Metrics for Linear.Quaternion:$clog from linear-1.19.1.3

start0.0ms (0%)

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

analyze25.0ms (1.2%)

Memory

-7.0MiB live, 33.9MiB allocated; 11ms collecting garbage

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
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
62.5%	62.4%	37.5%	0.1%	0%	0%	0%	5
66.7%	62.4%	31.2%	0.1%	0%	6.2%	0%	6
75%	65.6%	21.9%	0.1%	0%	12.5%	0%	7
80%	68.7%	17.2%	0.1%	0%	14%	0%	8
85.7%	70.2%	11.7%	0.1%	0%	18%	0%	9
88.9%	71.8%	9%	0.1%	0%	19.1%	0%	10
92.3%	72.6%	6%	0.1%	0%	21.3%	0%	11
94.1%	73.4%	4.6%	0.1%	0%	22%	0%	12

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample605.0ms (29.5%)

Memory

52.6MiB live, 895.5MiB allocated; 171ms collecting garbage

Samples

366.0ms	8 256×	0	valid
12.0ms	344×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 179.0ms

ival-sqrt: 91.0ms (50.9% of total)

ival-mult!: 65.0ms (36.4% of total)

ival-add!: 21.0ms (11.7% of total)

adjust: 2.0ms (1.1% of total)

Bogosity

preprocess58.0ms (2.8%)

Memory

-32.8MiB live, 56.5MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	38
1	51	38
2	141	38
3	304	38
4	764	38
5	3581	38

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	65.1%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Symmetry

(abs x)

Compiler

Compiled 10 to 10 computations (0% saved)

series12.0ms (0.6%)

Memory

32.1MiB live, 32.1MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	153	735

Stop Event

1×	iter-limit

Counts

5 → 30

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 y)))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 y) (.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 y) #s(literal 3 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 y) (.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 y) #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 y) #s(literal 3 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))))
#s(approx (+ (* x x) y) y)
#s(approx (+ (* x x) y) (+.f64 y (pow.f64 x #s(literal 2 binary64))))
#s(approx (* x x) (pow.f64 x #s(literal 2 binary64)))
#s(approx x x)
#s(approx (sqrt (+ (* x x) y)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (+ (* x x) y) (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) x))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))))
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 (pow.f64 x #s(literal 2 binary64))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (.f64 y (fma.f64 #s(literal -1/8 binary64) (/.f64 y (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (.f64 y (fma.f64 y (-.f64 (.f64 #s(literal 1/16 binary64) (/.f64 y (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
#s(approx (sqrt (+ (* x x) y)) (.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 5 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))))))
#s(approx (+ (* x x) y) (*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) y))))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(literal -1 binary64) (.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(literal -1 binary64) (.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(literal -1 binary64) (.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(literal -1 binary64) (.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 5 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))))))
#s(approx (+ (* x x) y) (.f64 #s(literal -1 binary64) (.f64 y (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) y)) #s(literal 1 binary64)))))

Calls

6 calls:

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

rewrite158.0ms (7.7%)

Memory

15.6MiB live, 196.9MiB allocated; 40ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	37	16
2	108	16
3	363	16
4	789	16
5	3241	16
0	8200	14
1	11393	14

Stop Event

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

Counts

5 → 47

Calls

Call 1

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

Outputs
(pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 4 binary64)) #s(literal 1/8 binary64))
(pow.f64 (*.f64 (fma.f64 x x y) (fma.f64 x x y)) #s(literal 1/4 binary64))
(pow.f64 (fma.f64 x x y) #s(literal 1/2 binary64))
(neg.f64 (neg.f64 (sqrt.f64 (fma.f64 x x y))))
(sqrt.f64 (fma.f64 x x y))
(fabs.f64 (neg.f64 (sqrt.f64 (fma.f64 x x y))))
(fabs.f64 (sqrt.f64 (fma.f64 x x y)))
(*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x y))) (neg.f64 (sqrt.f64 (fma.f64 x x y))))
(*.f64 (sqrt.f64 (fma.f64 x x y)) (sqrt.f64 (fma.f64 x x y)))
(pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 8 binary64)) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (fma.f64 x x y) (fma.f64 x x y)) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 (sqrt.f64 (fma.f64 x x y))) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (fma.f64 x x y)) #s(literal 2 binary64))
(pow.f64 (fma.f64 x x y) #s(literal 1 binary64))
(neg.f64 (neg.f64 (fma.f64 x x y)))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) y)
(fma.f64 (fabs.f64 x) (fabs.f64 x) y)
(fma.f64 (neg.f64 x) (neg.f64 x) y)
(fma.f64 x x y)
(sqrt.f64 (*.f64 (fma.f64 x x y) (fma.f64 x x y)))
(-.f64 y (*.f64 (neg.f64 x) x))
(-.f64 (*.f64 x x) (neg.f64 y))
(fabs.f64 (neg.f64 (fma.f64 x x y)))
(fabs.f64 (fma.f64 x x y))
(+.f64 y (*.f64 x x))
(+.f64 (*.f64 x x) y)
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (pow.f64 x #s(literal 16 binary64)) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/4 binary64))
(pow.f64 (.f64 (.f64 (*.f64 x x) x) x) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 (fabs.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))
(neg.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (.f64 (.f64 (*.f64 x x) x) x))
(fabs.f64 (*.f64 (fabs.f64 x) (neg.f64 x)))
(fabs.f64 (*.f64 (fabs.f64 x) x))
(fabs.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
x
y

eval10.0ms (0.5%)

Memory: -21.7MiB live, 24.2MiB allocated; 5ms collecting garbage
Compiler: Compiled 603 to 269 computations (55.4% saved)

prune4.0ms (0.2%)

Memory

12.9MiB live, 12.9MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	68	5	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	5	74

Accuracy

100.0%

Counts

74 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	65.1%	(sqrt.f64 (fma.f64 x x y))
▶	33.9%	(sqrt.f64 #s(approx (+ (* x x) y) y))
▶	33.7%	#s(approx (sqrt (+ (* x x) y)) (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
▶	68.2%	#s(approx (sqrt (+ (* x x) y)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))
▶	1.3%	#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) x))

Compiler

Compiled 84 to 84 computations (0% saved)

series29.0ms (1.4%)

Memory

0.1MiB live, 51.5MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	197	1011

Stop Event

1×	iter-limit

Counts

22 → 46

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 y)))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 y) (.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 y) #s(literal 3 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 y) (.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 y) #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 y) #s(literal 3 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (*.f64 #s(literal 1/2 binary64) (/.f64 y x)))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (/.f64 (fma.f64 #s(literal 1/2 binary64) y (pow.f64 x #s(literal 2 binary64))) x))
#s(approx x x)
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) (/.f64 (fma.f64 #s(literal 1/2 binary64) y (pow.f64 x #s(literal 2 binary64))) (pow.f64 x #s(literal 2 binary64))))
#s(approx (/ y (pow x 2)) (/.f64 y (pow.f64 x #s(literal 2 binary64))))
#s(approx (pow x 2) (pow.f64 x #s(literal 2 binary64)))
#s(approx (+ (* x x) y) y)
#s(approx (+ (* x x) y) (+.f64 y (pow.f64 x #s(literal 2 binary64))))
#s(approx (* -1 x) (*.f64 #s(literal -1 binary64) x))
#s(approx (sqrt (+ (* x x) y)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))
#s(approx (+ (* x x) y) (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (.f64 #s(literal -1 binary64) (.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))))
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 (pow.f64 x #s(literal 2 binary64))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (.f64 y (fma.f64 #s(literal -1/8 binary64) (/.f64 y (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (.f64 y (fma.f64 y (-.f64 (.f64 #s(literal 1/16 binary64) (/.f64 y (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 y x))))
#s(approx (sqrt (/ 1 y)) (/.f64 (sqrt.f64 y) y))
#s(approx (/ 1 y) (/.f64 #s(literal 1 binary64) y))
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
#s(approx (sqrt (+ (* x x) y)) (.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 5 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))))))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (*.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x) (/.f64 x y))))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) (.f64 y (+.f64 (/.f64 #s(literal 1 binary64) y) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (+ (* x x) y) (*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) y))))
#s(approx (sqrt (/ 1 y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(literal -1 binary64) (.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(literal -1 binary64) (.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(literal -1 binary64) (.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(literal -1 binary64) (.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 5 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))))))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (.f64 #s(literal -1 binary64) (.f64 y (-.f64 (.f64 #s(literal -1 binary64) (/.f64 x y)) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))))))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) (*.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) y))))
#s(approx (+ (* x x) y) (.f64 #s(literal -1 binary64) (.f64 y (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) y)) #s(literal 1 binary64)))))

Calls

6 calls:

Time	Variable		Point	Expression
10.0ms	y	@	0	((sqrt (+ (* x x) y)) (* x (+ 1 (* 1/2 (/ y (pow x 2))))) x (+ 1 (* 1/2 (/ y (pow x 2)))) 1 (* 1/2 (/ y (pow x 2))) 1/2 (/ y (pow x 2)) y (pow x 2) 2 (sqrt (+ (* x x) y)) (+ (* x x) y) (sqrt (+ (* x x) y)) (* -1 x) -1 (sqrt (+ (* x x) y)) (+ (* x x) y) (sqrt (+ (* x x) y)) (* y (sqrt (/ 1 y))) (sqrt (/ 1 y)) (/ 1 y))
3.0ms	y	@	inf	((sqrt (+ (* x x) y)) (* x (+ 1 (* 1/2 (/ y (pow x 2))))) x (+ 1 (* 1/2 (/ y (pow x 2)))) 1 (* 1/2 (/ y (pow x 2))) 1/2 (/ y (pow x 2)) y (pow x 2) 2 (sqrt (+ (* x x) y)) (+ (* x x) y) (sqrt (+ (* x x) y)) (* -1 x) -1 (sqrt (+ (* x x) y)) (+ (* x x) y) (sqrt (+ (* x x) y)) (* y (sqrt (/ 1 y))) (sqrt (/ 1 y)) (/ 1 y))
3.0ms	y	@	-inf	((sqrt (+ (* x x) y)) (* x (+ 1 (* 1/2 (/ y (pow x 2))))) x (+ 1 (* 1/2 (/ y (pow x 2)))) 1 (* 1/2 (/ y (pow x 2))) 1/2 (/ y (pow x 2)) y (pow x 2) 2 (sqrt (+ (* x x) y)) (+ (* x x) y) (sqrt (+ (* x x) y)) (* -1 x) -1 (sqrt (+ (* x x) y)) (+ (* x x) y) (sqrt (+ (* x x) y)) (* y (sqrt (/ 1 y))) (sqrt (/ 1 y)) (/ 1 y))
2.0ms	x	@	0	((sqrt (+ (* x x) y)) (* x (+ 1 (* 1/2 (/ y (pow x 2))))) x (+ 1 (* 1/2 (/ y (pow x 2)))) 1 (* 1/2 (/ y (pow x 2))) 1/2 (/ y (pow x 2)) y (pow x 2) 2 (sqrt (+ (* x x) y)) (+ (* x x) y) (sqrt (+ (* x x) y)) (* -1 x) -1 (sqrt (+ (* x x) y)) (+ (* x x) y) (sqrt (+ (* x x) y)) (* y (sqrt (/ 1 y))) (sqrt (/ 1 y)) (/ 1 y))
2.0ms	x	@	-inf	((sqrt (+ (* x x) y)) (* x (+ 1 (* 1/2 (/ y (pow x 2))))) x (+ 1 (* 1/2 (/ y (pow x 2)))) 1 (* 1/2 (/ y (pow x 2))) 1/2 (/ y (pow x 2)) y (pow x 2) 2 (sqrt (+ (* x x) y)) (+ (* x x) y) (sqrt (+ (* x x) y)) (* -1 x) -1 (sqrt (+ (* x x) y)) (+ (* x x) y) (sqrt (+ (* x x) y)) (* y (sqrt (/ 1 y))) (sqrt (/ 1 y)) (/ 1 y))

rewrite367.0ms (17.9%)

Memory

28.2MiB live, 531.6MiB allocated; 113ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	117
0	36	115
1	126	115
2	460	107
3	2046	107
0	8953	104
1	26207	104

Stop Event

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

Counts

22 → 1 751

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x))
(.f64 (.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64)) x)
(*.f64 (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(.f64 (fma.f64 (/.f64 y (.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
(*.f64 #s(literal 1 binary64) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x))
(.f64 x (.f64 #s(literal 1 binary64) (fma.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(.f64 x (fma.f64 (/.f64 y (.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 y (fabs.f64 x))) #s(literal 2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) (fabs.f64 x))) (*.f64 (fabs.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 y (fabs.f64 x))) #s(literal 2 binary64) (.f64 (.f64 #s(literal 2 binary64) x) (fabs.f64 x))) (*.f64 (fabs.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 (neg.f64 y) x)) #s(literal 2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) (neg.f64 x))) (*.f64 (neg.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 (neg.f64 y) x)) #s(literal 2 binary64) (.f64 (.f64 #s(literal 2 binary64) x) (neg.f64 x))) (*.f64 (neg.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 y x)) #s(literal 2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) x)) (*.f64 x #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 y x)) #s(literal 2 binary64) (.f64 (.f64 #s(literal 2 binary64) x) x)) (*.f64 x #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (neg.f64 y)) #s(literal 2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) (.f64 (neg.f64 x) x))) (.f64 (*.f64 (neg.f64 x) x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (neg.f64 y)) #s(literal 2 binary64) (.f64 (.f64 #s(literal 2 binary64) x) (.f64 (neg.f64 x) x))) (.f64 (*.f64 (neg.f64 x) x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 x (.f64 #s(literal 1/2 binary64) (/.f64 y (fabs.f64 x)))) #s(literal 2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) (fabs.f64 x))) (*.f64 (fabs.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 x (.f64 #s(literal 1/2 binary64) (/.f64 y (fabs.f64 x)))) #s(literal 2 binary64) (.f64 (.f64 #s(literal 2 binary64) x) (fabs.f64 x))) (*.f64 (fabs.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 x (.f64 (/.f64 y x) #s(literal -1/2 binary64))) #s(literal 2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) (neg.f64 x))) (*.f64 (neg.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 x (.f64 (/.f64 y x) #s(literal -1/2 binary64))) #s(literal 2 binary64) (.f64 (.f64 #s(literal 2 binary64) x) (neg.f64 x))) (*.f64 (neg.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 x (.f64 (/.f64 y x) #s(literal 1/2 binary64))) #s(literal 2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) x)) (*.f64 x #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 x (.f64 (/.f64 y x) #s(literal 1/2 binary64))) #s(literal 2 binary64) (.f64 (.f64 #s(literal 2 binary64) x) x)) (*.f64 x #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 x (.f64 #s(literal -1/2 binary64) y)) #s(literal 2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) (.f64 (neg.f64 x) x))) (.f64 (*.f64 (neg.f64 x) x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 x (.f64 #s(literal -1/2 binary64) y)) #s(literal 2 binary64) (.f64 (.f64 #s(literal 2 binary64) x) (.f64 (neg.f64 x) x))) (.f64 (*.f64 (neg.f64 x) x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y (fabs.f64 x))) x) #s(literal 2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) (fabs.f64 x))) (*.f64 (fabs.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y (fabs.f64 x))) x) #s(literal 2 binary64) (.f64 (.f64 #s(literal 2 binary64) x) (fabs.f64 x))) (*.f64 (fabs.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 (/.f64 y x) #s(literal -1/2 binary64)) x) #s(literal 2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) (neg.f64 x))) (*.f64 (neg.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 (/.f64 y x) #s(literal -1/2 binary64)) x) #s(literal 2 binary64) (.f64 (.f64 #s(literal 2 binary64) x) (neg.f64 x))) (*.f64 (neg.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) x) #s(literal 2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) x)) (*.f64 x #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) x) #s(literal 2 binary64) (.f64 (.f64 #s(literal 2 binary64) x) x)) (*.f64 x #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (/.f64 y (fabs.f64 x)) (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) (fabs.f64 x))) (*.f64 (fabs.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (/.f64 y (fabs.f64 x)) (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64) (.f64 (.f64 #s(literal 2 binary64) x) (fabs.f64 x))) (*.f64 (fabs.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (/.f64 (neg.f64 y) x) (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) (neg.f64 x))) (*.f64 (neg.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (/.f64 (neg.f64 y) x) (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64) (.f64 (.f64 #s(literal 2 binary64) x) (neg.f64 x))) (*.f64 (neg.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (/.f64 y x) (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) x)) (*.f64 x #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (/.f64 y x) (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64) (.f64 (.f64 #s(literal 2 binary64) x) x)) (*.f64 x #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (neg.f64 y) (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) (.f64 (neg.f64 x) x))) (.f64 (*.f64 (neg.f64 x) x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (neg.f64 y) (.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64) (.f64 (.f64 #s(literal 2 binary64) x) (.f64 (neg.f64 x) x))) (.f64 (*.f64 (neg.f64 x) x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) y) x) #s(literal 2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) (.f64 (neg.f64 x) x))) (.f64 (*.f64 (neg.f64 x) x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) y) x) #s(literal 2 binary64) (.f64 (.f64 #s(literal 2 binary64) x) (.f64 (neg.f64 x) x))) (.f64 (*.f64 (neg.f64 x) x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) y) x) (neg.f64 (fabs.f64 x))) #s(literal 2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) (neg.f64 (fabs.f64 x)))) (*.f64 (neg.f64 (fabs.f64 x)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) y) x) (neg.f64 (fabs.f64 x))) #s(literal 2 binary64) (.f64 (.f64 #s(literal 2 binary64) x) (neg.f64 (fabs.f64 x)))) (*.f64 (neg.f64 (fabs.f64 x)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) y) x) (fabs.f64 x)) #s(literal 2 binary64) (.f64 (.f64 x #s(literal 2 binary64)) (fabs.f64 x))) (*.f64 (fabs.f64 x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) y) x) (fabs.f64 x)) #s(literal 2 binary64) (.f64 (.f64 #s(literal 2 binary64) x) (fabs.f64 x))) (*.f64 (fabs.f64 x) #s(literal 2 binary64)))
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(fma.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1 binary64) (/.f64 #s(literal 0 binary64) y))
(fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (/.f64 #s(literal 0 binary64) (*.f64 y #s(literal 2 binary64))))
(fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (/.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) y)))
(fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (*.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 0 binary64)))
(fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) y)))
(fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (/.f64 #s(literal 0 binary64) y))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (/.f64 #s(literal 0 binary64) (*.f64 y #s(literal 2 binary64))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (/.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 0 binary64)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) y)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (/.f64 #s(literal 0 binary64) y))
(fma.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) (*.f64 y #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) y)))
(fma.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) y)))
(fma.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) y))
(fma.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)) (/.f64 #s(literal 0 binary64) (.f64 y #s(literal 2 binary64))))
(fma.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)) (/.f64 #s(literal 0 binary64) (.f64 #s(literal 2 binary64) y)))
(fma.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 0 binary64)))
(fma.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)) (.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) y)))
(fma.f64 #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)) (/.f64 #s(literal 0 binary64) y))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y) (/.f64 #s(literal 0 binary64) (*.f64 y #s(literal 2 binary64))))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y) (/.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) y)))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y) (*.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 0 binary64)))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y) (*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) y)))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y) (/.f64 #s(literal 0 binary64) y))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 0 binary64) (*.f64 y #s(literal 2 binary64))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) y)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) y) (*.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 0 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) y) (*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) y)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 0 binary64) y))
(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal -1 binary64) y) (/.f64 #s(literal -1 binary64) y)) #s(literal 1 binary64)))
(sqrt.f64 (.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) y) (/.f64 #s(literal -1 binary64) y))))
(sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) y) (/.f64 #s(literal -1 binary64) y)))
(-.f64 (/.f64 #s(literal -1 binary64) (.f64 (neg.f64 y) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (neg.f64 y) #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal -1 binary64) (.f64 #s(literal 2 binary64) (neg.f64 y))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (neg.f64 y))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 y #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (.f64 y #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) y)) (/.f64 #s(literal -1 binary64) (.f64 #s(literal 2 binary64) y)))
(-.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal -1/2 binary64) y))
(-.f64 (/.f64 #s(literal 0 binary64) y) (/.f64 #s(literal -1 binary64) y))
(-.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 0 binary64) y))
(fabs.f64 (neg.f64 (*.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
(fabs.f64 (neg.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
(fabs.f64 (*.f64 (neg.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
(fabs.f64 (*.f64 (neg.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(fabs.f64 (*.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (neg.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
(fabs.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (neg.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
(fabs.f64 (.f64 (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) #s(literal -1 binary64)))
(fabs.f64 (.f64 (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) #s(literal 1 binary64)))
(fabs.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) #s(literal -1 binary64)))
(fabs.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) #s(literal 1 binary64)))
(fabs.f64 (.f64 #s(literal -1 binary64) (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
(fabs.f64 (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
(fabs.f64 (.f64 #s(literal 1 binary64) (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
(fabs.f64 (.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
(fabs.f64 (*.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)))
(fabs.f64 (*.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -1 binary64)))
(fabs.f64 (*.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
(fabs.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
(fabs.f64 (/.f64 #s(literal -1 binary64) y))
(fabs.f64 (/.f64 #s(literal 1 binary64) y))
(+.f64 (/.f64 #s(literal -1 binary64) (.f64 (neg.f64 y) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (.f64 (neg.f64 y) #s(literal 2 binary64))))
(+.f64 (/.f64 #s(literal -1 binary64) (.f64 #s(literal 2 binary64) (neg.f64 y))) (/.f64 #s(literal -1 binary64) (.f64 #s(literal 2 binary64) (neg.f64 y))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 y #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (.f64 y #s(literal 2 binary64))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) y)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) y)))
(+.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 #s(literal 1/2 binary64) y))
(+.f64 (/.f64 #s(literal 0 binary64) y) (/.f64 #s(literal 1 binary64) y))
(+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 0 binary64) (*.f64 y #s(literal 2 binary64))))
(+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) y)))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 0 binary64)))
(+.f64 (/.f64 #s(literal 1 binary64) y) (*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) y)))
(+.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 0 binary64) y))

eval306.0ms (14.9%)

Memory: -40.4MiB live, 566.5MiB allocated; 231ms collecting garbage
Compiler: Compiled 18 322 to 7 576 computations (58.7% saved)

prune34.0ms (1.6%)

Memory

-2.0MiB live, 97.6MiB allocated; 11ms collecting garbage

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	1 779	2	1 781
Fresh	0	0	0
Picked	3	2	5
Done	0	0	0
Total	1 782	4	1 786

Accuracy

100.0%

Counts

1 786 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	65.1%	(sqrt.f64 (fma.f64 x x y))
✓	33.9%	(sqrt.f64 #s(approx (+ (* x x) y) y))
▶	68.1%	#s(approx (sqrt (+ (* x x) y)) (.f64 x #s(approx (+ 1 ( 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))))
▶	1.3%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 33 to 33 computations (0% saved)

series12.0ms (0.6%)

Memory

-14.2MiB live, 31.9MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	177	903

Stop Event

1×	iter-limit

Counts

7 → 36

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
(neg.f64 x)
x
#s(approx (sqrt (+ (* x x) y)) (.f64 x #s(approx (+ 1 ( 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))))
(.f64 x #s(approx (+ 1 ( 1/2 (/ y (pow x 2)))) #s(literal 1 binary64)))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))
#s(literal 1 binary64)

Outputs
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 y)))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 y) (.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 y) #s(literal 3 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 y) (.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 y) #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 y) #s(literal 3 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))))
#s(approx (neg x) (*.f64 #s(literal -1 binary64) x))
#s(approx x x)
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (*.f64 #s(literal 1/2 binary64) (/.f64 y x)))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (/.f64 (fma.f64 #s(literal 1/2 binary64) y (pow.f64 x #s(literal 2 binary64))) x))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) (/.f64 (fma.f64 #s(literal 1/2 binary64) y (pow.f64 x #s(literal 2 binary64))) (pow.f64 x #s(literal 2 binary64))))
#s(approx (sqrt (+ (* x x) y)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64))))))))))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (.f64 #s(literal -1 binary64) (.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y (pow.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))))
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 (pow.f64 x #s(literal 2 binary64))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (.f64 y (fma.f64 #s(literal -1/8 binary64) (/.f64 y (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* x x) y)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (.f64 y (fma.f64 y (-.f64 (.f64 #s(literal 1/16 binary64) (/.f64 y (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 y x))))
#s(approx (sqrt (+ (* x x) y)) (*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))
#s(approx (sqrt (+ (* x x) y)) (.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 5 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))))))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (*.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x) (/.f64 x y))))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) (.f64 y (+.f64 (/.f64 #s(literal 1 binary64) y) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(literal -1 binary64) (.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(literal -1 binary64) (.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(literal -1 binary64) (.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(literal -1 binary64) (.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal 5 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 (pow.f64 y #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))))))))
#s(approx (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (.f64 #s(literal -1 binary64) (.f64 y (-.f64 (.f64 #s(literal -1 binary64) (/.f64 x y)) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))))))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) (*.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) y))))

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((sqrt (+ (* x x) y)) (neg x) x (sqrt (+ (* x x) y)) (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (+ 1 (* 1/2 (/ y (pow x 2)))) 1)
1.0ms	x	@	inf	((sqrt (+ (* x x) y)) (neg x) x (sqrt (+ (* x x) y)) (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (+ 1 (* 1/2 (/ y (pow x 2)))) 1)
1.0ms	x	@	0	((sqrt (+ (* x x) y)) (neg x) x (sqrt (+ (* x x) y)) (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (+ 1 (* 1/2 (/ y (pow x 2)))) 1)
1.0ms	y	@	-inf	((sqrt (+ (* x x) y)) (neg x) x (sqrt (+ (* x x) y)) (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (+ 1 (* 1/2 (/ y (pow x 2)))) 1)
1.0ms	y	@	inf	((sqrt (+ (* x x) y)) (neg x) x (sqrt (+ (* x x) y)) (* x (+ 1 (* 1/2 (/ y (pow x 2))))) (+ 1 (* 1/2 (/ y (pow x 2)))) 1)

rewrite237.0ms (11.6%)

Memory

10.9MiB live, 388.1MiB allocated; 28ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	57
0	19	57
1	87	57
2	297	57
3	1227	57
0	8468	52
1	23530	52

Stop Event

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

Counts

7 → 10

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
(neg.f64 x)
x
#s(approx (sqrt (+ (* x x) y)) (.f64 x #s(approx (+ 1 ( 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))))
(.f64 x #s(approx (+ 1 ( 1/2 (/ y (pow x 2)))) #s(literal 1 binary64)))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))
#s(literal 1 binary64)

Outputs
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
(neg.f64 x)
x
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(approx (+ 1 ( 1/2 (/ y (pow x 2)))) #s(literal 1 binary64)) x))
(.f64 #s(approx (+ 1 ( 1/2 (/ y (pow x 2)))) #s(literal 1 binary64)) x)
(.f64 x #s(approx (+ 1 ( 1/2 (/ y (pow x 2)))) #s(literal 1 binary64)))
(neg.f64 (.f64 (neg.f64 x) #s(approx (+ 1 ( 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))))
(neg.f64 (.f64 #s(approx (+ 1 ( 1/2 (/ y (pow x 2)))) #s(literal 1 binary64)) (neg.f64 x)))
#s(approx (+ 1 (* 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))
#s(literal 1 binary64)

eval4.0ms (0.2%)

Memory: 12.8MiB live, 12.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 546 to 206 computations (62.3% saved)

prune3.0ms (0.2%)

Memory

11.4MiB live, 11.4MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	0	0
Picked	0	2	2
Done	0	2	2
Total	40	4	44

Accuracy

100.0%

Counts

44 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	65.1%	(sqrt.f64 (fma.f64 x x y))
✓	33.9%	(sqrt.f64 #s(approx (+ (* x x) y) y))
✓	68.1%	#s(approx (sqrt (+ (* x x) y)) (.f64 x #s(approx (+ 1 ( 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))))
✓	1.3%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 84 to 73 computations (13.1% saved)

regimes16.0ms (0.8%)

Memory

4.1MiB live, 50.3MiB allocated; 3ms collecting garbage

Counts

8 → 2

Calls

Call 1

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

Outputs
(sqrt.f64 (fma.f64 x x y))
#s(approx (sqrt (+ (* x x) y)) (.f64 x #s(approx (+ 1 ( 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))))

Calls

5 calls:

3.0ms	x
3.0ms	y
3.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
3.0ms	(+.f64 (*.f64 x x) y)
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	2	`(*.f64 x x)`
100.0%	2	`(+.f64 (*.f64 x x) y)`
100.0%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
100.0%	2	`x`
81.1%	2	`y`

Compiler

Compiled 13 to 16 computations (-23.1% saved)

regimes20.0ms (1%)

Memory

-33.5MiB live, 33.9MiB allocated; 15ms collecting garbage

Counts

4 → 2

Calls

Call 1

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

Outputs
(sqrt.f64 #s(approx (+ (* x x) y) y))
#s(approx (sqrt (+ (* x x) y)) (.f64 x #s(approx (+ 1 ( 1/2 (/ y (pow x 2)))) #s(literal 1 binary64))))

Calls

4 calls:

11.0ms	x
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
2.0ms	(+.f64 (*.f64 x x) y)
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
90.3%	2	`(*.f64 x x)`
75.8%	2	`(+.f64 (*.f64 x x) y)`
75.8%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
90.3%	2	`x`

Compiler

Compiled 12 to 14 computations (-16.7% saved)

regimes10.0ms (0.5%)

Memory

-19.9MiB live, 26.8MiB allocated; 3ms collecting garbage

Counts

3 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
(sqrt.f64 #s(approx (+ (* x x) y) y))
#s(approx (sqrt (+ (* x x) y)) (*.f64 #s(literal -1 binary64) x))

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

Calls

5 calls:

3.0ms	(+.f64 (*.f64 x x) y)
2.0ms	y
2.0ms	x
1.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
33.9%	1	`(+.f64 (*.f64 x x) y)`
33.9%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
33.9%	1	`y`
33.9%	1	`(*.f64 x x)`
33.9%	1	`x`

Compiler

Compiled 13 to 16 computations (-23.1% saved)

regimes5.0ms (0.3%)

Memory

17.3MiB live, 17.3MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
1.3%	1	`x`
1.3%	1	`(*.f64 x x)`
1.3%	1	`(+.f64 (*.f64 x x) y)`
1.3%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
1.3%	1	`y`

Compiler

Compiled 13 to 16 computations (-23.1% saved)

bsearch6.0ms (0.3%)

Memory

12.1MiB live, 12.1MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
6.0ms	2.2961869102139965e+97	6.4828971411083046e+97

Samples

3.0ms	80×	0	valid
0.0ms	3×	0	invalid

Compiler

Compiled 109 to 120 computations (-10.1% saved)

Precisions

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

ival-sqrt: 1.0ms (80.6% of total)

adjust: 0.0ms (0% of total)

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

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

bsearch26.0ms (1.3%)

Memory

-19.4MiB live, 26.9MiB allocated; 4ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
25.0ms	9.274485793859669e-75	2.439530894641848e-71

Samples

4.0ms	128×	0	valid
2.0ms	46×	0	invalid

Compiler

Compiled 185 to 202 computations (-9.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-sqrt: 1.0ms (38.5% of total)

ival-mult!: 1.0ms (38.5% of total)

adjust: 0.0ms (0% of total)

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

derivations50.0ms (2.4%)

Memory

-8.2MiB live, 37.4MiB allocated; 3ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 33 to 28 computations (15.2% saved)

preprocess53.0ms (2.6%)

Memory: 26.0MiB live, 76.4MiB allocated; 6ms collecting garbage
Remove: (abs x)
Compiler: Compiled 152 to 143 computations (5.9% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze25.0ms (1.2%)

sample605.0ms (29.5%)

preprocess58.0ms (2.8%)

series12.0ms (0.6%)

rewrite158.0ms (7.7%)

eval10.0ms (0.5%)

prune4.0ms (0.2%)

series29.0ms (1.4%)

rewrite367.0ms (17.9%)

eval306.0ms (14.9%)

prune34.0ms (1.6%)

series12.0ms (0.6%)

rewrite237.0ms (11.6%)

eval4.0ms (0.2%)

prune3.0ms (0.2%)

regimes16.0ms (0.8%)

regimes20.0ms (1%)

regimes10.0ms (0.5%)

regimes5.0ms (0.3%)

bsearch6.0ms (0.3%)

bsearch26.0ms (1.3%)

derivations50.0ms (2.4%)

preprocess53.0ms (2.6%)

end0.0ms (0%)

Profiling