Details

analyze2.2s (36.4%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	199.7%	-99.7%	0%	0%	0%	1
0%	0%	399.4%	-299.4%	0%	0%	0%	2
0%	0%	798.8%	-698.8%	0%	0%	0%	3
0%	0%	1597.7%	-1497.7%	0%	0%	0%	4
0%	0%	3195.3%	-3095.3%	0%	0%	0%	5
0%	0%	6390.6%	-6290.6%	0%	0%	0%	6
0%	0%	12781.3%	-12681.3%	0%	0%	0%	7
0%	0%	25562.5%	-25462.5%	0%	0%	0%	8
0%	0%	51125%	-51025%	0%	0%	0%	9
0%	0%	102250.1%	-102150.1%	0%	0%	0%	10
0%	0%	204500.1%	-204400.1%	0%	0%	0%	11
0%	0%	409000.3%	-408900.3%	0%	0%	0%	12

Compiler

Compiled 42 to 27 computations (35.7% saved)

sample3.5s (59.7%)

Results

2.5s	7543×	body	256	valid
770.0ms	2864×	body	256	invalid
267.0ms	713×	body	256	infinite

Bogosity

preprocess91.0ms (1.5%)

Algorithm

2×	egg-herbie

Rules

1154×	`associate-/l*`
1146×	`associate-/r*`
1138×	`div-sub`
982×	`fma-neg`
878×	`fma-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	444
1	148	396
2	414	396
3	943	380
4	1726	380
5	3260	380
6	7715	380
0	3	3

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
2

Call 2

Inputs
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
(if (>=.f64 a 0) (/.f64 (-.f64 (neg.f64 a) (sqrt.f64 (-.f64 (.f64 a a) (.f64 (.f64 4 b) c)))) (.f64 2 b)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 a) (sqrt.f64 (-.f64 (.f64 a a) (.f64 (.f64 4 b) c))))))
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 c) a)))) (.f64 2 c)) (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 c) a))))))
(if (>=.f64 c 0) (/.f64 (-.f64 (neg.f64 c) (sqrt.f64 (-.f64 (.f64 c c) (.f64 (.f64 4 a) b)))) (.f64 2 a)) (/.f64 (.f64 2 b) (+.f64 (neg.f64 c) (sqrt.f64 (-.f64 (.f64 c c) (.f64 (.f64 4 a) b))))))

Outputs
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 a 2)) (/.f64 (.f64 c 2) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))) (.f64 a 2)) (.f64 (/.f64 2 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b)) c))
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))) (.f64 a 2)) (.f64 c (/.f64 2 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b))))
(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))) a)) (.f64 c (/.f64 2 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b))))
(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)) (.f64 -2 (/.f64 c (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))))
(if (>=.f64 b 0) (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 -1/2 a)) (.f64 c (/.f64 -2 (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))))
(if (>=.f64 a 0) (/.f64 (-.f64 (neg.f64 a) (sqrt.f64 (-.f64 (.f64 a a) (.f64 (.f64 4 b) c)))) (.f64 2 b)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 a) (sqrt.f64 (-.f64 (.f64 a a) (.f64 (.f64 4 b) c))))))
(if (>=.f64 a 0) (/.f64 (-.f64 (neg.f64 a) (sqrt.f64 (-.f64 (.f64 a a) (.f64 c (.f64 b 4))))) (.f64 b 2)) (/.f64 (.f64 c 2) (+.f64 (neg.f64 a) (sqrt.f64 (-.f64 (.f64 a a) (.f64 c (.f64 b 4)))))))
(if (>=.f64 a 0) (/.f64 (-.f64 (neg.f64 a) (sqrt.f64 (fma.f64 a a (.f64 c (.f64 b -4))))) (.f64 b 2)) (.f64 (/.f64 2 (-.f64 (sqrt.f64 (fma.f64 a a (.f64 c (.f64 b -4)))) a)) c))
(if (>=.f64 a 0) (/.f64 (-.f64 (neg.f64 a) (sqrt.f64 (fma.f64 a a (.f64 b (.f64 c -4))))) (.f64 b 2)) (.f64 (/.f64 c (-.f64 (sqrt.f64 (fma.f64 a a (.f64 b (.f64 c -4)))) a)) 2))
(if (>=.f64 a 0) (.f64 -1/2 (/.f64 (+.f64 a (sqrt.f64 (fma.f64 b (.f64 c -4) (.f64 a a)))) b)) (.f64 2 (/.f64 c (-.f64 (sqrt.f64 (fma.f64 b (.f64 c -4) (.f64 a a))) a))))
(if (>=.f64 a 0) (.f64 -1/2 (/.f64 (+.f64 a (sqrt.f64 (fma.f64 b (.f64 c -4) (.f64 a a)))) b)) (/.f64 (.f64 c -2) (-.f64 a (sqrt.f64 (fma.f64 b (.f64 c -4) (.f64 a a))))))
(if (>=.f64 a 0) (.f64 -1/2 (/.f64 (+.f64 a (sqrt.f64 (fma.f64 a a (.f64 b (.f64 c -4))))) b)) (/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (fma.f64 a a (.f64 b (.f64 c -4)))) a)))
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 c) a)))) (.f64 2 c)) (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 c) a))))))
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))) (.f64 c 2)) (/.f64 (.f64 a 2) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a)))))))
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))) (.f64 c 2)) (.f64 (/.f64 2 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b)) a))
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))) (.f64 c 2)) (/.f64 (.f64 a 2) (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b)))
(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))) c)) (/.f64 (.f64 a 2) (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b)))
(if (>=.f64 b 0) (.f64 (/.f64 -1/2 c) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (.f64 2 (/.f64 a (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))))
(if (>=.f64 b 0) (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 -1/2 c)) (.f64 a (/.f64 -2 (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))))
(if (>=.f64 c 0) (/.f64 (-.f64 (neg.f64 c) (sqrt.f64 (-.f64 (.f64 c c) (.f64 (.f64 4 a) b)))) (.f64 2 a)) (/.f64 (.f64 2 b) (+.f64 (neg.f64 c) (sqrt.f64 (-.f64 (.f64 c c) (.f64 (.f64 4 a) b))))))
(if (>=.f64 c 0) (/.f64 (-.f64 (neg.f64 c) (sqrt.f64 (-.f64 (.f64 c c) (.f64 b (.f64 4 a))))) (.f64 a 2)) (/.f64 (.f64 b 2) (+.f64 (neg.f64 c) (sqrt.f64 (-.f64 (.f64 c c) (.f64 b (.f64 4 a)))))))
(if (>=.f64 c 0) (/.f64 (-.f64 (neg.f64 c) (sqrt.f64 (fma.f64 c c (.f64 b (.f64 a -4))))) (.f64 a 2)) (/.f64 b (/.f64 (-.f64 (sqrt.f64 (fma.f64 c c (.f64 b (*.f64 a -4)))) c) 2)))
(if (>=.f64 c 0) (/.f64 (-.f64 (neg.f64 c) (sqrt.f64 (fma.f64 b (.f64 a -4) (.f64 c c)))) (.f64 a 2)) (.f64 (/.f64 b (-.f64 (sqrt.f64 (fma.f64 b (.f64 a -4) (.f64 c c))) c)) 2))
(if (>=.f64 c 0) (.f64 -1/2 (/.f64 (+.f64 c (sqrt.f64 (fma.f64 b (.f64 a -4) (.f64 c c)))) a)) (.f64 2 (/.f64 b (-.f64 (sqrt.f64 (fma.f64 b (.f64 a -4) (.f64 c c))) c))))
(if (>=.f64 c 0) (.f64 -1/2 (/.f64 (+.f64 c (sqrt.f64 (fma.f64 b (.f64 a -4) (.f64 c c)))) a)) (/.f64 (.f64 b -2) (-.f64 c (sqrt.f64 (fma.f64 b (.f64 a -4) (.f64 c c))))))

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify127.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

3498×	`fma-def`
1224×	`div-sub`
1014×	`times-frac`
746×	`sub-neg`
718×	`distribute-rgt-in`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	26	111
1	52	99
2	128	99
3	309	95
4	550	95
5	987	95
6	2043	95
7	3787	95
8	5009	95
9	6435	95
10	7982	95

Stop Event

1×	node limit

Counts

1 → 7

Calls

Call 1

Inputs

(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)) (/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))

Outputs
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 a 2)) (/.f64 2 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c)))
(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (.f64 a 2)) (/.f64 c (/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 c (*.f64 a -4)))) b) 2)))
(if (>=.f64 b 0) (neg.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (.f64 -4 c))))) (.f64 a 2))) (.f64 (/.f64 c (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 -4 c)))) b)) 2))
(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))) a)) (.f64 2 (/.f64 c (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b))))
(if (>=.f64 b 0) (.f64 (/.f64 -1/2 a) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))))) (.f64 c (/.f64 -2 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))))))
(if (>=.f64 b 0) (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))) a)) (.f64 c (/.f64 -2 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))))))

eval3.0ms (0.1%)

Compiler: Compiled 251 to 152 computations (39.4% saved)

prune5.0ms (0.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	4	3	7
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	4	4	8

Accurracy

73.1%

Counts

8 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	73.1%	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
▶	72.6%	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 a 2)) (/.f64 2 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c)))
▶	72.9%	(if (>=.f64 b 0) (.f64 (/.f64 -1/2 a) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))))) (.f64 c (/.f64 -2 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))))))
▶	73.1%	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
▶	72.6%	(if (>=.f64 b 0) (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 a 2)) (/.f64 2 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c)))
▶	72.9%	(if (>=.f64 b 0) (.f64 (/.f64 -1/2 a) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))))) (.f64 c (/.f64 -2 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))))))

Compiler

Compiled 238 to 150 computations (37% saved)

localize2.0ms (0%)

Compiler: Compiled 443 to 229 computations (48.3% saved)

jeff quadratic root 1

Details

analyze2.2s (36.4%)

sample3.5s (59.7%)

preprocess91.0ms (1.5%)

simplify127.0ms (2.1%)

eval3.0ms (0.1%)

prune5.0ms (0.1%)

localize2.0ms (0%)

end0.0ms (0%)

Profiling