Metrics for quadp (p42, positive)

analyze188.0ms (7.4%)

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)

Precisions

Click to see histograms. Total time spent on operations: 107.0ms

ival-mult: 58.0ms (54.2% of total)

ival-div: 14.0ms (13.1% of total)

ival-sqrt: 11.0ms (10.3% of total)

ival-neg: 8.0ms (7.5% of total)

ival-sub: 7.0ms (6.5% of total)

ival-add: 7.0ms (6.5% of total)

const: 2.0ms (1.9% of total)

sample2.0s (77.7%)

Results

558.0ms	5714×	256	valid
455.0ms	1096×	2048	valid
191.0ms	406×	4096	valid
190.0ms	674×	1024	valid
90.0ms	993×	256	invalid
69.0ms	366×	512	valid

Precisions

Click to see histograms. Total time spent on operations: 1.1s

ival-mult: 483.0ms (45.5% of total)

ival-sqrt: 142.0ms (13.4% of total)

ival-div: 126.0ms (11.9% of total)

ival-sub: 99.0ms (9.3% of total)

ival-add: 94.0ms (8.8% of total)

ival-neg: 92.0ms (8.7% of total)

const: 26.0ms (2.4% of total)

Bogosity

preprocess136.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

834×	`div-sub`
688×	`fma-neg`
551×	`fma-define`
496×	`sub-neg`
390×	`associate-/r*`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	67	779
1	184	687
2	463	671
3	1378	671
4	3677	671
5	7597	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 #s(literal 4 binary64) (.f64 a c))))) (.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 #s(literal -4 binary64) a)))) b) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c #s(literal -4 binary64))))) b) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c #s(literal -4 binary64)))))) (*.f64 a #s(literal -2 binary64)))
(/.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)))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 #s(literal -4 binary64) a)))) b) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c #s(literal -4 binary64))))) b) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c #s(literal -4 binary64)))))) (*.f64 a #s(literal -2 binary64)))
(/.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 #s(literal 4 binary64) (.f64 a (neg.f64 c)))))) (neg.f64 (.f64 a #s(literal 2 binary64))))
(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 #s(literal -4 binary64) a)))) b) (.f64 a #s(literal -2 binary64)))
(.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (sqrt.f64 (fma.f64 #s(literal 4 binary64) (.f64 a c) (*.f64 b b))) b) a))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 #s(literal 4 binary64) (.f64 a c) (.f64 b b))) b) (*.f64 a #s(literal -2 binary64)))
(/.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 #s(literal 4 binary64) (.f64 a c))))) (.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 b b (.f64 a (.f64 c #s(literal -4 binary64)))))) (*.f64 a #s(literal 2 binary64)))
(/.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 #s(literal 4 binary64) (.f64 a (neg.f64 c)))))) (.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 #s(literal -4 binary64) a)))) b) (.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 #s(literal 4 binary64) (.f64 a c) (.f64 b b))) b) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 b (sqrt.f64 (fma.f64 #s(literal 4 binary64) (.f64 a c) (.f64 b b)))) (*.f64 a #s(literal -2 binary64)))
(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 #s(literal 4 binary64) (.f64 a (neg.f64 c)))))) (.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 #s(literal -4 binary64) a)))) b) (.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 #s(literal 4 binary64) (.f64 a c) (.f64 b b))) b) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 b (sqrt.f64 (fma.f64 #s(literal 4 binary64) (.f64 a c) (.f64 b b)))) (*.f64 a #s(literal -2 binary64)))
(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 #s(literal 4 binary64) (.f64 a c))))) (neg.f64 (.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 #s(literal -1/2 binary64) (/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c #s(literal -4 binary64)))))) a))
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c #s(literal -4 binary64)))))) (*.f64 a #s(literal -2 binary64)))
(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 #s(literal 4 binary64) (.f64 a (neg.f64 c)))))) (neg.f64 (.f64 a #s(literal 2 binary64))))
(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 #s(literal -4 binary64) a)))) b) (.f64 a #s(literal -2 binary64)))
(.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (sqrt.f64 (fma.f64 #s(literal 4 binary64) (.f64 a c) (*.f64 b b))) b) a))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 #s(literal 4 binary64) (.f64 a c) (.f64 b b))) b) (*.f64 a #s(literal -2 binary64)))
(/.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 (sqrt.f64 (fma.f64 a a (.f64 (.f64 b c) #s(literal -4 binary64)))) a) (*.f64 b #s(literal 2 binary64)))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 a a (.f64 c (.f64 b #s(literal -4 binary64))))) a) (*.f64 b #s(literal 2 binary64)))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b (.f64 c #s(literal -4 binary64)) (.f64 a a))) a) (*.f64 b #s(literal 2 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 #s(literal 4 binary64) (.f64 a c))))) (.f64 c #s(literal 2 binary64)))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (.f64 #s(literal -4 binary64) a)))) b) (*.f64 c #s(literal 2 binary64)))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c #s(literal -4 binary64))))) b) (*.f64 c #s(literal 2 binary64)))
(/.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 (sqrt.f64 (fma.f64 c c (.f64 (.f64 b a) #s(literal -4 binary64)))) c) (*.f64 a #s(literal 2 binary64)))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 c c (.f64 b (.f64 a #s(literal -4 binary64))))) c) (*.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 c (sqrt.f64 (fma.f64 b (.f64 a #s(literal -4 binary64)) (.f64 c c)))) (*.f64 a #s(literal -2 binary64)))

explain193.0ms (7.6%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
92	-	2	(4.785718880724937e-305 -4.237608528218221e-162 1.2914635232116218e-102)	`(sqrt.f64 (-.f64 (.f64 b b) (.f64 #s(literal 4 binary64) (*.f64 a c))))`
67	-	0	-	`(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 #s(literal 4 binary64) (*.f64 a c)))))`
10	-	0	-	`(/.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))`
3	-	0	-	`(-.f64 (.f64 b b) (.f64 #s(literal 4 binary64) (*.f64 a c)))`
0	-	0	-	`b`
0	-	0	-	`(neg.f64 b)`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`c`
0	-	0	-	`(*.f64 #s(literal 2 binary64) a)`
0	-	0	-	`(*.f64 b b)`
0	-	0	-	`#s(literal 4 binary64)`
0	-	0	-	`(*.f64 a c)`
0	-	0	-	`(.f64 #s(literal 4 binary64) (.f64 a c))`
0	-	0	-	`a`

Results

53.0ms	348×	256	valid
50.0ms	76×	2048	valid
20.0ms	44×	1024	valid
12.0ms	20×	4096	valid
6.0ms	24×	512	valid

Compiler

Compiled 168 to 44 computations (73.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 71.0ms

ival-mult: 34.0ms (47.7% of total)

ival-neg: 11.0ms (15.4% of total)

ival-sqrt: 8.0ms (11.2% of total)

ival-div: 7.0ms (9.8% of total)

ival-sub: 5.0ms (7% of total)

ival-add: 5.0ms (7% of total)

const: 2.0ms (2.8% of total)

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
	54.4%	(/.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)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative`
8×	`+-commutative`
7×	`sub-neg`
6×	`neg-sub0`
6×	`neg-mul-1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	69
1	34	65
2	47	65
3	60	65
4	68	65
5	73	65
6	75	65

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)))

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

soundness0.0ms (0%)

Stop Event

1×

fuel

Compiler

Compiled 19 to 13 computations (31.6% saved)

preprocess43.0ms (1.7%)

Compiler: Compiled 294 to 110 computations (62.6% saved)

quadp (p42, positive)

analyze188.0ms (7.4%)

sample2.0s (77.7%)

preprocess136.0ms (5.4%)

explain193.0ms (7.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

soundness0.0ms (0%)

preprocess43.0ms (1.7%)

end0.0ms (0%)

Profiling