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

start0.0ms (0%)

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

analyze32.0ms (1.7%)

Memory

-6.5MiB live, 45.7MiB allocated; 23ms 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)

sample1.2s (63%)

Memory

21.7MiB live, 1 076.2MiB allocated; 334ms collecting garbage

Samples

931.0ms	8 256×	0	valid
12.0ms	321×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 294.0ms

ival-sqrt: 181.0ms (61.6% of total)

ival-add!: 57.0ms (19.4% of total)

ival-mult!: 55.0ms (18.7% of total)

adjust: 2.0ms (0.7% of total)

Bogosity

preprocess109.0ms (5.9%)

Memory

-31.1MiB live, 65.1MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	40
1	42	40
2	107	40
3	185	40
4	418	40
5	2020	40
6	4663	40

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	67.7%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Symmetry

(abs x)

Compiler

Compiled 10 to 10 computations (0% saved)

series6.0ms (0.3%)

Memory

10.9MiB live, 10.9MiB allocated; 0ms collecting garbage

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)) #s(hole binary64 (sqrt y)))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* 1/2 (/ (pow x 2) (sqrt y))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt y) 3))) (* 1/2 (/ 1 (sqrt y))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt y) 5))) (* 1/8 (/ 1 (pow (sqrt y) 3))))) (* 1/2 (/ 1 (sqrt y))))))))
#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 (sqrt (+ (* x x) y)) #s(hole binary64 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))))
#s(approx (+ (* x x) y) #s(hole binary64 (* (pow x 2) (+ 1 (/ y (pow x 2))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (sqrt (pow x 2))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt (pow x 2)) (* 1/2 (/ y (sqrt (pow x 2)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt (pow x 2)) (* y (+ (* -1/8 (/ y (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2)))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt (pow x 2)) (* y (+ (* y (- (* 1/16 (/ y (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2)))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (sqrt (/ 1 y)))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (/ (pow x 2) (* (pow y 2) (sqrt (/ 1 y)))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 4) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (* 1/2 (/ (pow x 2) (* (pow y 2) (sqrt (/ 1 y))))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 4) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow y 6) (pow (sqrt (/ 1 y)) 5)))) (* 1/2 (/ (pow x 2) (* (pow y 2) (sqrt (/ 1 y)))))))))))
#s(approx (+ (* x x) y) #s(hole binary64 (* y (+ 1 (/ (pow x 2) y)))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (sqrt (/ 1 y))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (* 1/2 (/ (pow x 2) (* (pow y 2) (sqrt (/ 1 y))))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 4) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (* 1/2 (/ (pow x 2) (* (pow y 2) (sqrt (/ 1 y)))))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 4) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow y 6) (pow (sqrt (/ 1 y)) 5)))) (* 1/2 (/ (pow x 2) (* (pow y 2) (sqrt (/ 1 y))))))))))))
#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	((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)

rewrite148.0ms (8%)

Memory

38.8MiB live, 225.1MiB allocated; 21ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	156	795
0	159	761
1	831	704
0	8176	638

Stop Event

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

Counts

35 → 97

Calls

Call 1

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

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

eval10.0ms (0.5%)

Memory: -26.6MiB live, 20.3MiB allocated; 2ms collecting garbage
Compiler: Compiled 832 to 340 computations (59.1% saved)

prune3.0ms (0.2%)

Memory

6.3MiB live, 6.3MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	4	94

Accuracy

100.0%

Counts

94 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	67.7%	(sqrt.f64 (fma.f64 x x y))
▶	27.5%	(sqrt.f64 #s(approx (+ (* x x) y) y))
▶	1.2%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
▶	75.2%	#s(approx (sqrt (+ (* x x) y)) x)

Compiler

Compiled 23 to 23 computations (0% saved)

series4.0ms (0.2%)

Memory

7.7MiB live, 7.7MiB allocated; 0ms collecting garbage

Counts

9 → 30

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (sqrt y)))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* 1/2 (/ (pow x 2) (sqrt y))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt y) 3))) (* 1/2 (/ 1 (sqrt y))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt y) 5))) (* 1/8 (/ 1 (pow (sqrt y) 3))))) (* 1/2 (/ 1 (sqrt y))))))))
#s(approx x #s(hole binary64 x))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx (+ (* x x) y) #s(hole binary64 y))
#s(approx (+ (* x x) y) #s(hole binary64 (+ y (pow x 2))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))))
#s(approx (+ (* x x) y) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) y) #s(hole binary64 (* (pow x 2) (+ 1 (/ y (pow x 2))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (sqrt (pow x 2))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt (pow x 2)) (* 1/2 (/ y (sqrt (pow x 2)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt (pow x 2)) (* y (+ (* -1/8 (/ y (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2)))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt (pow x 2)) (* y (+ (* y (- (* 1/16 (/ y (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2)))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (sqrt (/ 1 y)))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (/ (pow x 2) (* (pow y 2) (sqrt (/ 1 y)))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 4) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (* 1/2 (/ (pow x 2) (* (pow y 2) (sqrt (/ 1 y))))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 4) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow y 6) (pow (sqrt (/ 1 y)) 5)))) (* 1/2 (/ (pow x 2) (* (pow y 2) (sqrt (/ 1 y)))))))))))
#s(approx (+ (* x x) y) #s(hole binary64 (* y (+ 1 (/ (pow x 2) y)))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (sqrt (/ 1 y))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (* 1/2 (/ (pow x 2) (* (pow y 2) (sqrt (/ 1 y))))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 4) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (* 1/2 (/ (pow x 2) (* (pow y 2) (sqrt (/ 1 y)))))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 4) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow y 6) (pow (sqrt (/ 1 y)) 5)))) (* 1/2 (/ (pow x 2) (* (pow y 2) (sqrt (/ 1 y))))))))))))
#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	((sqrt (+ (* x x) y)) x (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (+ (* x x) y) y (sqrt (+ (* x x) y)) (+ (* x x) y))
1.0ms	x	@	inf	((sqrt (+ (* x x) y)) x (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (+ (* x x) y) y (sqrt (+ (* x x) y)) (+ (* x x) y))
1.0ms	y	@	-inf	((sqrt (+ (* x x) y)) x (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (+ (* x x) y) y (sqrt (+ (* x x) y)) (+ (* x x) y))
0.0ms	y	@	inf	((sqrt (+ (* x x) y)) x (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (+ (* x x) y) y (sqrt (+ (* x x) y)) (+ (* x x) y))
0.0ms	x	@	0	((sqrt (+ (* x x) y)) x (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (+ (* x x) y) y (sqrt (+ (* x x) y)) (+ (* x x) y))

rewrite172.0ms (9.3%)

Memory

-16.5MiB live, 166.2MiB allocated; 21ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	160	790
0	163	752
1	833	698
0	8204	663

Stop Event

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

Counts

39 → 79

Calls

Call 1

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

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

eval7.0ms (0.4%)

Memory: 12.2MiB live, 12.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 708 to 262 computations (63% saved)

prune3.0ms (0.2%)

Memory

5.1MiB live, 5.1MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	70	4	74

Accuracy

100.0%

Counts

74 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	67.7%	(sqrt.f64 (fma.f64 x x y))
✓	27.5%	(sqrt.f64 #s(approx (+ (* x x) y) y))
✓	1.2%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
✓	75.2%	#s(approx (sqrt (+ (* x x) y)) x)

Compiler

Compiled 43 to 38 computations (11.6% saved)

regimes10.0ms (0.5%)

Memory

18.9MiB live, 18.9MiB allocated; 0ms collecting garbage

Counts

5 → 2

Calls

Call 1

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

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

Calls

5 calls:

2.0ms	y
2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
2.0ms	(+.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`
86.7%	2	`y`

Compiler

Compiled 13 to 16 computations (-23.1% saved)

regimes9.0ms (0.5%)

Memory

-31.2MiB live, 12.2MiB allocated; 6ms collecting garbage

Counts

3 → 2

Calls

Call 1

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

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

Calls

4 calls:

5.0ms	(+.f64 (*.f64 x x) y)
1.0ms	x
1.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
93.2%	2	`(*.f64 x x)`
75.2%	1	`(+.f64 (*.f64 x x) y)`
75.2%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
93.2%	2	`x`

Compiler

Compiled 12 to 14 computations (-16.7% saved)

regimes6.0ms (0.3%)

Memory

15.8MiB live, 15.8MiB allocated; 0ms collecting garbage

Accuracy

Total -47.4b remaining (-298.1%)

Threshold costs -47.4b (-298.1%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
75.2%	1	`(+.f64 (*.f64 x x) y)`
75.2%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
75.2%	1	`y`
75.2%	1	`(*.f64 x x)`
75.2%	1	`x`

Compiler

Compiled 13 to 16 computations (-23.1% saved)

bsearch10.0ms (0.5%)

Memory

19.5MiB live, 19.5MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
9.0ms	1.094633625763479e+119	4.593629469091283e+123

Samples

4.0ms	128×	0	valid
0.0ms	4×	0	invalid

Compiler

Compiled 89 to 106 computations (-19.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-sqrt: 1.0ms (50.5% of total)

ival-mult!: 1.0ms (50.5% of total)

adjust: 0.0ms (0% of total)

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

bsearch9.0ms (0.5%)

Memory

-36.3MiB live, 9.4MiB allocated; 5ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
8.0ms	7.365707582992677e-118	1.032211530945684e-117

Samples

5.0ms	48×	0	valid
1.0ms	26×	0	invalid

Compiler

Compiled 45 to 52 computations (-15.6% saved)

Precisions

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

ival-sqrt: 1.0ms (91% of total)

adjust: 0.0ms (0% of total)

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

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

derivations126.0ms (6.8%)

Memory

-19.1MiB live, 94.4MiB allocated; 25ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 18 to 16 computations (11.1% saved)

preprocess23.0ms (1.2%)

Memory: 4.7MiB live, 48.8MiB allocated; 5ms collecting garbage
Compiler: Compiled 83 to 77 computations (7.2% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze32.0ms (1.7%)

sample1.2s (63%)

preprocess109.0ms (5.9%)

series6.0ms (0.3%)

rewrite148.0ms (8%)

eval10.0ms (0.5%)

prune3.0ms (0.2%)

series4.0ms (0.2%)

rewrite172.0ms (9.3%)

eval7.0ms (0.4%)

prune3.0ms (0.2%)

regimes10.0ms (0.5%)

regimes9.0ms (0.5%)

regimes6.0ms (0.3%)

bsearch10.0ms (0.5%)

bsearch9.0ms (0.5%)

derivations126.0ms (6.8%)

preprocess23.0ms (1.2%)

end0.0ms (0%)

Profiling