Metrics for Data.Random.Distribution.Normal:normalTail from random-fu-0.2.6.2

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample589.0ms (60.1%)

Memory

-14.2MiB live, 660.8MiB allocated; 164ms collecting garbage

Samples

376.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 111.0ms

ival-mult!: 69.0ms (62.3% of total)

ival-add!: 40.0ms (36.1% of total)

adjust: 2.0ms (1.8% of total)

Bogosity

preprocess60.0ms (6.1%)

Memory

-4.2MiB live, 39.5MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	48
1	52	45
2	140	43
3	248	42
4	557	42
5	2382	42

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)

Symmetry

(abs x)

Compiler

Compiled 10 to 10 computations (0% saved)

series4.0ms (0.4%)

Memory

5.4MiB live, 5.4MiB allocated; 0ms collecting garbage

Counts

5 → 12

Calls

Call 1

Inputs
(+.f64 (+.f64 (*.f64 x x) y) y)
(+.f64 (*.f64 x x) y)
(*.f64 x x)
x
y

Outputs
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* 2 y)))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (+ (* 2 y) (pow x 2))))
#s(approx (+ (* x x) y) #s(hole binary64 y))
#s(approx (+ (* x x) y) #s(hole binary64 (+ y (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))))
#s(approx (+ (* x x) y) #s(hole binary64 (* (pow x 2) (+ 1 (/ y (pow x 2))))))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* y (+ 2 (/ (pow x 2) y)))))
#s(approx (+ (* x x) y) #s(hole binary64 (* y (+ 1 (/ (pow x 2) y)))))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))))
#s(approx (+ (* x x) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((+ (+ (* x x) y) y) (+ (* x x) y) (* x x) x y)
1.0ms	x	@	-inf	((+ (+ (* x x) y) y) (+ (* x x) y) (* x x) x y)
1.0ms	x	@	0	((+ (+ (* x x) y) y) (+ (* x x) y) (* x x) x y)
1.0ms	y	@	0	((+ (+ (* x x) y) y) (+ (* x x) y) (* x x) x y)
1.0ms	y	@	-inf	((+ (+ (* x x) y) y) (+ (* x x) y) (* x x) x y)

rewrite85.0ms (8.7%)

Memory

-0.7MiB live, 98.2MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	181
0	48	177
1	227	177
0	1983	160

Stop Event

1×	iter-limit
1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

17 → 130

Calls

Call 1

Inputs
(+.f64 (+.f64 (*.f64 x x) y) y)
(+.f64 (*.f64 x x) y)
(*.f64 x x)
x
y
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* 2 y)))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (+ (* 2 y) (pow x 2))))
#s(approx (+ (* x x) y) #s(hole binary64 y))
#s(approx (+ (* x x) y) #s(hole binary64 (+ y (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))))
#s(approx (+ (* x x) y) #s(hole binary64 (* (pow x 2) (+ 1 (/ y (pow x 2))))))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* y (+ 2 (/ (pow x 2) y)))))
#s(approx (+ (* x x) y) #s(hole binary64 (* y (+ 1 (/ (pow x 2) y)))))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))))
#s(approx (+ (* x x) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))))

Outputs
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 y y) #s(literal 4 binary64))) (-.f64 (.f64 x x) (+.f64 y y)))
(/.f64 (-.f64 (.f64 y y) (.f64 (fma.f64 x x y) (fma.f64 x x y))) (-.f64 y (fma.f64 x x y)))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 y y) #s(literal 4 binary64)) (.f64 (.f64 (.f64 x x) x) x))) (neg.f64 (+.f64 y (-.f64 y (.f64 x x)))))
(/.f64 (neg.f64 (*.f64 (+.f64 (fma.f64 x x y) y) (-.f64 (fma.f64 x x y) y))) (neg.f64 (-.f64 (fma.f64 x x y) y)))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 y y) y) #s(literal 8 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)))) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) (+.f64 y y)) (.f64 (*.f64 y y) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 y y) y (pow.f64 (fma.f64 x x y) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (fma.f64 x x y) (fma.f64 x x y) (.f64 y (-.f64 y (fma.f64 x x y))))))
(/.f64 (-.f64 (.f64 (.f64 y y) #s(literal 4 binary64)) (.f64 (.f64 (.f64 x x) x) x)) (+.f64 y (-.f64 y (.f64 x x))))
(/.f64 (*.f64 (+.f64 (fma.f64 x x y) y) (-.f64 (fma.f64 x x y) y)) (-.f64 (fma.f64 x x y) y))
(/.f64 (fma.f64 (.f64 (.f64 y y) y) #s(literal 8 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x))) (fma.f64 (.f64 (.f64 x x) x) x (-.f64 (.f64 (.f64 y y) #s(literal 4 binary64)) (.f64 (*.f64 (+.f64 y y) x) x))))
(/.f64 (fma.f64 (.f64 (.f64 y y) y) #s(literal 8 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x))) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) (+.f64 y y)) (.f64 (*.f64 y y) #s(literal 4 binary64))))
(/.f64 (fma.f64 (.f64 y y) y (pow.f64 (fma.f64 x x y) #s(literal 3 binary64))) (fma.f64 y y (-.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)) (*.f64 (fma.f64 x x y) y))))
(/.f64 (fma.f64 (.f64 y y) y (pow.f64 (fma.f64 x x y) #s(literal 3 binary64))) (fma.f64 (fma.f64 x x y) (fma.f64 x x y) (.f64 y (-.f64 y (fma.f64 x x y)))))
(fma.f64 (.f64 #s(literal 1 binary64) (fabs.f64 x)) (.f64 #s(literal 1 binary64) (fabs.f64 x)) (+.f64 y y))
(fma.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (fabs.f64 x) (+.f64 y y))
(fma.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (.f64 #s(literal 1 binary64) (neg.f64 x)) (+.f64 y y))
(fma.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 x) (+.f64 y y))
(fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x) (+.f64 y y))
(fma.f64 (*.f64 #s(literal 1 binary64) x) x (+.f64 y y))
(fma.f64 (.f64 (fabs.f64 x) #s(literal 1 binary64)) (.f64 (fabs.f64 x) #s(literal 1 binary64)) (+.f64 y y))
(fma.f64 (.f64 (neg.f64 x) #s(literal 1 binary64)) (.f64 (neg.f64 x) #s(literal 1 binary64)) (+.f64 y y))
(fma.f64 (.f64 x #s(literal 1 binary64)) (.f64 x #s(literal 1 binary64)) (+.f64 y y))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) (+.f64 y y))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (+.f64 y y))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (+.f64 y y))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (+.f64 y y))
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 1 binary64)) (+.f64 y y))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (+.f64 y y))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 1 binary64)) (+.f64 y y))
(fma.f64 (neg.f64 x) (neg.f64 x) (+.f64 y y))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) (+.f64 y y))
(fma.f64 (*.f64 x x) #s(literal 1 binary64) (+.f64 y y))
(fma.f64 #s(literal 2 binary64) y (*.f64 x x))
(fma.f64 y #s(literal 2 binary64) (*.f64 x x))
(fma.f64 x (*.f64 x #s(literal 1 binary64)) (+.f64 y y))
(fma.f64 x x (+.f64 y y))
(-.f64 (/.f64 (.f64 (.f64 y y) #s(literal 4 binary64)) (+.f64 y (-.f64 y (.f64 x x)))) (/.f64 (.f64 (.f64 (.f64 x x) x) x) (+.f64 y (-.f64 y (*.f64 x x)))))
(-.f64 (/.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)) (-.f64 (fma.f64 x x y) y)) (/.f64 (.f64 y y) (-.f64 (fma.f64 x x y) y)))
(-.f64 (.f64 x x) (.f64 #s(literal -2 binary64) y))
(-.f64 (.f64 x x) (.f64 (neg.f64 y) #s(literal 2 binary64)))
(-.f64 (+.f64 y y) (*.f64 (neg.f64 x) x))
(+.f64 (/.f64 (.f64 (.f64 (.f64 y y) y) #s(literal 8 binary64)) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) (+.f64 y y)) (.f64 (.f64 y y) #s(literal 4 binary64)))) (/.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) (+.f64 y y)) (.f64 (.f64 y y) #s(literal 4 binary64)))))
(+.f64 (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 3 binary64)) (fma.f64 (fma.f64 x x y) (fma.f64 x x y) (.f64 y (-.f64 y (fma.f64 x x y))))) (/.f64 (.f64 (.f64 y y) y) (fma.f64 (fma.f64 x x y) (fma.f64 x x y) (.f64 y (-.f64 y (fma.f64 x x y))))))
(+.f64 (*.f64 x x) (+.f64 y y))
(+.f64 (+.f64 y y) (*.f64 x x))
(+.f64 (fma.f64 x x y) y)
(+.f64 y (fma.f64 x x y))
(/.f64 (neg.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y))) (neg.f64 (-.f64 (*.f64 x x) y)))
(/.f64 (neg.f64 (.f64 (fma.f64 x x y) (-.f64 y (.f64 x x)))) (neg.f64 (-.f64 y (*.f64 x x))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x) (.f64 (.f64 y y) y))) (neg.f64 (fma.f64 (.f64 (.f64 x x) x) x (.f64 y (-.f64 y (.f64 x x))))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x) (.f64 (.f64 y y) y))) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))
(/.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y)) (-.f64 (*.f64 x x) y))
(/.f64 (.f64 (fma.f64 x x y) (-.f64 y (.f64 x x))) (-.f64 y (*.f64 x x)))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x) (.f64 (.f64 y y) y)) (fma.f64 (.f64 (.f64 x x) x) x (.f64 y (-.f64 y (.f64 x x)))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x) (.f64 (.f64 y y) y)) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))
(fma.f64 (.f64 #s(literal 1 binary64) (fabs.f64 x)) (.f64 #s(literal 1 binary64) (fabs.f64 x)) y)
(fma.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (fabs.f64 x) y)
(fma.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (.f64 #s(literal 1 binary64) (neg.f64 x)) y)
(fma.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 x) y)
(fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x) y)
(fma.f64 (*.f64 #s(literal 1 binary64) x) x y)
(fma.f64 (.f64 (fabs.f64 x) #s(literal 1 binary64)) (.f64 (fabs.f64 x) #s(literal 1 binary64)) y)
(fma.f64 (.f64 (neg.f64 x) #s(literal 1 binary64)) (.f64 (neg.f64 x) #s(literal 1 binary64)) y)
(fma.f64 (.f64 x #s(literal 1 binary64)) (.f64 x #s(literal 1 binary64)) y)
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) y)
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) y)
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) y)
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) y)
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 1 binary64)) y)
(fma.f64 (fabs.f64 x) (fabs.f64 x) y)
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 1 binary64)) y)
(fma.f64 (neg.f64 x) (neg.f64 x) y)
(fma.f64 #s(literal 1 binary64) (*.f64 x x) y)
(fma.f64 (*.f64 x x) #s(literal 1 binary64) y)
(fma.f64 x (*.f64 x #s(literal 1 binary64)) y)
(fma.f64 x x y)
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) x) x) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)))
(-.f64 (/.f64 (.f64 y y) (-.f64 y (.f64 x x))) (/.f64 (.f64 (.f64 (.f64 x x) x) x) (-.f64 y (.f64 x x))))
(-.f64 y (*.f64 (neg.f64 x) x))
(+.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (fma.f64 (.f64 (.f64 x x) x) x (.f64 y (-.f64 y (.f64 x x))))) (/.f64 (.f64 (.f64 y y) y) (fma.f64 (.f64 (.f64 x x) x) x (.f64 y (-.f64 y (*.f64 x x))))))
(+.f64 (/.f64 (.f64 (.f64 y y) y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (/.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))
(+.f64 (*.f64 x x) y)
(+.f64 y (*.f64 x x))
(.f64 (.f64 #s(literal 1 binary64) (fabs.f64 x)) (*.f64 #s(literal 1 binary64) (fabs.f64 x)))
(.f64 (.f64 #s(literal 1 binary64) (fabs.f64 x)) (fabs.f64 x))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (*.f64 #s(literal 1 binary64) (neg.f64 x)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 #s(literal 1 binary64) x) (*.f64 #s(literal 1 binary64) x))
(.f64 (.f64 #s(literal 1 binary64) x) x)
(.f64 (.f64 (fabs.f64 x) #s(literal 1 binary64)) (*.f64 (fabs.f64 x) #s(literal 1 binary64)))
(.f64 (.f64 (neg.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 x) #s(literal 1 binary64)))
(.f64 (.f64 x #s(literal 1 binary64)) (*.f64 x #s(literal 1 binary64)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) #s(literal 1 binary64)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 x (.f64 x #s(literal 1 binary64)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(/.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (+.f64 #s(literal 0 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) #s(literal 0 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
x
y
#s(approx (+ (+ (* x x) y) y) (+.f64 y y))
#s(approx (+ (+ (* x x) y) y) (+.f64 (fma.f64 x x y) y))
#s(approx (+ (* x x) y) y)
#s(approx (+ (* x x) y) (fma.f64 x x y))
#s(approx (* x x) (*.f64 x x))
#s(approx x x)
#s(approx (+ (+ (* x x) y) y) (.f64 (.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal 2 binary64) #s(literal 1 binary64)) x) x))
#s(approx (+ (* x x) y) (.f64 (.f64 (-.f64 (/.f64 y (*.f64 x x)) #s(literal -1 binary64)) x) x))
#s(approx (+ (+ (* x x) y) y) (*.f64 (fma.f64 x (/.f64 x y) #s(literal 2 binary64)) y))
#s(approx (+ (* x x) y) (fma.f64 (/.f64 (*.f64 x x) y) y y))
#s(approx (+ (+ (* x x) y) y) (.f64 (neg.f64 y) (-.f64 (/.f64 (.f64 (neg.f64 x) x) y) #s(literal 2 binary64))))
#s(approx (+ (* x x) y) (.f64 (neg.f64 y) (-.f64 (/.f64 (.f64 (neg.f64 x) x) y) #s(literal 1 binary64))))

eval11.0ms (1.1%)

Memory: 22.2MiB live, 22.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 881 to 360 computations (59.1% saved)

prune4.0ms (0.4%)

Memory

7.6MiB live, 7.6MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	125	2	127

Accuracy

100.0%

Counts

127 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 x x (+.f64 y y))
▶	51.3%	(+.f64 #s(approx (+ (* x x) y) y) y)

Compiler

Compiled 10 to 10 computations (0% saved)

series3.0ms (0.3%)

Memory

6.1MiB live, 6.1MiB allocated; 0ms collecting garbage

Counts

6 → 12

Calls

Call 1

Inputs
(+.f64 #s(approx (+ (* x x) y) y) y)
#s(approx (+ (* x x) y) y)
y
(fma.f64 x x (+.f64 y y))
x
(+.f64 y y)

Outputs
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* 2 y)))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (+ (* 2 y) (pow x 2))))
#s(approx (+ (* x x) y) #s(hole binary64 y))
#s(approx (+ (* x x) y) #s(hole binary64 (+ y (pow x 2))))
#s(approx x #s(hole binary64 x))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (pow x 2)))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))))
#s(approx (+ (* x x) y) #s(hole binary64 (* (pow x 2) (+ 1 (/ y (pow x 2))))))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* y (+ 2 (/ (pow x 2) y)))))
#s(approx (+ (* x x) y) #s(hole binary64 (* y (+ 1 (/ (pow x 2) y)))))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))))
#s(approx (+ (* x x) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	((+ (+ (* x x) y) y) (+ (* x x) y) y (+ (* x x) (+ y y)) x (+ y y))
1.0ms	x	@	inf	((+ (+ (* x x) y) y) (+ (* x x) y) y (+ (* x x) (+ y y)) x (+ y y))
0.0ms	x	@	-inf	((+ (+ (* x x) y) y) (+ (* x x) y) y (+ (* x x) (+ y y)) x (+ y y))
0.0ms	y	@	inf	((+ (+ (* x x) y) y) (+ (* x x) y) y (+ (* x x) (+ y y)) x (+ y y))
0.0ms	y	@	0	((+ (+ (* x x) y) y) (+ (* x x) y) y (+ (* x x) (+ y y)) x (+ y y))

rewrite47.0ms (4.8%)

Memory

-26.4MiB live, 20.3MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	195
0	48	184
0	258	175

Stop Event

1×	iter-limit
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

18 → 40

Calls

Call 1

Inputs
(+.f64 #s(approx (+ (* x x) y) y) y)
#s(approx (+ (* x x) y) y)
y
(fma.f64 x x (+.f64 y y))
x
(+.f64 y y)
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* 2 y)))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (+ (* 2 y) (pow x 2))))
#s(approx (+ (* x x) y) #s(hole binary64 y))
#s(approx (+ (* x x) y) #s(hole binary64 (+ y (pow x 2))))
#s(approx x #s(hole binary64 x))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (pow x 2)))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))))
#s(approx (+ (* x x) y) #s(hole binary64 (* (pow x 2) (+ 1 (/ y (pow x 2))))))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* y (+ 2 (/ (pow x 2) y)))))
#s(approx (+ (* x x) y) #s(hole binary64 (* y (+ 1 (/ (pow x 2) y)))))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))))
#s(approx (+ (* x x) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))))

Outputs
(/.f64 (-.f64 (.f64 #s(approx (+ ( x x) y) y) #s(approx (+ (* x x) y) y)) (.f64 y y)) (-.f64 #s(approx (+ ( x x) y) y) y))
(/.f64 (+.f64 (pow.f64 #s(approx (+ (* x x) y) y) #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 #s(approx (+ (* x x) y) y) #s(approx (+ (* x x) y) y) (-.f64 (.f64 y y) (.f64 #s(approx (+ (* x x) y) y) y))))
(+.f64 #s(approx (+ (* x x) y) y) y)
(+.f64 y #s(approx (+ (* x x) y) y))
#s(approx (+ (* x x) y) y)
y
(/.f64 (-.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)) (.f64 y y)) (-.f64 (fma.f64 x x y) y))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (+.f64 y y) (+.f64 y y))) (-.f64 (*.f64 x x) (+.f64 y y)))
(/.f64 (-.f64 (.f64 (+.f64 y y) (+.f64 y y)) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (+.f64 y y) (*.f64 x x)))
(/.f64 (+.f64 (pow.f64 (fma.f64 x x y) #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (fma.f64 x x y) (fma.f64 x x y) (-.f64 (.f64 y y) (.f64 (fma.f64 x x y) y))))
(/.f64 (+.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) (pow.f64 (+.f64 y y) #s(literal 3 binary64))) (fma.f64 (.f64 x x) (.f64 x x) (-.f64 (.f64 (+.f64 y y) (+.f64 y y)) (.f64 (.f64 x x) (+.f64 y y)))))
(/.f64 (+.f64 (pow.f64 (+.f64 y y) #s(literal 3 binary64)) (pow.f64 (.f64 x x) #s(literal 3 binary64))) (fma.f64 (+.f64 y y) (+.f64 y y) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (+.f64 y y) (.f64 x x)))))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (+.f64 y y))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (+.f64 y y))
(fma.f64 (neg.f64 x) (neg.f64 x) (+.f64 y y))
(fma.f64 #s(literal 2 binary64) y (*.f64 x x))
(fma.f64 y #s(literal 2 binary64) (*.f64 x x))
(fma.f64 x x (+.f64 y y))
(+.f64 (*.f64 x x) (+.f64 y y))
(+.f64 (+.f64 y y) (*.f64 x x))
(+.f64 (fma.f64 x x y) y)
(+.f64 y (fma.f64 x x y))
x
(*.f64 #s(literal 2 binary64) y)
(*.f64 y #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 y y) (.f64 y y)) (-.f64 y y))
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 y y (-.f64 (.f64 y y) (.f64 y y))))
(+.f64 y y)
#s(approx (+ (+ (* x x) y) y) (+.f64 y y))
#s(approx (+ (+ (* x x) y) y) (+.f64 (fma.f64 x x y) y))
#s(approx (+ (* x x) y) y)
#s(approx (+ (* x x) y) (fma.f64 x x y))
#s(approx x x)
#s(approx (+ (+ (* x x) y) y) (*.f64 x x))
#s(approx (+ (+ (* x x) y) y) (.f64 (fma.f64 (/.f64 y (.f64 x x)) #s(literal 2 binary64) #s(literal 1 binary64)) (*.f64 x x)))
#s(approx (+ (* x x) y) (.f64 (+.f64 (/.f64 y (.f64 x x)) #s(literal 1 binary64)) (*.f64 x x)))
#s(approx (+ (+ (* x x) y) y) (.f64 (+.f64 (/.f64 (.f64 x x) y) #s(literal 2 binary64)) y))
#s(approx (+ (* x x) y) (.f64 (+.f64 (/.f64 (.f64 x x) y) #s(literal 1 binary64)) y))
#s(approx (+ (+ (* x x) y) y) (neg.f64 (.f64 (-.f64 (neg.f64 (/.f64 (.f64 x x) y)) #s(literal 2 binary64)) y)))
#s(approx (+ (* x x) y) (neg.f64 (.f64 (-.f64 (neg.f64 (/.f64 (.f64 x x) y)) #s(literal 1 binary64)) y)))

eval3.0ms (0.3%)

Memory: 3.3MiB live, 3.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 241 to 112 computations (53.5% saved)

prune2.0ms (0.2%)

Memory

3.9MiB live, 3.9MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	32	1	33
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	32	3	35

Accuracy

100.0%

Counts

35 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x x (+.f64 y y))
✓	51.3%	(+.f64 #s(approx (+ (* x x) y) y) y)
▶	50.6%	#s(approx (+ (+ (* x x) y) y) (*.f64 x x))

Compiler

Compiled 17 to 17 computations (0% saved)

series2.0ms (0.2%)

Memory

2.8MiB live, 2.8MiB allocated; 0ms collecting garbage

Counts

3 → 7

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) y) y) (*.f64 x x))
(*.f64 x x)
x

Outputs
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* 2 y)))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (+ (* 2 y) (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* y (+ 2 (/ (pow x 2) y)))))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))))

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((+ (+ (* x x) y) y) (* x x) x)
1.0ms	x	@	inf	((+ (+ (* x x) y) y) (* x x) x)
0.0ms	x	@	0	((+ (+ (* x x) y) y) (* x x) x)
0.0ms	y	@	-inf	((+ (+ (* x x) y) y) (* x x) x)
0.0ms	y	@	inf	((+ (+ (* x x) y) y) (* x x) x)

rewrite73.0ms (7.5%)

Memory

-1.0MiB live, 46.4MiB allocated; 1ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	110
0	32	108
1	160	108
0	1326	99

Stop Event

1×	iter-limit
1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

10 → 43

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) y) y) (*.f64 x x))
(*.f64 x x)
x
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* 2 y)))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (+ (* 2 y) (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* y (+ 2 (/ (pow x 2) y)))))
#s(approx (+ (+ (* x x) y) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))))

Outputs
#s(approx (+ (+ (* x x) y) y) (*.f64 x x))
(.f64 (.f64 #s(literal 1 binary64) (fabs.f64 x)) (*.f64 #s(literal 1 binary64) (fabs.f64 x)))
(.f64 (.f64 #s(literal 1 binary64) (fabs.f64 x)) (fabs.f64 x))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (*.f64 #s(literal 1 binary64) (neg.f64 x)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 #s(literal 1 binary64) x) (*.f64 #s(literal 1 binary64) x))
(.f64 (.f64 #s(literal 1 binary64) x) x)
(.f64 (.f64 (fabs.f64 x) #s(literal 1 binary64)) (*.f64 (fabs.f64 x) #s(literal 1 binary64)))
(.f64 (.f64 (neg.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 x) #s(literal 1 binary64)))
(.f64 (.f64 x #s(literal 1 binary64)) (*.f64 x #s(literal 1 binary64)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) #s(literal 1 binary64)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 x (.f64 x #s(literal 1 binary64)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(/.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (+.f64 #s(literal 0 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) #s(literal 0 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
x
#s(approx (+ (+ (* x x) y) y) (+.f64 y y))
#s(approx (+ (+ (* x x) y) y) (+.f64 (fma.f64 x x y) y))
#s(approx (* x x) (*.f64 x x))
#s(approx x x)
#s(approx (+ (+ (* x x) y) y) (.f64 (.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal 2 binary64) #s(literal 1 binary64)) x) x))
#s(approx (+ (+ (* x x) y) y) (*.f64 (fma.f64 x (/.f64 x y) #s(literal 2 binary64)) y))
#s(approx (+ (+ (* x x) y) y) (.f64 (neg.f64 y) (-.f64 (/.f64 (.f64 (neg.f64 x) x) y) #s(literal 2 binary64))))

eval3.0ms (0.3%)

Memory: 7.3MiB live, 7.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 200 to 120 computations (40% saved)

prune2.0ms (0.2%)

Memory

4.4MiB live, 4.4MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	40	3	43

Accuracy

100.0%

Counts

43 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x x (+.f64 y y))
✓	51.3%	(+.f64 #s(approx (+ (* x x) y) y) y)
✓	50.6%	#s(approx (+ (+ (* x x) y) y) (*.f64 x x))

Compiler

Compiled 33 to 30 computations (9.1% saved)

regimes18.0ms (1.9%)

Memory

-29.8MiB live, 14.9MiB allocated; 5ms collecting garbage

Counts

4 → 1

Calls

Call 1

Inputs
(+.f64 #s(approx (+ (* x x) y) y) y)
#s(approx (+ (+ (* x x) y) y) (*.f64 x x))
(fma.f64 x x (+.f64 y y))
(+.f64 (+.f64 (*.f64 x x) y) y)

Outputs
(fma.f64 x x (+.f64 y y))

Calls

4 calls:

13.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
2.0ms	y
2.0ms	x
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	1	`(*.f64 x x)`
100.0%	1	`(+.f64 (+.f64 (*.f64 x x) y) y)`
100.0%	1	`x`
100.0%	1	`y`

Compiler

Compiled 9 to 12 computations (-33.3% saved)

regimes5.0ms (0.5%)

Memory

12.2MiB live, 12.2MiB allocated; 0ms collecting garbage

Counts

2 → 2

Calls

Call 1

Inputs
(+.f64 #s(approx (+ (* x x) y) y) y)
#s(approx (+ (+ (* x x) y) y) (*.f64 x x))

Outputs
(+.f64 #s(approx (+ (* x x) y) y) y)
#s(approx (+ (+ (* x x) y) y) (*.f64 x x))

Calls

4 calls:

1.0ms	y
1.0ms	x
1.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
88.8%	2	`(*.f64 x x)`
80.3%	2	`(+.f64 (+.f64 (*.f64 x x) y) y)`
88.8%	2	`x`
68.3%	3	`y`

Compiler

Compiled 9 to 12 computations (-33.3% saved)

regimes4.0ms (0.4%)

Memory

10.2MiB live, 10.2MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(+.f64 #s(approx (+ (* x x) y) y) y)

Outputs
(+.f64 #s(approx (+ (* x x) y) y) y)

Calls

4 calls:

1.0ms	x
1.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
1.0ms	y
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
51.3%	1	`y`
51.3%	1	`(+.f64 (+.f64 (*.f64 x x) y) y)`
51.3%	1	`(*.f64 x x)`
51.3%	1	`x`

Compiler

Compiled 9 to 12 computations (-33.3% saved)

bsearch8.0ms (0.8%)

Memory

10.6MiB live, 10.6MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
7.0ms	2734883412251024000.0	2.43245863434899e+20

Samples

3.0ms

112×

valid

Compiler

Compiled 101 to 115 computations (-13.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-mult!: 1.0ms (89.6% of total)

adjust: 0.0ms (0% of total)

ival-add!: 0.0ms (0% of total)

derivations26.0ms (2.6%)

Memory

-24.8MiB live, 27.5MiB allocated; 6ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 16 to 14 computations (12.5% saved)

preprocess30.0ms (3.1%)

Memory: -4.1MiB live, 42.3MiB allocated; 3ms collecting garbage
Remove: (abs x)
Compiler: Compiled 69 to 63 computations (8.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze0.0ms (0%)

sample589.0ms (60.1%)

preprocess60.0ms (6.1%)

series4.0ms (0.4%)

rewrite85.0ms (8.7%)

eval11.0ms (1.1%)

prune4.0ms (0.4%)

series3.0ms (0.3%)

rewrite47.0ms (4.8%)

eval3.0ms (0.3%)

prune2.0ms (0.2%)

series2.0ms (0.2%)

rewrite73.0ms (7.5%)

eval3.0ms (0.3%)

prune2.0ms (0.2%)

regimes18.0ms (1.9%)

regimes5.0ms (0.5%)

regimes4.0ms (0.4%)

bsearch8.0ms (0.8%)

derivations26.0ms (2.6%)

preprocess30.0ms (3.1%)

end0.0ms (0%)

Profiling