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

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.2MiB live, 0.2MiB 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)

sample791.0ms (63.5%)

Memory

21.6MiB live, 809.9MiB allocated; 240ms collecting garbage

Samples

528.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 191.0ms

ival-mult!: 135.0ms (70.7% of total)

ival-add!: 55.0ms (28.8% of total)

adjust: 2.0ms (1% of total)

Bogosity

preprocess48.0ms (3.9%)

Memory

0.9MiB live, 45.3MiB allocated; 9ms 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 14 to 10 computations (28.6% saved)

series4.0ms (0.3%)

Memory

13.1MiB live, 13.1MiB 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)

rewrite176.0ms (14.1%)

Memory

-4.1MiB live, 143.2MiB allocated; 156ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	181
0	48	177
1	227	177
0	1978	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 (0.9%)

Memory: 32.4MiB live, 32.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 836 to 360 computations (80.4% saved)

prune20.0ms (1.6%)

Memory

-37.5MiB live, 7.3MiB allocated; 7ms 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))
▶	54.4%	(+.f64 #s(approx (+ (* x x) y) y) y)

Compiler

Compiled 15 to 10 computations (33.3% saved)

series3.0ms (0.2%)

Memory

8.4MiB live, 8.4MiB 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))
0.0ms	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))

rewrite46.0ms (3.7%)

Memory

14.0MiB live, 60.9MiB allocated; 2ms 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: 8.4MiB live, 8.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 524 to 112 computations (78.6% saved)

prune2.0ms (0.1%)

Memory

5.7MiB live, 5.7MiB 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))
✓	54.4%	(+.f64 #s(approx (+ (* x x) y) y) y)
▶	48.1%	#s(approx (+ (+ (* x x) y) y) (*.f64 x x))

Compiler

Compiled 26 to 17 computations (34.6% saved)

series6.0ms (0.5%)

Memory

-44.6MiB live, 7.1MiB allocated; 10ms 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
4.0ms	y	@	-inf	((+ (+ (* x x) y) y) (* x x) x)
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)

rewrite59.0ms (4.8%)

Memory

24.6MiB live, 114.3MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	110
0	32	108
1	160	108
0	1321	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))))

eval4.0ms (0.3%)

Memory: 12.9MiB live, 12.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 583 to 120 computations (79.4% saved)

prune2.0ms (0.2%)

Memory

7.6MiB live, 7.6MiB 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))
✓	54.4%	(+.f64 #s(approx (+ (* x x) y) y) y)
✓	48.1%	#s(approx (+ (+ (* x x) y) y) (*.f64 x x))

Compiler

Compiled 59 to 30 computations (49.2% saved)

regimes9.0ms (0.7%)

Memory

-16.6MiB live, 29.4MiB allocated; 3ms 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:

3.0ms	x
2.0ms	y
2.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
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 12 to 12 computations (0% saved)

regimes5.0ms (0.4%)

Memory

21.1MiB live, 21.1MiB 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	(+.f64 (+.f64 (*.f64 x x) y) y)
1.0ms	y
1.0ms	x
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
92.1%	2	`(*.f64 x x)`
83.5%	2	`(+.f64 (+.f64 (*.f64 x x) y) y)`
92.1%	2	`x`
65.4%	3	`y`

Compiler

Compiled 12 to 12 computations (0% saved)

regimes9.0ms (0.7%)

Memory

-33.6MiB live, 23.6MiB allocated; 4ms 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:

6.0ms	(*.f64 x x)
1.0ms	x
1.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
1.0ms	y

Results

Accuracy	Segments	Branch
54.4%	1	`y`
54.4%	1	`(+.f64 (+.f64 (*.f64 x x) y) y)`
54.4%	1	`(*.f64 x x)`
54.4%	1	`x`

Compiler

Compiled 12 to 12 computations (0% saved)

bsearch5.0ms (0.4%)

Memory

11.8MiB live, 11.8MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
4.0ms	0.053080322929135136	0.09461340589839463

Samples

2.0ms

64×

valid

Compiler

Compiled 90 to 70 computations (22.2% saved)

Precisions

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

adjust: 0.0ms (0% of total)

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

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

derivations18.0ms (1.5%)

Memory

0.1MiB live, 45.6MiB allocated; 4ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 39 to 14 computations (64.1% saved)

preprocess24.0ms (1.9%)

Memory: -11.9MiB live, 80.5MiB allocated; 6ms collecting garbage
Remove: (abs x)
Compiler: Compiled 124 to 63 computations (49.2% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample791.0ms (63.5%)

preprocess48.0ms (3.9%)

series4.0ms (0.3%)

rewrite176.0ms (14.1%)

eval11.0ms (0.9%)

prune20.0ms (1.6%)

series3.0ms (0.2%)

rewrite46.0ms (3.7%)

eval3.0ms (0.3%)

prune2.0ms (0.1%)

series6.0ms (0.5%)

rewrite59.0ms (4.8%)

eval4.0ms (0.3%)

prune2.0ms (0.2%)

regimes9.0ms (0.7%)

regimes5.0ms (0.4%)

regimes9.0ms (0.7%)

bsearch5.0ms (0.4%)

derivations18.0ms (1.5%)

preprocess24.0ms (1.9%)

end0.0ms (0%)

Profiling