Metrics for Statistics.Math.RootFinding:ridders from math-functions-0.1.5.2

analyze742.0ms (3.4%)

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
0%	0%	99.8%	0.2%	0%	0%	0%	5
25%	24.9%	74.8%	0.2%	0%	0%	0%	6
25%	24.9%	74.8%	0.2%	0%	0%	0%	7
25%	24.9%	74.8%	0.2%	0%	0%	0%	8
37.5%	37.4%	62.3%	0.2%	0%	0%	0%	9
40.6%	40.5%	59.2%	0.2%	0%	0%	0%	10
51.7%	48.3%	45.2%	0.2%	0%	6.2%	0%	11
51.7%	48.3%	45.2%	0.2%	0%	6.2%	0%	12

Compiler

Compiled 20 to 13 computations (35% saved)

sample20.3s (93.8%)

Results

2.6s	8256×	valid-rival
1.1s	8143×	valid-sollya
596.0ms	2079×	invalid-rival
652.0ms	2043×	invalid-sollya
745.0ms	149×	exit-sollya

Bogosity

preprocess236.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

819×	`fma-neg`
763×	`unsub-neg`
602×	`div-sub`
591×	`times-frac`
514×	`associate-/l*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	103	1384
1	285	1368
2	671	1368
3	1816	1368
4	4847	1368
5	7163	1368

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
(/.f64 (.f64 (.f64 (neg.f64 x) y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
(/.f64 (.f64 (.f64 x (neg.f64 y)) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
(/.f64 (.f64 (.f64 x y) (neg.f64 z)) (sqrt.f64 (-.f64 (.f64 (neg.f64 z) (neg.f64 z)) (.f64 t a))))
(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 (neg.f64 t) a))))
(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t (neg.f64 a)))))
(neg.f64 (/.f64 (.f64 (.f64 (neg.f64 x) y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
(neg.f64 (/.f64 (.f64 (.f64 x (neg.f64 y)) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
(neg.f64 (/.f64 (.f64 (.f64 x y) (neg.f64 z)) (sqrt.f64 (-.f64 (.f64 (neg.f64 z) (neg.f64 z)) (.f64 t a)))))
(neg.f64 (/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 (neg.f64 t) a)))))
(neg.f64 (/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t (neg.f64 a))))))
(/.f64 (.f64 (.f64 y x) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
(/.f64 (.f64 (.f64 z y) x) (sqrt.f64 (-.f64 (.f64 x x) (.f64 t a))))
(/.f64 (.f64 (.f64 t y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 x a))))
(/.f64 (.f64 (.f64 a y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t x))))
(/.f64 (.f64 (.f64 x z) y) (sqrt.f64 (-.f64 (.f64 y y) (.f64 t a))))
(/.f64 (.f64 (.f64 x t) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 y a))))
(/.f64 (.f64 (.f64 x a) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t y))))
(/.f64 (.f64 (.f64 x y) t) (sqrt.f64 (-.f64 (.f64 t t) (.f64 z a))))
(/.f64 (.f64 (.f64 x y) a) (sqrt.f64 (-.f64 (.f64 a a) (.f64 t z))))
(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t))))

Outputs
(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
(.f64 y (/.f64 (.f64 x z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
(.f64 y (/.f64 (.f64 x z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
(/.f64 (.f64 (.f64 (neg.f64 x) y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
(.f64 (.f64 x (neg.f64 y)) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
(.f64 x (.f64 (neg.f64 y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
(.f64 x (.f64 y (/.f64 (neg.f64 z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
(/.f64 (.f64 (.f64 x (neg.f64 y)) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
(.f64 (.f64 x (neg.f64 y)) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
(.f64 x (.f64 (neg.f64 y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
(.f64 x (.f64 y (/.f64 (neg.f64 z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
(/.f64 (.f64 (.f64 x y) (neg.f64 z)) (sqrt.f64 (-.f64 (.f64 (neg.f64 z) (neg.f64 z)) (.f64 t a))))
(.f64 (.f64 x (neg.f64 y)) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
(.f64 x (.f64 (neg.f64 y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
(.f64 x (.f64 y (/.f64 (neg.f64 z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 (neg.f64 t) a))))
(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (+.f64 (.f64 z z) (.f64 t a)))))
(.f64 x (/.f64 (.f64 y z) (sqrt.f64 (fma.f64 z z (*.f64 t a)))))
(/.f64 (.f64 x (.f64 y z)) (sqrt.f64 (fma.f64 z z (*.f64 t a))))
(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (fma.f64 z z (*.f64 t a)))))
(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t (neg.f64 a)))))
(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (+.f64 (.f64 z z) (.f64 t a)))))
(.f64 x (/.f64 (.f64 y z) (sqrt.f64 (fma.f64 z z (*.f64 t a)))))
(/.f64 (.f64 x (.f64 y z)) (sqrt.f64 (fma.f64 z z (*.f64 t a))))
(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (fma.f64 z z (*.f64 t a)))))
(neg.f64 (/.f64 (.f64 (.f64 (neg.f64 x) y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
(.f64 y (/.f64 (.f64 x z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
(neg.f64 (/.f64 (.f64 (.f64 x (neg.f64 y)) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
(.f64 y (/.f64 (.f64 x z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
(neg.f64 (/.f64 (.f64 (.f64 x y) (neg.f64 z)) (sqrt.f64 (-.f64 (.f64 (neg.f64 z) (neg.f64 z)) (.f64 t a)))))
(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
(.f64 y (/.f64 (.f64 x z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
(neg.f64 (/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 (neg.f64 t) a)))))
(/.f64 (.f64 (.f64 x y) (neg.f64 z)) (sqrt.f64 (+.f64 (.f64 z z) (.f64 t a))))
(.f64 x (/.f64 (.f64 z (neg.f64 y)) (sqrt.f64 (fma.f64 z z (*.f64 t a)))))
(neg.f64 (/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t (neg.f64 a))))))
(/.f64 (.f64 (.f64 x y) (neg.f64 z)) (sqrt.f64 (+.f64 (.f64 z z) (.f64 t a))))
(.f64 x (/.f64 (.f64 z (neg.f64 y)) (sqrt.f64 (fma.f64 z z (*.f64 t a)))))
(/.f64 (.f64 (.f64 y x) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
(.f64 y (/.f64 (.f64 x z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
(/.f64 (.f64 (.f64 z y) x) (sqrt.f64 (-.f64 (.f64 x x) (.f64 t a))))
(/.f64 (.f64 x (.f64 y z)) (sqrt.f64 (-.f64 (.f64 x x) (.f64 t a))))
(.f64 y (/.f64 (.f64 x z) (sqrt.f64 (-.f64 (.f64 x x) (.f64 t a)))))
(.f64 y (.f64 x (/.f64 z (sqrt.f64 (-.f64 (.f64 x x) (.f64 t a))))))
(/.f64 (.f64 (.f64 t y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 x a))))
(.f64 (.f64 y t) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 x a)))))
(.f64 z (/.f64 (.f64 y t) (sqrt.f64 (-.f64 (.f64 z z) (.f64 x a)))))
(.f64 y (/.f64 (.f64 z t) (sqrt.f64 (fma.f64 x (neg.f64 a) (*.f64 z z)))))
(/.f64 (.f64 (.f64 a y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t x))))
(/.f64 (.f64 z (.f64 y a)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 x t))))
(.f64 z (/.f64 (.f64 y a) (sqrt.f64 (-.f64 (.f64 z z) (.f64 x t)))))
(.f64 y (.f64 a (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 x t))))))
(/.f64 (.f64 (.f64 x z) y) (sqrt.f64 (-.f64 (.f64 y y) (.f64 t a))))
(.f64 (.f64 x z) (/.f64 y (sqrt.f64 (fma.f64 y y (*.f64 a (neg.f64 t))))))
(.f64 x (/.f64 (.f64 y z) (sqrt.f64 (fma.f64 y y (*.f64 a (neg.f64 t))))))
(.f64 z (.f64 x (/.f64 y (sqrt.f64 (fma.f64 a (neg.f64 t) (*.f64 y y))))))
(.f64 y (.f64 x (/.f64 z (sqrt.f64 (fma.f64 a (neg.f64 t) (*.f64 y y))))))
(/.f64 (.f64 (.f64 x t) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 y a))))
(.f64 (.f64 x t) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 y a)))))
(.f64 x (/.f64 (.f64 z t) (sqrt.f64 (-.f64 (.f64 z z) (.f64 y a)))))
(.f64 x (.f64 z (/.f64 t (sqrt.f64 (fma.f64 z z (neg.f64 (*.f64 y a)))))))
(.f64 x (.f64 z (/.f64 t (sqrt.f64 (-.f64 (.f64 z z) (.f64 y a))))))
(/.f64 (.f64 (.f64 x a) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t y))))
(/.f64 (.f64 x (.f64 z a)) (sqrt.f64 (-.f64 (.f64 z z) (.f64 y t))))
(.f64 x (/.f64 (.f64 z a) (sqrt.f64 (-.f64 (.f64 z z) (.f64 y t)))))
(.f64 a (/.f64 (.f64 x z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 y t)))))
(.f64 z (/.f64 (.f64 x a) (sqrt.f64 (-.f64 (.f64 z z) (.f64 y t)))))
(/.f64 (.f64 (.f64 x y) t) (sqrt.f64 (-.f64 (.f64 t t) (.f64 z a))))
(/.f64 (.f64 x (.f64 y t)) (sqrt.f64 (-.f64 (.f64 t t) (.f64 z a))))
(.f64 x (/.f64 (.f64 y t) (sqrt.f64 (-.f64 (.f64 t t) (.f64 z a)))))
(.f64 x (/.f64 (.f64 y t) (sqrt.f64 (fma.f64 t t (neg.f64 (*.f64 z a))))))
(.f64 x (.f64 y (/.f64 t (sqrt.f64 (-.f64 (.f64 t t) (.f64 z a))))))
(/.f64 (.f64 (.f64 x y) a) (sqrt.f64 (-.f64 (.f64 a a) (.f64 t z))))
(/.f64 (.f64 x (.f64 y a)) (sqrt.f64 (-.f64 (.f64 a a) (.f64 z t))))
(.f64 a (/.f64 (.f64 x y) (sqrt.f64 (-.f64 (.f64 a a) (.f64 z t)))))
(.f64 x (.f64 y (/.f64 a (sqrt.f64 (-.f64 (.f64 a a) (.f64 z t))))))
(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 a t))))
(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
(.f64 y (/.f64 (.f64 x z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))

Symmetry

(negabs x)

(negabs y)

(negabs z)

(sort x y)

(sort t a)

Compiler

Compiled 19 to 12 computations (36.8% saved)

eval0.0ms (0%)

Compiler: Compiled 5 to 5 computations (0% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
	63.1%	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

Compiler

Compiled 38 to 24 computations (36.8% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative`
4×	`sub-neg`
4×	`+-commutative`
3×	`neg-sub0`
3×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	62
1	29	62
2	41	62
3	47	62
4	51	62
5	52	62

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

Outputs
(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))

soundness0.0ms (0%)

Stop Event

1×

fuel

Compiler

Compiled 19 to 12 computations (36.8% saved)

preprocess359.0ms (1.7%)

Remove

(sort t a)

(sort x y)

(negabs z)

(negabs y)

(negabs x)

Compiler

Compiled 524 to 328 computations (37.4% saved)

Statistics.Math.RootFinding:ridders from math-functions-0.1.5.2

analyze742.0ms (3.4%)

sample20.3s (93.8%)

preprocess236.0ms (1.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0%)

soundness0.0ms (0%)

preprocess359.0ms (1.7%)

end0.0ms (0%)

Profiling