya-point	status	Sollya status	Rival iter	sollya-time	check
(-1.5190631739246409e+30 -4.274118812248458e-262 -6.249398432274884e-299)	#f	(+nan.0 +nan.0)	+nan.0	invalid	exit	0	0.08605600000000001	#f
(-2.0854859096640133e-263 -2.01028733486648e-257 9.586052241753546e-265)	4.76849855017853e-8	(4.7684936278625015e-8 4.76850228385182e-8)	+nan.0	valid	exit	1	0.125344	#f

Sollya timings

Total time spent in Sollya 1.2s

Bogosity

preprocess282.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1892×	`fma-neg`
379×	`fma-define`
372×	`sub-neg`
364×	`div-sub`
281×	`associate-/r*`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	779
1	216	723
2	635	691
3	2137	671
4	5143	671
5	6383	671
6	6747	671
7	6881	671
8	6920	671
9	7073	671

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 #s(literal 4 binary64) (.f64 a c))))) (.f64 #s(literal 2 binary64) a))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 #s(literal 4 binary64) (.f64 a c))))) (.f64 #s(literal 2 binary64) a))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 #s(literal 4 binary64) (.f64 (neg.f64 a) c))))) (.f64 #s(literal 2 binary64) (neg.f64 a)))
(/.f64 (-.f64 (neg.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 #s(literal 4 binary64) (.f64 a c))))) (.f64 #s(literal 2 binary64) a))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 #s(literal 4 binary64) (.f64 a (neg.f64 c)))))) (.f64 #s(literal 2 binary64) a))
(neg.f64 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 #s(literal 4 binary64) (.f64 (neg.f64 a) c))))) (.f64 #s(literal 2 binary64) (neg.f64 a))))
(neg.f64 (/.f64 (-.f64 (neg.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 #s(literal 4 binary64) (.f64 a c))))) (.f64 #s(literal 2 binary64) a)))
(neg.f64 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 #s(literal 4 binary64) (.f64 a (neg.f64 c)))))) (.f64 #s(literal 2 binary64) a)))
(/.f64 (-.f64 (neg.f64 a) (sqrt.f64 (-.f64 (.f64 a a) (.f64 #s(literal 4 binary64) (.f64 b c))))) (.f64 #s(literal 2 binary64) b))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 #s(literal 4 binary64) (.f64 c a))))) (.f64 #s(literal 2 binary64) c))
(/.f64 (-.f64 (neg.f64 c) (sqrt.f64 (-.f64 (.f64 c c) (.f64 #s(literal 4 binary64) (.f64 a b))))) (.f64 #s(literal 2 binary64) a))

Outputs
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 #s(literal 4 binary64) (.f64 a c))))) (.f64 #s(literal 2 binary64) a))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 #s(literal 4 binary64) c) a)))) (.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 #s(literal -4 binary64) a))))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 a (.f64 c #s(literal -4 binary64)) (.f64 b b)))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c #s(literal -4 binary64)) (.f64 b b)))) (*.f64 a #s(literal -2 binary64)))
(.f64 (/.f64 #s(literal -1/2 binary64) a) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c #s(literal -4 binary64)) (*.f64 b b)))))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 #s(literal 4 binary64) (.f64 a c))))) (.f64 #s(literal 2 binary64) a))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 #s(literal 4 binary64) c) a)))) (.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 #s(literal -4 binary64) a))))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 a (.f64 c #s(literal -4 binary64)) (.f64 b b)))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c #s(literal -4 binary64)) (.f64 b b)))) (*.f64 a #s(literal -2 binary64)))
(.f64 (/.f64 #s(literal -1/2 binary64) a) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c #s(literal -4 binary64)) (*.f64 b b)))))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 #s(literal 4 binary64) (.f64 (neg.f64 a) c))))) (.f64 #s(literal 2 binary64) (neg.f64 a)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 #s(literal 4 binary64) a) (neg.f64 c))))) (.f64 #s(literal 2 binary64) (neg.f64 a)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 #s(literal 4 binary64) c))))) (.f64 a #s(literal -2 binary64)))
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (.f64 #s(literal 4 binary64) c))))) (*.f64 a #s(literal 2 binary64)))
(.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 #s(literal 4 binary64) c))))) (/.f64 #s(literal 1/2 binary64) a))
(/.f64 (-.f64 (neg.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 #s(literal 4 binary64) (.f64 a c))))) (.f64 #s(literal 2 binary64) a))
(/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 #s(literal 4 binary64) c) a)))) (.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 #s(literal -4 binary64) a))))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c #s(literal -4 binary64)) (.f64 b b)))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c #s(literal -4 binary64)) (.f64 b b))) b) (*.f64 a #s(literal -2 binary64)))
(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c #s(literal -4 binary64)) (*.f64 b b))) b) (/.f64 #s(literal -1/2 binary64) a))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 #s(literal 4 binary64) (.f64 a (neg.f64 c)))))) (.f64 #s(literal 2 binary64) a))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 #s(literal 4 binary64) a) (neg.f64 c))))) (.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 #s(literal 4 binary64) c))))) (.f64 a #s(literal 2 binary64)))
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (.f64 #s(literal 4 binary64) c))))) (*.f64 a #s(literal -2 binary64)))
(.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 #s(literal 4 binary64) c))))) (/.f64 #s(literal -1/2 binary64) a))
(neg.f64 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 #s(literal 4 binary64) (.f64 (neg.f64 a) c))))) (.f64 #s(literal 2 binary64) (neg.f64 a))))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 #s(literal 4 binary64) a) (neg.f64 c))))) (.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 #s(literal 4 binary64) c))))) (.f64 a #s(literal 2 binary64)))
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (.f64 #s(literal 4 binary64) c))))) (*.f64 a #s(literal -2 binary64)))
(.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 #s(literal 4 binary64) c))))) (/.f64 #s(literal -1/2 binary64) a))
(neg.f64 (/.f64 (-.f64 (neg.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 #s(literal 4 binary64) (.f64 a c))))) (.f64 #s(literal 2 binary64) a)))
(/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 #s(literal 4 binary64) c) a)))) (.f64 #s(literal 2 binary64) (neg.f64 a)))
(/.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 c (.f64 #s(literal -4 binary64) a))))) (*.f64 a #s(literal -2 binary64)))
(.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c #s(literal -4 binary64)) (*.f64 b b))) b) a))
(.f64 (/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c #s(literal -4 binary64)) (*.f64 b b))) b) a) #s(literal 1/2 binary64))
(.f64 (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c #s(literal -4 binary64)) (*.f64 b b)))) (/.f64 #s(literal -1/2 binary64) a))
(neg.f64 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 #s(literal 4 binary64) (.f64 a (neg.f64 c)))))) (.f64 #s(literal 2 binary64) a)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 #s(literal 4 binary64) a) (neg.f64 c))))) (.f64 #s(literal 2 binary64) (neg.f64 a)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 #s(literal 4 binary64) c))))) (.f64 a #s(literal -2 binary64)))
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (.f64 #s(literal 4 binary64) c))))) (*.f64 a #s(literal 2 binary64)))
(.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 #s(literal 4 binary64) c))))) (/.f64 #s(literal 1/2 binary64) a))
(/.f64 (-.f64 (neg.f64 a) (sqrt.f64 (-.f64 (.f64 a a) (.f64 #s(literal 4 binary64) (.f64 b c))))) (.f64 #s(literal 2 binary64) b))
(/.f64 (-.f64 (neg.f64 a) (sqrt.f64 (+.f64 (.f64 a a) (.f64 #s(literal -4 binary64) (.f64 b c))))) (.f64 b #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 a) (sqrt.f64 (fma.f64 a a (.f64 (.f64 #s(literal -4 binary64) b) c)))) (*.f64 b #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 a) (sqrt.f64 (fma.f64 a a (.f64 c (.f64 b #s(literal -4 binary64)))))) (*.f64 b #s(literal 2 binary64)))
(/.f64 (/.f64 (+.f64 a (sqrt.f64 (fma.f64 a a (.f64 c (.f64 b #s(literal -4 binary64)))))) #s(literal -2 binary64)) b)
(.f64 (/.f64 #s(literal -1/2 binary64) b) (+.f64 a (sqrt.f64 (fma.f64 a a (.f64 c (*.f64 b #s(literal -4 binary64)))))))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 #s(literal 4 binary64) (.f64 c a))))) (.f64 #s(literal 2 binary64) c))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 #s(literal 4 binary64) c) a)))) (.f64 c #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 #s(literal -4 binary64) a))))) (*.f64 c #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 a (.f64 c #s(literal -4 binary64)) (.f64 b b)))) (*.f64 c #s(literal 2 binary64)))
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c #s(literal -4 binary64)) (.f64 b b)))) (*.f64 c #s(literal -2 binary64)))
(.f64 (/.f64 #s(literal -1/2 binary64) c) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c #s(literal -4 binary64)) (*.f64 b b)))))
(/.f64 (-.f64 (neg.f64 c) (sqrt.f64 (-.f64 (.f64 c c) (.f64 #s(literal 4 binary64) (.f64 a b))))) (.f64 #s(literal 2 binary64) a))
(/.f64 (-.f64 (neg.f64 c) (sqrt.f64 (+.f64 (.f64 c c) (.f64 #s(literal -4 binary64) (.f64 b a))))) (.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 c) (sqrt.f64 (fma.f64 c c (.f64 (.f64 #s(literal -4 binary64) a) b)))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (neg.f64 c) (sqrt.f64 (fma.f64 c c (.f64 b (.f64 a #s(literal -4 binary64)))))) (*.f64 a #s(literal 2 binary64)))
(/.f64 (+.f64 c (sqrt.f64 (fma.f64 c c (.f64 b (.f64 a #s(literal -4 binary64)))))) (*.f64 a #s(literal -2 binary64)))
(.f64 (/.f64 #s(literal -1/2 binary64) a) (+.f64 c (sqrt.f64 (fma.f64 c c (.f64 b (*.f64 a #s(literal -4 binary64)))))))

Compiler

Compiled 20 to 14 computations (30% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
	52.4%	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 #s(literal 4 binary64) (.f64 a c))))) (.f64 #s(literal 2 binary64) a))

Compiler

Compiled 40 to 28 computations (30% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative`
14×	`+-commutative`
13×	`sub-neg`
11×	`neg-sub0`
11×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	69
1	35	69
2	52	69
3	74	69
4	89	69
5	104	69
6	111	69
7	114	69
8	115	69

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 #s(literal 4 binary64) (.f64 a c))))) (.f64 #s(literal 2 binary64) a))

Outputs

(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 #s(literal 4 binary64) (*.f64 a c))))) (*.f64 #s(literal 2 binary64) a))

(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 #s(literal 4 binary64) (*.f64 a c))))) (*.f64 a #s(literal 2 binary64)))

soundness0.0ms (0%)

Stop Event

1×

fuel

Compiler

Compiled 20 to 14 computations (30% saved)

preprocess78.0ms (0.9%)

Compiler: Compiled 170 to 98 computations (42.4% saved)

The quadratic formula (r2)

analyze131.0ms (1.5%)

sample7.9s (94.1%)

preprocess282.0ms (3.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

soundness0.0ms (0%)

preprocess78.0ms (0.9%)

end0.0ms (0%)

Profiling