Metrics for Numeric.AD.Rank1.Halley:findZero from ad-4.2.4

analyze905.0ms (4.3%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.8%	0.2%	0%	0%	0%	0
0%	0%	99.8%	0.2%	0%	0%	0%	1
0%	0%	99.8%	0.2%	0%	0%	0%	2
0%	0%	99.8%	0.2%	0%	0%	0%	3
0%	0%	99.8%	0.2%	0%	0%	0%	4
25%	25%	74.9%	0.2%	0%	0%	0%	5
25%	25%	74.9%	0.2%	0%	0%	0%	6
31.3%	31.2%	68.6%	0.2%	0%	0%	0%	7
40.6%	40.5%	59.3%	0.2%	0%	0%	0%	8
50%	49.9%	49.9%	0.2%	0%	0%	0%	9
50%	49.9%	49.9%	0.2%	0%	0%	0%	10
54.7%	54.6%	45.2%	0.2%	0%	0%	0%	11
62.5%	62.4%	37.4%	0.2%	0%	0%	0%	12

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample19.1s (91.6%)

Results

2.6s	8256×	valid-rival
1.1s	8188×	valid-sollya
340.0ms	68×	exit-sollya

Bogosity

preprocess541.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

501×	`fma-define`
448×	`fma-neg`
424×	`div-sub`
419×	`associate-/l*`
411×	`times-frac`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	1168
1	241	1124
2	648	1028
3	2149	1008
4	5416	1008
5	7254	1008

Stop Event

1×	node limit

Calls

Call 1

Inputs
(-.f64 x (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 y t))))
(-.f64 x (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 y t))))
(-.f64 (neg.f64 x) (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 y t))))
(-.f64 x (/.f64 (.f64 (.f64 (neg.f64 y) #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 (neg.f64 y) t))))
(-.f64 x (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) (neg.f64 z)) (-.f64 (.f64 (.f64 (neg.f64 z) #s(literal 2 binary64)) (neg.f64 z)) (*.f64 y t))))
(-.f64 x (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 y (neg.f64 t)))))
(neg.f64 (-.f64 (neg.f64 x) (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 y t)))))
(neg.f64 (-.f64 x (/.f64 (.f64 (.f64 (neg.f64 y) #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 (neg.f64 y) t)))))
(neg.f64 (-.f64 x (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) (neg.f64 z)) (-.f64 (.f64 (.f64 (neg.f64 z) #s(literal 2 binary64)) (neg.f64 z)) (*.f64 y t)))))
(neg.f64 (-.f64 x (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 y (neg.f64 t))))))
(-.f64 y (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 x t))))
(-.f64 z (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) x) (-.f64 (.f64 (.f64 x #s(literal 2 binary64)) x) (*.f64 y t))))
(-.f64 t (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 y x))))
(-.f64 x (/.f64 (.f64 (.f64 z #s(literal 2 binary64)) y) (-.f64 (.f64 (.f64 y #s(literal 2 binary64)) y) (*.f64 z t))))
(-.f64 x (/.f64 (.f64 (.f64 t #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 t y))))
(-.f64 x (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) t) (-.f64 (.f64 (.f64 t #s(literal 2 binary64)) t) (*.f64 y z))))

Outputs
(-.f64 x (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 y t))))
(-.f64 x (.f64 (.f64 y #s(literal 2 binary64)) (/.f64 z (-.f64 (.f64 z (.f64 #s(literal 2 binary64) z)) (*.f64 y t)))))
(+.f64 x (.f64 (.f64 y #s(literal -2 binary64)) (/.f64 z (-.f64 (.f64 #s(literal 2 binary64) (.f64 z z)) (*.f64 y t)))))
(fma.f64 (.f64 y #s(literal 2 binary64)) (/.f64 z (fma.f64 z (.f64 z #s(literal -2 binary64)) (*.f64 y t))) x)
(fma.f64 y (.f64 z (/.f64 #s(literal 2 binary64) (fma.f64 z (.f64 z #s(literal -2 binary64)) (*.f64 y t)))) x)
(-.f64 x (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 y t))))
(-.f64 x (.f64 (.f64 y #s(literal 2 binary64)) (/.f64 z (-.f64 (.f64 z (.f64 #s(literal 2 binary64) z)) (*.f64 y t)))))
(+.f64 x (.f64 (.f64 y #s(literal -2 binary64)) (/.f64 z (-.f64 (.f64 #s(literal 2 binary64) (.f64 z z)) (*.f64 y t)))))
(fma.f64 (.f64 y #s(literal 2 binary64)) (/.f64 z (fma.f64 z (.f64 z #s(literal -2 binary64)) (*.f64 y t))) x)
(fma.f64 y (.f64 z (/.f64 #s(literal 2 binary64) (fma.f64 z (.f64 z #s(literal -2 binary64)) (*.f64 y t)))) x)
(-.f64 (neg.f64 x) (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 y t))))
(-.f64 (neg.f64 x) (.f64 (.f64 y #s(literal 2 binary64)) (/.f64 z (-.f64 (.f64 z (.f64 #s(literal 2 binary64) z)) (*.f64 y t)))))
(fma.f64 #s(literal -1 binary64) x (.f64 (.f64 y #s(literal -2 binary64)) (/.f64 z (-.f64 (.f64 #s(literal 2 binary64) (.f64 z z)) (*.f64 y t)))))
(-.f64 (.f64 y (/.f64 (.f64 #s(literal 2 binary64) z) (fma.f64 z (.f64 z #s(literal -2 binary64)) (.f64 y t)))) x)
(-.f64 (.f64 y (.f64 z (/.f64 #s(literal 2 binary64) (fma.f64 z (.f64 z #s(literal -2 binary64)) (.f64 y t))))) x)
(-.f64 x (/.f64 (.f64 (.f64 (neg.f64 y) #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 (neg.f64 y) t))))
(-.f64 x (.f64 (neg.f64 (.f64 y #s(literal 2 binary64))) (/.f64 z (+.f64 (.f64 z (.f64 #s(literal 2 binary64) z)) (*.f64 y t)))))
(+.f64 x (.f64 y (/.f64 (.f64 #s(literal 2 binary64) z) (fma.f64 z (.f64 #s(literal 2 binary64) z) (.f64 y t)))))
(fma.f64 (.f64 y #s(literal 2 binary64)) (/.f64 z (fma.f64 #s(literal 2 binary64) (.f64 z z) (*.f64 y t))) x)
(fma.f64 y (.f64 z (/.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) (.f64 z z) (*.f64 y t)))) x)
(-.f64 x (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) (neg.f64 z)) (-.f64 (.f64 (.f64 (neg.f64 z) #s(literal 2 binary64)) (neg.f64 z)) (*.f64 y t))))
(-.f64 x (/.f64 (.f64 y (.f64 #s(literal 2 binary64) (neg.f64 z))) (-.f64 (.f64 (neg.f64 z) (.f64 #s(literal 2 binary64) (neg.f64 z))) (*.f64 y t))))
(-.f64 x (.f64 y (/.f64 (.f64 z #s(literal -2 binary64)) (-.f64 (.f64 (neg.f64 z) (.f64 z #s(literal -2 binary64))) (*.f64 y t)))))
(fma.f64 (.f64 y #s(literal -2 binary64)) (/.f64 z (fma.f64 z (.f64 z #s(literal -2 binary64)) (*.f64 y t))) x)
(fma.f64 y (/.f64 (.f64 z #s(literal -2 binary64)) (fma.f64 z (.f64 z #s(literal -2 binary64)) (*.f64 y t))) x)
(-.f64 x (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 y (neg.f64 t)))))
(-.f64 x (.f64 (.f64 y #s(literal 2 binary64)) (/.f64 z (+.f64 (.f64 z (.f64 #s(literal 2 binary64) z)) (*.f64 y t)))))
(+.f64 x (.f64 z (/.f64 (.f64 y #s(literal -2 binary64)) (fma.f64 z (.f64 #s(literal 2 binary64) z) (.f64 y t)))))
(fma.f64 (.f64 y #s(literal -2 binary64)) (/.f64 z (fma.f64 #s(literal 2 binary64) (.f64 z z) (*.f64 y t))) x)
(neg.f64 (-.f64 (neg.f64 x) (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 y t)))))
(-.f64 x (/.f64 (.f64 y (.f64 #s(literal 2 binary64) (neg.f64 z))) (-.f64 (.f64 (neg.f64 z) (.f64 #s(literal 2 binary64) (neg.f64 z))) (*.f64 y t))))
(-.f64 x (.f64 y (/.f64 (.f64 z #s(literal -2 binary64)) (-.f64 (.f64 (neg.f64 z) (.f64 z #s(literal -2 binary64))) (*.f64 y t)))))
(fma.f64 (.f64 y #s(literal -2 binary64)) (/.f64 z (fma.f64 z (.f64 z #s(literal -2 binary64)) (*.f64 y t))) x)
(fma.f64 y (/.f64 (.f64 z #s(literal -2 binary64)) (fma.f64 z (.f64 z #s(literal -2 binary64)) (*.f64 y t))) x)
(neg.f64 (-.f64 x (/.f64 (.f64 (.f64 (neg.f64 y) #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 (neg.f64 y) t)))))
(neg.f64 (-.f64 x (.f64 (neg.f64 (.f64 y #s(literal 2 binary64))) (/.f64 z (+.f64 (.f64 z (.f64 #s(literal 2 binary64) z)) (*.f64 y t))))))
(+.f64 (neg.f64 x) (.f64 z (/.f64 (.f64 y #s(literal -2 binary64)) (fma.f64 z (.f64 #s(literal 2 binary64) z) (.f64 y t)))))
(neg.f64 (fma.f64 (.f64 y #s(literal 2 binary64)) (/.f64 z (fma.f64 #s(literal 2 binary64) (.f64 z z) (*.f64 y t))) x))
(neg.f64 (fma.f64 y (.f64 z (/.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) (.f64 z z) (*.f64 y t)))) x))
(neg.f64 (-.f64 x (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) (neg.f64 z)) (-.f64 (.f64 (.f64 (neg.f64 z) #s(literal 2 binary64)) (neg.f64 z)) (*.f64 y t)))))
(-.f64 (neg.f64 x) (.f64 (.f64 y #s(literal 2 binary64)) (/.f64 z (-.f64 (.f64 z (.f64 #s(literal 2 binary64) z)) (*.f64 y t)))))
(fma.f64 #s(literal -1 binary64) x (.f64 (.f64 y #s(literal -2 binary64)) (/.f64 z (-.f64 (.f64 #s(literal 2 binary64) (.f64 z z)) (*.f64 y t)))))
(-.f64 (.f64 y (/.f64 (.f64 #s(literal 2 binary64) z) (fma.f64 z (.f64 z #s(literal -2 binary64)) (.f64 y t)))) x)
(-.f64 (.f64 y (.f64 z (/.f64 #s(literal 2 binary64) (fma.f64 z (.f64 z #s(literal -2 binary64)) (.f64 y t))))) x)
(neg.f64 (-.f64 x (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 y (neg.f64 t))))))
(neg.f64 (-.f64 x (.f64 (.f64 y #s(literal 2 binary64)) (/.f64 z (+.f64 (.f64 z (.f64 #s(literal 2 binary64) z)) (*.f64 y t))))))
(+.f64 (neg.f64 x) (.f64 y (/.f64 (.f64 #s(literal 2 binary64) z) (fma.f64 z (.f64 #s(literal 2 binary64) z) (.f64 y t)))))
(-.f64 (.f64 y (.f64 z (/.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) (.f64 z z) (.f64 y t))))) x)
(-.f64 y (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 x t))))
(-.f64 y (.f64 (.f64 x #s(literal 2 binary64)) (/.f64 z (-.f64 (.f64 z (.f64 #s(literal 2 binary64) z)) (*.f64 x t)))))
(-.f64 y (.f64 x (/.f64 (.f64 #s(literal 2 binary64) z) (-.f64 (.f64 #s(literal 2 binary64) (.f64 z z)) (*.f64 x t)))))
(fma.f64 (.f64 x #s(literal -2 binary64)) (/.f64 z (-.f64 (.f64 #s(literal 2 binary64) (.f64 z z)) (.f64 x t))) y)
(fma.f64 x (/.f64 (.f64 #s(literal 2 binary64) z) (fma.f64 x t (.f64 z (*.f64 z #s(literal -2 binary64))))) y)
(-.f64 z (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) x) (-.f64 (.f64 (.f64 x #s(literal 2 binary64)) x) (*.f64 y t))))
(-.f64 z (/.f64 (.f64 x (.f64 y #s(literal 2 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 2 binary64))) (*.f64 y t))))
(+.f64 z (.f64 (.f64 y #s(literal -2 binary64)) (/.f64 x (-.f64 (.f64 x (.f64 x #s(literal 2 binary64))) (*.f64 y t)))))
(fma.f64 (.f64 y #s(literal -2 binary64)) (/.f64 x (fma.f64 x (.f64 x #s(literal 2 binary64)) (neg.f64 (*.f64 y t)))) z)
(fma.f64 x (/.f64 (.f64 y #s(literal 2 binary64)) (fma.f64 y t (.f64 x (*.f64 x #s(literal -2 binary64))))) z)
(-.f64 t (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 y x))))
(-.f64 t (/.f64 (.f64 y (.f64 #s(literal 2 binary64) z)) (-.f64 (.f64 z (.f64 #s(literal 2 binary64) z)) (*.f64 x y))))
(+.f64 t (/.f64 (.f64 y (.f64 z #s(literal -2 binary64))) (-.f64 (.f64 #s(literal 2 binary64) (.f64 z z)) (*.f64 x y))))
(fma.f64 (.f64 y #s(literal 2 binary64)) (/.f64 z (+.f64 (.f64 x y) (.f64 z (.f64 z #s(literal -2 binary64))))) t)
(fma.f64 (.f64 #s(literal 2 binary64) z) (/.f64 y (fma.f64 x y (.f64 z (*.f64 z #s(literal -2 binary64))))) t)
(-.f64 x (/.f64 (.f64 (.f64 z #s(literal 2 binary64)) y) (-.f64 (.f64 (.f64 y #s(literal 2 binary64)) y) (*.f64 z t))))
(-.f64 x (.f64 (.f64 #s(literal 2 binary64) z) (/.f64 y (-.f64 (.f64 y (.f64 y #s(literal 2 binary64))) (*.f64 z t)))))
(+.f64 x (/.f64 (.f64 y (.f64 z #s(literal -2 binary64))) (-.f64 (.f64 y (.f64 y #s(literal 2 binary64))) (*.f64 z t))))
(fma.f64 (.f64 z #s(literal -2 binary64)) (/.f64 y (-.f64 (.f64 y (.f64 y #s(literal 2 binary64))) (.f64 z t))) x)
(fma.f64 #s(literal 2 binary64) (/.f64 (.f64 y z) (fma.f64 z t (.f64 y (*.f64 y #s(literal -2 binary64))))) x)
(-.f64 x (/.f64 (.f64 (.f64 t #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 t y))))
(-.f64 x (.f64 (.f64 #s(literal 2 binary64) t) (/.f64 z (-.f64 (.f64 z (.f64 #s(literal 2 binary64) z)) (*.f64 y t)))))
(-.f64 x (.f64 t (.f64 #s(literal 2 binary64) (/.f64 z (-.f64 (.f64 #s(literal 2 binary64) (.f64 z z)) (*.f64 y t))))))
(fma.f64 (.f64 #s(literal 2 binary64) t) (/.f64 z (fma.f64 z (.f64 z #s(literal -2 binary64)) (*.f64 y t))) x)
(fma.f64 t (.f64 z (/.f64 #s(literal 2 binary64) (fma.f64 z (.f64 z #s(literal -2 binary64)) (*.f64 y t)))) x)
(-.f64 x (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) t) (-.f64 (.f64 (.f64 t #s(literal 2 binary64)) t) (*.f64 y z))))
(-.f64 x (/.f64 (.f64 y (.f64 #s(literal 2 binary64) t)) (-.f64 (.f64 t (.f64 #s(literal 2 binary64) t)) (*.f64 y z))))
(-.f64 x (.f64 t (/.f64 (.f64 y #s(literal 2 binary64)) (-.f64 (.f64 t (.f64 #s(literal 2 binary64) t)) (*.f64 y z)))))
(fma.f64 (.f64 y #s(literal -2 binary64)) (/.f64 t (fma.f64 z (neg.f64 y) (.f64 #s(literal 2 binary64) (*.f64 t t)))) x)
(fma.f64 y (/.f64 (.f64 #s(literal 2 binary64) t) (fma.f64 y z (.f64 t (*.f64 t #s(literal -2 binary64))))) x)

Compiler

Compiled 21 to 13 computations (38.1% saved)

eval1.0ms (0%)

Compiler: Compiled 4 to 4 computations (0% saved)

prune3.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
	79.5%	(-.f64 x (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 y t))))

Compiler

Compiled 42 to 26 computations (38.1% saved)

simplify17.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

105×	`unsub-neg`
69×	`neg-mul-1`
63×	`distribute-lft-neg-in`
35×	`distribute-rgt-neg-in`
28×	`remove-double-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	70
1	33	70
2	52	70
3	74	70
4	120	70
5	170	70
6	211	70
7	300	70
8	473	70
9	559	70

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 x (/.f64 (.f64 (.f64 y #s(literal 2 binary64)) z) (-.f64 (.f64 (.f64 z #s(literal 2 binary64)) z) (*.f64 y t))))

Outputs

(-.f64 x (/.f64 (*.f64 (*.f64 y #s(literal 2 binary64)) z) (-.f64 (*.f64 (*.f64 z #s(literal 2 binary64)) z) (*.f64 y t))))

(-.f64 x (/.f64 (*.f64 (*.f64 y #s(literal 2 binary64)) z) (-.f64 (*.f64 z (*.f64 #s(literal 2 binary64) z)) (*.f64 y t))))

(-.f64 x (/.f64 (*.f64 (*.f64 y #s(literal 2 binary64)) z) (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) z) z) (*.f64 y t))))

soundness1.0ms (0%)

Stop Event

1×

fuel

Compiler

Compiled 21 to 13 computations (38.1% saved)

preprocess291.0ms (1.4%)

Compiler: Compiled 118 to 76 computations (35.6% saved)

Numeric.AD.Rank1.Halley:findZero from ad-4.2.4

analyze905.0ms (4.3%)

sample19.1s (91.6%)

preprocess541.0ms (2.6%)

eval1.0ms (0%)

prune3.0ms (0%)

simplify17.0ms (0.1%)

soundness1.0ms (0%)

preprocess291.0ms (1.4%)

end0.0ms (0%)

Profiling