Metrics for Quadratic roots, narrow range

analyze636.0ms (17.5%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	0%	100%	0%	0%	0%	0
0%	0%	0%	100%	0%	0%	0%	1
0%	0%	0%	100%	0%	0%	0%	2
0%	0%	0%	100%	0%	0%	0%	3
0%	0%	0%	100%	0%	0%	0%	4
0%	0%	0%	100%	0%	0%	0%	5
0%	0%	0%	100%	0%	0%	0%	6
0%	0%	0%	100%	0%	0%	0%	7
2.3%	0%	0%	100%	0%	0%	0%	8
11.3%	0%	0%	100%	0%	0%	0%	9
21.1%	0%	0%	100%	0%	0%	0%	10
28%	0%	0%	100%	0%	0%	0%	11
40.1%	0%	0%	100%	0%	0%	0%	12

Compiler

Compiled 43 to 27 computations (37.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 248.0ms

...c/correct-round.rkt:104:19: 74.0ms (29.9% of total)

ival-mult: 57.0ms (23% of total)

ival-<: 43.0ms (17.4% of total)

ival-sqrt: 15.0ms (6.1% of total)

ival-div: 13.0ms (5.2% of total)

ival-add: 11.0ms (4.4% of total)

ival-sub: 11.0ms (4.4% of total)

ival-neg: 11.0ms (4.4% of total)

ival-and: 9.0ms (3.6% of total)

const: 2.0ms (0.8% of total)

sample2.7s (74%)

Results

1.7s	8256×	256	valid
369.0ms	1396×	256	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.6s

...c/correct-round.rkt:104:19: 424.0ms (25.9% of total)

ival-mult: 417.0ms (25.4% of total)

ival-<: 282.0ms (17.2% of total)

ival-sqrt: 154.0ms (9.4% of total)

ival-div: 91.0ms (5.5% of total)

ival-sub: 82.0ms (5% of total)

ival-neg: 68.0ms (4.1% of total)

ival-add: 67.0ms (4.1% of total)

ival-and: 44.0ms (2.7% of total)

const: 10.0ms (0.6% of total)

Bogosity

preprocess130.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

837×	`div-sub`
698×	`fma-neg`
688×	`fma-define`
507×	`sub-neg`
395×	`associate-/r*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	65	779
1	186	671
2	513	671
3	1362	671
4	3699	671
5	7725	671

Stop Event

1×	node limit

Calls

Call 1

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

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

explain144.0ms (4%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
223	4	(16740773.576390978 7595.601283544391 0.0006205880034133266)	3	(1.6576281939498065e-7 0.8563656514511748 31920.749127495073)	`(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 #s(literal 4 binary64) a) c))))`
1	0	-	1	(6662.262543621674 26.823962113065534 0.02670270144843464)	`(-.f64 (.f64 b b) (.f64 (*.f64 #s(literal 4 binary64) a) c))`
0	0	-	0	-	`(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 #s(literal 4 binary64) a) c)))) (.f64 #s(literal 2 binary64) a))`
0	0	-	0	-	`b`
0	0	-	0	-	`(*.f64 #s(literal 4 binary64) a)`
0	0	-	0	-	`(neg.f64 b)`
0	0	-	0	-	`#s(literal 2 binary64)`
0	0	-	0	-	`c`
0	0	-	0	-	`(*.f64 #s(literal 2 binary64) a)`
0	0	-	0	-	`(.f64 (.f64 #s(literal 4 binary64) a) c)`
0	0	-	0	-	`(*.f64 b b)`
0	0	-	0	-	`(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 #s(literal 4 binary64) a) c)))`
0	0	-	0	-	`#s(literal 4 binary64)`
0	0	-	0	-	`a`

Results

80.0ms

512×

256

valid

Compiler

Compiled 168 to 44 computations (73.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-mult: 13.0ms (38.3% of total)

ival-neg: 6.0ms (17.7% of total)

ival-div: 4.0ms (11.8% of total)

ival-sqrt: 4.0ms (11.8% of total)

ival-sub: 3.0ms (8.8% of total)

ival-add: 3.0ms (8.8% of total)

const: 1.0ms (2.9% of total)

eval0.0ms (0%)

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

prune6.0ms (0.2%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
	54.6%	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 #s(literal 4 binary64) 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	53	65
3	64	65
4	72	65
5	75	65

Stop Event

1×

saturated

Calls

Call 1

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

Outputs

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

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

preprocess22.0ms (0.6%)

Compiler: Compiled 78 to 54 computations (30.8% saved)

Quadratic roots, narrow range

analyze636.0ms (17.5%)

sample2.7s (74%)

preprocess130.0ms (3.6%)

explain144.0ms (4%)

eval0.0ms (0%)

prune6.0ms (0.2%)

simplify3.0ms (0.1%)

soundness0.0ms (0%)

preprocess22.0ms (0.6%)

end0.0ms (0%)

Profiling