Metrics for Quadratic roots, full range

analyze158.0ms (3.1%)

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: 93.0ms

Operation ival-mult, time spent: 43.0ms, 46.0% of total-time

Operation ival-sqrt, time spent: 19.0ms, 20.0% of total-time

Operation ival-div, time spent: 8.0ms, 9.0% of total-time

Operation ival-sub, time spent: 8.0ms, 9.0% of total-time

Operation ival-add, time spent: 7.0ms, 7.0% of total-time

Operation ival-neg, time spent: 7.0ms, 7.0% of total-time

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

sample1.9s (36.4%)

Results

1.4s	7488×	0	valid
146.0ms	955×	0	invalid
128.0ms	691×	0	infinite
25.0ms	76×	1	valid
0.0ms	1×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 904.0ms

Operation ival-mult, time spent: 260.0ms, 29.0% of total-time

Operation ival-sub, time spent: 176.0ms, 19.0% of total-time

Operation ival-add, time spent: 158.0ms, 17.0% of total-time

Operation ival-sqrt, time spent: 150.0ms, 17.0% of total-time

Operation ival-div, time spent: 73.0ms, 8.0% of total-time

Operation ival-neg, time spent: 55.0ms, 6.0% of total-time

Operation const, time spent: 31.0ms, 3.0% of total-time

Bogosity

preprocess1.4s (27.8%)

Algorithm

1×	egg-herbie

Rules

1648×	`div-sub`
1546×	`fma-def`
1212×	`sub-neg`
596×	`associate-*r/`
576×	`cancel-sign-sub-inv`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))`
-	-	`(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))`
-	-	`b`
-	-	`(neg.f64 b)`
-	-	`(*.f64 4 a)`
-	-	`(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))`
-	-	`c`
-	-	`(*.f64 b b)`
-	-	`4`
-	-	`(.f64 (.f64 4 a) c)`
-	-	`a`
-	-	`(*.f64 2 a)`
-	-	`2`
-	-	`(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	779
1	182	675
2	490	671
3	1246	671
4	3197	671
5	7858	671

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 (neg.f64 a)) c)))) (.f64 2 (neg.f64 a)))
(/.f64 (+.f64 (neg.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (.f64 4 a) c)))) (.f64 2 a))
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) (neg.f64 c))))) (.f64 2 a))
(neg.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 (neg.f64 a)) c)))) (.f64 2 (neg.f64 a))))
(neg.f64 (/.f64 (+.f64 (neg.f64 (neg.f64 b)) (sqrt.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (.f64 4 a) c)))) (.f64 2 a)))
(neg.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) (neg.f64 c))))) (.f64 2 a)))
(/.f64 (+.f64 (neg.f64 a) (sqrt.f64 (-.f64 (.f64 a a) (.f64 (.f64 4 b) c)))) (.f64 2 b))
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 c) a)))) (.f64 2 c))
(/.f64 (+.f64 (neg.f64 c) (sqrt.f64 (-.f64 (.f64 c c) (.f64 (.f64 4 a) b)))) (.f64 2 a))

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

Compiler

Compiled 168 to 92 computations (45.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 970.0ms

Operation ival-mult, time spent: 356.0ms, 37.0% of total-time

Operation ival-sub, time spent: 255.0ms, 26.0% of total-time

Operation ival-sqrt, time spent: 164.0ms, 17.0% of total-time

Operation ival-add, time spent: 118.0ms, 12.0% of total-time

Operation const, time spent: 31.0ms, 3.0% of total-time

Operation ival-div, time spent: 28.0ms, 3.0% of total-time

Operation ival-neg, time spent: 19.0ms, 2.0% of total-time

eval1.0ms (0%)

Compiler: Compiled 65 to 40 computations (38.5% saved)

prune2.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	66.1%	(/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (*.f64 a 2))
▶	66.0%	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 a 2))

Compiler

Compiled 38 to 26 computations (31.6% saved)

localize1.5s (28.3%)

Compiler: Compiled 131 to 65 computations (50.4% saved)
Precisions: Click to see histograms. Total time spent on operations: 1.2s
Operation ival-div, time spent: 418.0ms, 35.0% of total-time
Operation ival-mult, time spent: 261.0ms, 22.0% of total-time
Operation ival-sub, time spent: 186.0ms, 16.0% of total-time
Operation ival-sqrt, time spent: 154.0ms, 13.0% of total-time
Operation ival-fma, time spent: 81.0ms, 7.0% of total-time
Operation ival-add, time spent: 58.0ms, 5.0% of total-time
Operation const, time spent: 27.0ms, 2.0% of total-time
Operation ival-neg, time spent: 15.0ms, 1.0% of total-time

eval0.0ms (0%)

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

prune2.0ms (0%)

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

66.1%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	66.1%	(/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (*.f64 a 2))
✓	66.0%	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 a 2))

Compiler

Compiled 90 to 57 computations (36.7% saved)

regimes16.0ms (0.3%)

Counts

3 → 1

Calls

Call 1

Inputs

(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))

(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 a 2))

(/.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (*.f64 a 2))

Outputs
(/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (*.f64 a 2))

Calls

4 calls:

6.0ms	c
3.0ms	b
3.0ms	a
3.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))

Results

Accuracy	Segments	Branch
66.1%	1	`a`
66.1%	1	`b`
66.1%	1	`c`
66.1%	1	`(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))`

Compiler

Compiled 32 to 23 computations (28.1% saved)

regimes12.0ms (0.2%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 a 2))

Outputs
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))

Calls

4 calls:

3.0ms	a
3.0ms	b
3.0ms	c
2.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))

Results

Accuracy	Segments	Branch
66.0%	1	`c`
66.0%	1	`a`
66.0%	1	`(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))`
66.0%	1	`b`

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

20×	`*-commutative`
18×	`+-commutative`
16×	`sub-neg`
12×	`neg-mul-1`
12×	`neg-sub0`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	130
1	44	126
2	64	126
3	75	126
4	83	126
5	86	126

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (*.f64 a 2))
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))

Outputs
(/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (*.f64 a 2))
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (.f64 a 2))
(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))) b) (.f64 a 2))

Compiler

Compiled 37 to 25 computations (32.4% saved)

soundness161.0ms (3.1%)

Rules

1648×	`div-sub`
1546×	`fma-def`
1212×	`sub-neg`
596×	`associate-*r/`
576×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	779
1	182	675
2	490	671
3	1246	671
4	3197	671
5	7858	671

Stop Event

1×	node limit

Compiler

Compiled 20 to 14 computations (30% saved)

end0.0ms (0%)

preprocess33.0ms (0.6%)

Compiler: Compiled 108 to 70 computations (35.2% saved)

analyze158.0ms (3.1%)

sample1.9s (36.4%)

preprocess1.4s (27.8%)

eval1.0ms (0%)

prune2.0ms (0%)

localize1.5s (28.3%)

eval0.0ms (0%)

prune2.0ms (0%)

regimes16.0ms (0.3%)

regimes12.0ms (0.2%)

simplify6.0ms (0.1%)

soundness161.0ms (3.1%)

end0.0ms (0%)

preprocess33.0ms (0.6%)

Profiling