Details

analyze284.0ms (8.3%)

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
0%	0%	99.9%	0.1%	0%	0%	0%	4
0%	0%	99.9%	0.1%	0%	0%	0%	5
0%	0%	99.9%	0.1%	0%	0%	0%	6
0%	0%	93.6%	0.1%	0%	6.2%	0%	7
6.7%	6.2%	87.4%	0.1%	0%	6.2%	0%	8
11.1%	10.1%	81.1%	0.1%	0%	8.6%	0%	9
18%	15.6%	71%	0.1%	0%	13.3%	0%	10
25.9%	22%	63%	0.1%	0.8%	14%	0%	11
35.5%	29.1%	52.9%	0.1%	1.6%	16.4%	0%	12

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.8s (81.3%)

Results

829.0ms	1192×	body	2048	valid
688.0ms	5542×	body	256	valid
508.0ms	420×	body	4096	valid
372.0ms	751×	body	1024	valid
219.0ms	1069×	body	256	invalid
78.0ms	351×	body	512	valid
72.0ms	617×	body	256	infinite

Bogosity

preprocess80.0ms (2.3%)

Algorithm

2×	egg-herbie

Rules

1160×	`associate-/r*`
892×	`associate-*r/`
866×	`fma-def`
762×	`*-commutative`
728×	`associate-+l-`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	204
1	102	172
2	207	172
3	412	172
4	717	172
5	1212	172
6	2361	172
7	4498	172
0	3	3

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
2

Call 2

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

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify106.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1416×	`associate--l-`
814×	`times-frac`
694×	`fma-neg`
642×	`*-commutative`
562×	`associate-+l-`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	51
1	36	43
2	72	43
3	154	43
4	235	43
5	417	43
6	813	43
7	1436	43
8	2954	43
9	4198	43
10	5402	43
11	6805	43

Stop Event

1×	node limit

Counts

1 → 8

Calls

Call 1

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

eval2.0ms (0.1%)

Compiler: Compiled 127 to 77 computations (39.4% saved)

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	6	2	8
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	7	2	9

Error

47.6%

Counts

9 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	47.6%	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 a 2))
▶	47.4%	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4))) b) (/.f64 1/2 a))

Compiler

Compiled 38 to 26 computations (31.6% saved)

localize22.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	99.7%	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4))) b) (/.f64 1/2 a))
✓	99.6%	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) b)
✓	99.2%	(fma.f64 b b (.f64 (.f64 a c) -4))
✓	65.8%	(sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))

Compiler

Compiled 62 to 30 computations (51.6% saved)

series16.0ms (0.5%)

Counts

4 → 96

Calls

36 calls:

Time	Variable		Point	Expression
2.0ms	b	@	0	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4))) b) (/.f64 1/2 a))
1.0ms	b	@	0	(sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))
1.0ms	a	@	inf	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4))) b) (/.f64 1/2 a))
1.0ms	c	@	inf	(sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))
1.0ms	c	@	inf	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4))) b) (/.f64 1/2 a))

rewrite129.0ms (3.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1730×	`associate-*l/`
850×	`distribute-lft-in`
608×	`associate-/r*`
374×	`associate-/l*`
344×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	120
1	337	114
2	4276	114

Stop Event

1×	node limit

Calls

Call 1

Inputs
(sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))
(fma.f64 b b (.f64 (.f64 a c) -4))
(-.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) b)
(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4))) b) (/.f64 1/2 a))

Outputs
((((x -.f64 (exp.f64 (log1p.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) 1))) (((x .f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) 1))) (((x .f64 1 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) (((x .f64 (pow.f64 (fma.f64 b b (.f64 a (.f64 c -4))) 1/4) (pow.f64 (fma.f64 b b (.f64 a (.f64 c -4))) 1/4)))) (((x .f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))))) (((x .f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) (cbrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))) (((x .f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))))))) (((x .f64 (pow.f64 1 1/2) (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) (((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) 1/2)))) (((x pow.f64 (fma.f64 b b (.f64 a (.f64 c -4))) 1/2))) (((x pow.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) 1))) (((x pow.f64 (pow.f64 (fma.f64 b b (.f64 a (.f64 c -4))) 1/4) 2))) (((x pow.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) 3))) (((x pow.f64 (pow.f64 (fma.f64 b b (.f64 a (.f64 c -4))) 3/2) 1/3))) (((x fabs.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) (((x log.f64 (exp.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))) (((x log.f64 (+.f64 1 (expm1.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))))) (((x cbrt.f64 (pow.f64 (fma.f64 b b (.f64 a (.f64 c -4))) 3/2)))) (((x expm1.f64 (log1p.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))) (((x hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (((x exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))) (((x exp.f64 (.f64 (log.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) 1/2)))) (((x exp.f64 (.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) 1)))) (((x log1p.f64 (expm1.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))))
((((x +.f64 (.f64 a (.f64 c -4)) (.f64 b b)))) (((x +.f64 (.f64 a (.f64 c -4)) (.f64 (.f64 b b) 1)))) (((x +.f64 (.f64 b b) (.f64 a (.f64 c -4))))) (((x +.f64 (.f64 (.f64 b b) 1) (.f64 a (.f64 c -4))))) (((x +.f64 (.f64 1 (.f64 (.f64 b b) 1)) (.f64 a (.f64 c -4))))) (((x -.f64 (exp.f64 (log1p.f64 (.f64 a (.f64 c -4)))) (-.f64 1 (.f64 b b))))) (((x -.f64 (exp.f64 (log1p.f64 (fma.f64 b b (.f64 a (.f64 c -4))))) 1))) (((x -.f64 (+.f64 (.f64 b b) (exp.f64 (log1p.f64 (.f64 a (.f64 c -4))))) 1))) (((x -.f64 (+.f64 (.f64 (.f64 b b) 1) (exp.f64 (log1p.f64 (.f64 a (.f64 c -4))))) 1))) (((x .f64 (fma.f64 b b (.f64 a (.f64 c -4))) 1))) (((x .f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) (((x .f64 1 (fma.f64 b b (.f64 a (.f64 c -4)))))) (((x .f64 (pow.f64 (fma.f64 b b (.f64 a (.f64 c -4))) 1/4) (.f64 (pow.f64 (fma.f64 b b (.f64 a (.f64 c -4))) 1/4) (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))) (((x .f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) 2)))) (((x .f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) (.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))) (((x .f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) 2) (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))))) (((x .f64 (.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) (pow.f64 (fma.f64 b b (.f64 a (.f64 c -4))) 1/4)) (pow.f64 (fma.f64 b b (.f64 a (.f64 c -4))) 1/4)))) (((x .f64 (.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))) (cbrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))) (((x /.f64 (-.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 16 (pow.f64 (.f64 a c) 2))) (-.f64 (.f64 b b) (.f64 a (.f64 c -4)))))) (((x /.f64 (+.f64 (pow.f64 (.f64 a (.f64 c -4)) 3) (pow.f64 (.f64 b b) 3)) (-.f64 (+.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 16 (pow.f64 (.f64 a c) 2))) (.f64 (.f64 b b) (.f64 a (.f64 c -4))))))) (((x /.f64 (.f64 (-.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 16 (pow.f64 (.f64 a c) 2))) 1) (-.f64 (.f64 b b) (.f64 a (.f64 c -4)))))) (((x /.f64 (.f64 (+.f64 (pow.f64 (.f64 a (.f64 c -4)) 3) (pow.f64 (.f64 b b) 3)) 1) (-.f64 (+.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 16 (pow.f64 (.f64 a c) 2))) (.f64 (.f64 b b) (.f64 a (.f64 c -4))))))) (((x pow.f64 (fma.f64 b b (.f64 a (.f64 c -4))) 1))) (((x pow.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) 2))) (((x pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) 3))) (((x pow.f64 (pow.f64 (fma.f64 b b (.f64 a (.f64 c -4))) 2) 1/2))) (((x pow.f64 (pow.f64 (fma.f64 b b (.f64 a (.f64 c -4))) 3) 1/3))) (((x sqrt.f64 (pow.f64 (fma.f64 b b (.f64 a (.f64 c -4))) 2)))) (((x log.f64 (exp.f64 (fma.f64 b b (.f64 a (.f64 c -4))))))) (((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 b b (.f64 a (.f64 c -4)))))))) (((x cbrt.f64 (pow.f64 (fma.f64 b b (.f64 a (.f64 c -4))) 3)))) (((x expm1.f64 (log1p.f64 (fma.f64 b b (.f64 a (.f64 c -4))))))) (((x exp.f64 (log.f64 (fma.f64 b b (.f64 a (.f64 c -4))))))) (((x exp.f64 (.f64 (log.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) 1)))) (((x log1p.f64 (expm1.f64 (fma.f64 b b (.f64 a (*.f64 c -4))))))))
((((x +.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) (neg.f64 b)))) (((x +.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) (.f64 (neg.f64 b) 1)))) (((x +.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) (+.f64 (neg.f64 b) (fma.f64 (neg.f64 b) 1 b))))) (((x +.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) (+.f64 (.f64 (neg.f64 b) 1) (fma.f64 (neg.f64 b) 1 b))))) (((x +.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) (+.f64 (neg.f64 b) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) b))))) (((x +.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) (+.f64 (.f64 (neg.f64 b) 1) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) b))))) (((x +.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) (+.f64 (neg.f64 b) (fma.f64 (neg.f64 (cbrt.f64 b)) (pow.f64 (cbrt.f64 b) 2) b))))) (((x +.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) (+.f64 (.f64 (neg.f64 b) 1) (fma.f64 (neg.f64 (cbrt.f64 b)) (pow.f64 (cbrt.f64 b) 2) b))))) (((x +.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) (.f64 1 (.f64 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Details

analyze284.0ms (8.3%)

sample2.8s (81.3%)

preprocess80.0ms (2.3%)

simplify106.0ms (3.1%)

eval2.0ms (0.1%)

prune2.0ms (0.1%)

localize22.0ms (0.6%)

series16.0ms (0.5%)

rewrite129.0ms (3.8%)

end0.0ms (0%)

Profiling