Metrics for Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3

start0.0ms (0%)

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

analyze2.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	50%	0%	0%	50%	0%	3
50%	25%	25%	0%	0%	50%	0%	4
75%	37.5%	12.5%	0%	0%	50%	0%	5
87.5%	43.7%	6.2%	0%	0%	50%	0%	6
93.8%	46.9%	3.1%	0%	0%	50%	0%	7
96.9%	48.4%	1.6%	0%	0%	50%	0%	8
98.4%	49.2%	0.8%	0%	0%	50%	0%	9
99.2%	49.6%	0.4%	0%	0%	50%	0%	10
99.6%	49.8%	0.2%	0%	0%	50%	0%	11
99.8%	49.9%	0.1%	0%	0%	50%	0%	12

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample478.0ms (36.7%)

Memory

21.1MiB live, 862.5MiB allocated; 159ms collecting garbage

Samples

290.0ms	8 256×	0	valid
0.0ms	3×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 158.0ms

ival-sqrt: 70.0ms (44.4% of total)

ival-mult!: 62.0ms (39.3% of total)

ival-sub!: 24.0ms (15.2% of total)

adjust: 1.0ms (0.6% of total)

Bogosity

preprocess31.0ms (2.4%)

Memory

11.0MiB live, 60.6MiB allocated; 14ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	10
1	47	10
2	151	10
3	1026	10

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

Symmetry

(abs x)

Compiler

Compiled 12 to 10 computations (16.7% saved)

series14.0ms (1.1%)

Memory

-9.5MiB live, 36.1MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	347

Stop Event

1×	iter-limit

Counts

5 → 17

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)
x

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

Calls

3 calls:

Time	Variable	Point
5.0ms	x	0
1.0ms	x	inf
1.0ms	x	-inf

rewrite116.0ms (8.9%)

Memory

-1.3MiB live, 230.2MiB allocated; 29ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	13
1	30	13
2	98	13
3	711	13
0	4179	13

Stop Event

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

Counts

5 → 398

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)
x

Outputs
(pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(sin.f64 (acos.f64 (sin.f64 (fabs.f64 (asin.f64 x)))))
(sin.f64 (acos.f64 (sin.f64 (asin.f64 (fabs.f64 x)))))
(sin.f64 (acos.f64 (sin.f64 (asin.f64 (neg.f64 x)))))
(sin.f64 (acos.f64 (sin.f64 (asin.f64 x))))
(sin.f64 (acos.f64 (neg.f64 (neg.f64 (fabs.f64 x)))))
(sin.f64 (+.f64 (fabs.f64 (asin.f64 x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(sin.f64 (+.f64 (asin.f64 (fabs.f64 x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(sin.f64 (+.f64 (asin.f64 (neg.f64 x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(sin.f64 (acos.f64 (neg.f64 (fabs.f64 x))))
(sin.f64 (acos.f64 (fabs.f64 x)))
(sin.f64 (acos.f64 (neg.f64 x)))
(sin.f64 (acos.f64 x))
(fma.f64 (sin.f64 (asin.f64 x)) (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (/.f64 (-.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))) #s(literal 2 binary64)))
(fma.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (cos.f64 (acos.f64 x)) (/.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) #s(literal 2 binary64)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 (/.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) #s(literal 2 binary64)) (.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (sin.f64 (asin.f64 x))))
(cos.f64 (asin.f64 (sin.f64 (fabs.f64 (asin.f64 x)))))
(cos.f64 (asin.f64 (sin.f64 (asin.f64 (fabs.f64 x)))))
(cos.f64 (asin.f64 (sin.f64 (asin.f64 (neg.f64 x)))))
(cos.f64 (asin.f64 (sin.f64 (asin.f64 x))))
(cos.f64 (asin.f64 (neg.f64 (neg.f64 (fabs.f64 x)))))
(cos.f64 (neg.f64 (fabs.f64 (asin.f64 x))))
(cos.f64 (asin.f64 (neg.f64 (fabs.f64 x))))
(cos.f64 (fabs.f64 (fabs.f64 (asin.f64 x))))
(cos.f64 (fabs.f64 (asin.f64 (fabs.f64 x))))
(cos.f64 (asin.f64 (neg.f64 x)))
(cos.f64 (fabs.f64 (asin.f64 x)))
(cos.f64 (asin.f64 (fabs.f64 x)))
(cos.f64 (asin.f64 x))
(fabs.f64 (neg.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))))
(fabs.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(fabs.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(+.f64 (/.f64 (+.f64 (sin.f64 (-.f64 (asin.f64 x) (.f64 (PI.f64) #s(literal 1/2 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) #s(literal 2 binary64)) (/.f64 (-.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))))) #s(literal 2 binary64)))
(+.f64 (/.f64 (+.f64 (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (acos.f64 x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) #s(literal 2 binary64)) (/.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) #s(literal 2 binary64)))
(*.f64 (neg.f64 (-.f64 (fabs.f64 x) #s(literal -1 binary64))) (-.f64 (fabs.f64 x) #s(literal 1 binary64)))
(*.f64 (neg.f64 (-.f64 (neg.f64 x) #s(literal -1 binary64))) (-.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (neg.f64 (-.f64 x #s(literal -1 binary64))) (-.f64 x #s(literal 1 binary64)))
(*.f64 (-.f64 (fabs.f64 x) #s(literal -1 binary64)) (neg.f64 (-.f64 (fabs.f64 x) #s(literal 1 binary64))))
(*.f64 (-.f64 (neg.f64 x) #s(literal -1 binary64)) (neg.f64 (-.f64 (neg.f64 x) #s(literal 1 binary64))))
(*.f64 (-.f64 x #s(literal -1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64))))
(.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(pow.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 2 binary64))
(pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (acos.f64 (fabs.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (acos.f64 (fabs.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))))) (cos.f64 (-.f64 (+.f64 (acos.f64 (fabs.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (acos.f64 (fabs.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (acos.f64 (fabs.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (acos.f64 (neg.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))))) (cos.f64 (-.f64 (+.f64 (acos.f64 (fabs.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (acos.f64 (neg.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (acos.f64 (fabs.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (acos.f64 x) (.f64 (PI.f64) #s(literal 1/2 binary64))))) (cos.f64 (-.f64 (+.f64 (acos.f64 (fabs.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (acos.f64 x) (.f64 (PI.f64) #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (acos.f64 (fabs.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (fabs.f64 (asin.f64 x)) (PI.f64)))) (cos.f64 (-.f64 (+.f64 (acos.f64 (fabs.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (fabs.f64 (asin.f64 x)) (PI.f64))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (acos.f64 (fabs.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (asin.f64 (fabs.f64 x)) (PI.f64)))) (cos.f64 (-.f64 (+.f64 (acos.f64 (fabs.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (asin.f64 (fabs.f64 x)) (PI.f64))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (acos.f64 (fabs.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (asin.f64 (neg.f64 x)) (PI.f64)))) (cos.f64 (-.f64 (+.f64 (acos.f64 (fabs.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (asin.f64 (neg.f64 x)) (PI.f64))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (acos.f64 (fabs.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (asin.f64 x) (PI.f64)))) (cos.f64 (-.f64 (+.f64 (acos.f64 (fabs.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (asin.f64 x) (PI.f64))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (acos.f64 (neg.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (acos.f64 (fabs.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))))) (cos.f64 (-.f64 (+.f64 (acos.f64 (neg.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (acos.f64 (fabs.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (acos.f64 (neg.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (acos.f64 (neg.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))))) (cos.f64 (-.f64 (+.f64 (acos.f64 (neg.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (acos.f64 (neg.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (acos.f64 (neg.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (acos.f64 x) (.f64 (PI.f64) #s(literal 1/2 binary64))))) (cos.f64 (-.f64 (+.f64 (acos.f64 (neg.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (acos.f64 x) (.f64 (PI.f64) #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (acos.f64 (neg.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (fabs.f64 (asin.f64 x)) (PI.f64)))) (cos.f64 (-.f64 (+.f64 (acos.f64 (neg.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (fabs.f64 (asin.f64 x)) (PI.f64))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (acos.f64 (neg.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (asin.f64 (fabs.f64 x)) (PI.f64)))) (cos.f64 (-.f64 (+.f64 (acos.f64 (neg.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (asin.f64 (fabs.f64 x)) (PI.f64))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (acos.f64 (neg.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (asin.f64 (neg.f64 x)) (PI.f64)))) (cos.f64 (-.f64 (+.f64 (acos.f64 (neg.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (asin.f64 (neg.f64 x)) (PI.f64))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (acos.f64 (neg.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (asin.f64 x) (PI.f64)))) (cos.f64 (-.f64 (+.f64 (acos.f64 (neg.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (asin.f64 x) (PI.f64))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (acos.f64 x) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (acos.f64 (fabs.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))))) (cos.f64 (-.f64 (+.f64 (acos.f64 x) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (acos.f64 (fabs.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (acos.f64 x) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (acos.f64 (neg.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64))))) (cos.f64 (-.f64 (+.f64 (acos.f64 x) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (acos.f64 (neg.f64 x)) (.f64 (PI.f64) #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (acos.f64 x) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (acos.f64 x) (.f64 (PI.f64) #s(literal 1/2 binary64))))) (cos.f64 (-.f64 (+.f64 (acos.f64 x) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (acos.f64 x) (.f64 (PI.f64) #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 (acos.f64 x) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (fabs.f64 (asin.f64 x)) (PI.f64)))) (cos.f64 (-.f64 (+.f64 (acos.f64 x) (.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (fabs.f64 (asin.f64 x)) (PI.f64))))) #s(literal 2 binary64))
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(/.f64 (-.f64 (cos.f64 (-.f64 (acos.f64 (fabs.f64 x)) (acos.f64 (neg.f64 x)))) (cos.f64 (+.f64 (acos.f64 (fabs.f64 x)) (acos.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (acos.f64 (fabs.f64 x)) (acos.f64 x))) (cos.f64 (+.f64 (acos.f64 (fabs.f64 x)) (acos.f64 x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (acos.f64 (neg.f64 x)) (acos.f64 (fabs.f64 x)))) (cos.f64 (+.f64 (acos.f64 (neg.f64 x)) (acos.f64 (fabs.f64 x))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (acos.f64 (neg.f64 x)) (acos.f64 (neg.f64 x)))) (cos.f64 (+.f64 (acos.f64 (neg.f64 x)) (acos.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (acos.f64 (neg.f64 x)) (acos.f64 x))) (cos.f64 (+.f64 (acos.f64 (neg.f64 x)) (acos.f64 x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (acos.f64 x) (acos.f64 (fabs.f64 x)))) (cos.f64 (+.f64 (acos.f64 x) (acos.f64 (fabs.f64 x))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (acos.f64 x) (acos.f64 (neg.f64 x)))) (cos.f64 (+.f64 (acos.f64 x) (acos.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (acos.f64 x) (acos.f64 x))) (cos.f64 (+.f64 (acos.f64 x) (acos.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (acos.f64 (fabs.f64 x)) (fabs.f64 (asin.f64 x)))) (sin.f64 (+.f64 (acos.f64 (fabs.f64 x)) (fabs.f64 (asin.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (acos.f64 (fabs.f64 x)) (asin.f64 (fabs.f64 x)))) (sin.f64 (+.f64 (acos.f64 (fabs.f64 x)) (asin.f64 (fabs.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (acos.f64 (fabs.f64 x)) (asin.f64 (neg.f64 x)))) (sin.f64 (+.f64 (acos.f64 (fabs.f64 x)) (asin.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (acos.f64 (fabs.f64 x)) (asin.f64 x))) (sin.f64 (+.f64 (acos.f64 (fabs.f64 x)) (asin.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (acos.f64 (neg.f64 x)) (fabs.f64 (asin.f64 x)))) (sin.f64 (+.f64 (acos.f64 (neg.f64 x)) (fabs.f64 (asin.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (acos.f64 (neg.f64 x)) (asin.f64 (fabs.f64 x)))) (sin.f64 (+.f64 (acos.f64 (neg.f64 x)) (asin.f64 (fabs.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (acos.f64 (neg.f64 x)) (asin.f64 (neg.f64 x)))) (sin.f64 (+.f64 (acos.f64 (neg.f64 x)) (asin.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (acos.f64 (neg.f64 x)) (asin.f64 x))) (sin.f64 (+.f64 (acos.f64 (neg.f64 x)) (asin.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (acos.f64 x) (fabs.f64 (asin.f64 x)))) (sin.f64 (+.f64 (acos.f64 x) (fabs.f64 (asin.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (acos.f64 x) (asin.f64 (fabs.f64 x)))) (sin.f64 (+.f64 (acos.f64 x) (asin.f64 (fabs.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (acos.f64 x) (asin.f64 (neg.f64 x)))) (sin.f64 (+.f64 (acos.f64 x) (asin.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (acos.f64 x) (asin.f64 x))) (sin.f64 (+.f64 (acos.f64 x) (asin.f64 x)))) #s(literal 2 binary64))
(neg.f64 (fma.f64 x x #s(literal -1 binary64)))
(fma.f64 (neg.f64 (-.f64 (fabs.f64 x) #s(literal -1 binary64))) (-.f64 (fabs.f64 x) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (neg.f64 (-.f64 (neg.f64 x) #s(literal -1 binary64))) (-.f64 (neg.f64 x) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (neg.f64 (-.f64 x #s(literal -1 binary64))) (-.f64 x #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (neg.f64 (neg.f64 (fabs.f64 x))) (neg.f64 (fabs.f64 x)) #s(literal 1 binary64))
(fma.f64 (-.f64 (fabs.f64 x) #s(literal -1 binary64)) (neg.f64 (-.f64 (fabs.f64 x) #s(literal 1 binary64))) #s(literal 0 binary64))
(fma.f64 (-.f64 (neg.f64 x) #s(literal -1 binary64)) (neg.f64 (-.f64 (neg.f64 x) #s(literal 1 binary64))) #s(literal 0 binary64))
(fma.f64 (-.f64 x #s(literal -1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64))) #s(literal 0 binary64))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (neg.f64 (fabs.f64 x))) #s(literal 1 binary64))
(fma.f64 (neg.f64 (fabs.f64 x)) (fabs.f64 x) #s(literal 1 binary64))
(fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) #s(literal 0 binary64))
(fma.f64 (fabs.f64 x) (neg.f64 (fabs.f64 x)) #s(literal 1 binary64))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 0 binary64))
(fma.f64 x (neg.f64 x) #s(literal 1 binary64))
(sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(-.f64 (*.f64 (neg.f64 x) x) #s(literal -1 binary64))
(-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (acos.f64 (fabs.f64 x))))))
(-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (acos.f64 (neg.f64 x))))))
(-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (acos.f64 x)))))
(-.f64 #s(literal 1 binary64) (*.f64 (sin.f64 (fabs.f64 (asin.f64 x))) (sin.f64 (fabs.f64 (asin.f64 x)))))
(-.f64 #s(literal 1 binary64) (*.f64 (sin.f64 (asin.f64 (fabs.f64 x))) (sin.f64 (asin.f64 (fabs.f64 x)))))
(-.f64 #s(literal 1 binary64) (*.f64 (sin.f64 (asin.f64 (neg.f64 x))) (sin.f64 (asin.f64 (neg.f64 x)))))
(-.f64 #s(literal 1 binary64) (*.f64 (sin.f64 (asin.f64 x)) (sin.f64 (asin.f64 x))))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(fabs.f64 (.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(fabs.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))))
(fabs.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(+.f64 (*.f64 (neg.f64 x) x) #s(literal 1 binary64))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (fabs.f64 (asin.f64 x))))))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (asin.f64 (fabs.f64 x))))))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (asin.f64 (neg.f64 x))))))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (asin.f64 x)))))
(+.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 0 binary64))
(+.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (*.f64 (neg.f64 x) x)))
(+.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x))
#s(literal 1 binary64)
(*.f64 (neg.f64 (neg.f64 (fabs.f64 x))) (neg.f64 (neg.f64 (fabs.f64 x))))
(*.f64 (neg.f64 (neg.f64 (fabs.f64 x))) (fabs.f64 x))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 x) (neg.f64 (neg.f64 (fabs.f64 x))))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(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 x x) (*.f64 x x)))
(fabs.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
x

eval59.0ms (4.5%)

Memory: -2.4MiB live, 141.9MiB allocated; 15ms collecting garbage
Compiler: Compiled 8 865 to 2 452 computations (72.3% saved)

prune7.0ms (0.5%)

Memory

19.8MiB live, 19.8MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	407	3	410
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	407	4	411

Accuracy

100.0%

Counts

411 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
▶	100.0%	(sqrt.f64 (*.f64 (-.f64 x #s(literal -1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64)))))
▶	99.6%	#s(approx (sqrt (- 1 (* x x))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64)))))
▶	99.0%	#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Compiler

Compiled 37 to 32 computations (13.5% saved)

series10.0ms (0.7%)

Memory

-23.5MiB live, 23.2MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	112	484

Stop Event

1×	iter-limit

Counts

15 → 29

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable	Point
3.0ms	x	-inf
1.0ms	x	inf
1.0ms	x	0

rewrite154.0ms (11.8%)

Memory

9.4MiB live, 290.8MiB allocated; 74ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	69
0	26	60
1	69	53
2	205	53
3	1056	53
0	4533	51

Stop Event

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

Counts

15 → 517

Calls

Call 1

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

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

eval111.0ms (8.5%)

Memory: -8.1MiB live, 181.3MiB allocated; 74ms collecting garbage
Compiler: Compiled 10 581 to 2 851 computations (73.1% saved)

prune8.0ms (0.6%)

Memory

20.9MiB live, 20.9MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	531	2	533
Fresh	0	0	0
Picked	2	1	3
Done	0	1	1
Total	533	4	537

Accuracy

100.0%

Counts

537 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
▶	100.0%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)))
▶	99.6%	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓	99.0%	#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Compiler

Compiled 35 to 29 computations (17.1% saved)

series8.0ms (0.6%)

Memory

15.7MiB live, 15.7MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	109	448

Stop Event

1×	iter-limit

Counts

11 → 26

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable	Point
1.0ms	x	0
1.0ms	x	inf
1.0ms	x	-inf

rewrite117.0ms (9%)

Memory

-10.2MiB live, 182.0MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	47
0	21	44
1	58	37
2	179	37
3	1000	37
0	4468	37

Stop Event

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

Counts

11 → 453

Calls

Call 1

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

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

eval72.0ms (5.6%)

Memory: 7.1MiB live, 96.7MiB allocated; 14ms collecting garbage
Compiler: Compiled 9 720 to 2 627 computations (73% saved)

prune30.0ms (2.3%)

Memory

-28.4MiB live, 17.6MiB allocated; 6ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	468	0	468
Fresh	0	0	0
Picked	0	2	2
Done	0	2	2
Total	468	4	472

Accuracy

100.0%

Counts

472 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	100.0%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)))
✓	99.6%	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓	99.0%	#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Compiler

Compiled 35 to 29 computations (17.1% saved)

regimes15.0ms (1.2%)

Memory

29.2MiB live, 29.2MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

3 → 1

6 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Outputs
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Call 2

Inputs

#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

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

Outputs
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

Call 3

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

Outputs
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)))

Calls

12 calls:

2.0ms	x
2.0ms	(*.f64 x x)
1.0ms	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
1.0ms	(-.f64 #s(literal 1 binary64) (*.f64 x x))
1.0ms	x

Results

Accuracy	Segments	Branch
99.0%	1	`(*.f64 x x)`
99.0%	1	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
99.0%	1	`(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
99.0%	1	`x`
100.0%	1	`(*.f64 x x)`
100.0%	1	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
100.0%	1	`(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
100.0%	1	`x`
100.0%	1	`(*.f64 x x)`
100.0%	1	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
100.0%	1	`(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
100.0%	1	`x`

Compiler

Compiled 103 to 63 computations (38.8% saved)

derivations50.0ms (3.9%)

Memory

-42.9MiB live, 16.9MiB allocated; 51ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 22 to 15 computations (31.8% saved)

preprocess20.0ms (1.5%)

Memory: 40.6MiB live, 40.6MiB allocated; 0ms collecting garbage
Remove: (abs x)
Compiler: Compiled 72 to 58 computations (19.4% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze2.0ms (0.1%)

sample478.0ms (36.7%)

preprocess31.0ms (2.4%)

series14.0ms (1.1%)

rewrite116.0ms (8.9%)

eval59.0ms (4.5%)

prune7.0ms (0.5%)

series10.0ms (0.7%)

rewrite154.0ms (11.8%)

eval111.0ms (8.5%)

prune8.0ms (0.6%)

series8.0ms (0.6%)

rewrite117.0ms (9%)

eval72.0ms (5.6%)

prune30.0ms (2.3%)

regimes15.0ms (1.2%)

derivations50.0ms (3.9%)

preprocess20.0ms (1.5%)

end0.0ms (0%)

Profiling