Metrics for arccos

start0.0ms (0%)

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

analyze4.0ms (0.3%)

Memory

7.1MiB live, 7.1MiB 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%	100%	0%	0%	0%	0%	3
33.3%	25%	50%	0%	0%	25%	0%	4
60%	37.5%	25%	0%	0%	37.5%	0%	5
77.8%	43.7%	12.5%	0%	0%	43.7%	0%	6
88.2%	46.9%	6.2%	0%	0%	46.9%	0%	7
93.9%	48.4%	3.1%	0%	0%	48.4%	0%	8
96.9%	49.2%	1.6%	0%	0%	49.2%	0%	9
98.4%	49.6%	0.8%	0%	0%	49.6%	0%	10
99.2%	49.8%	0.4%	0%	0%	49.8%	0%	11
99.6%	49.9%	0.2%	0%	0%	49.9%	0%	12

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample743.0ms (52.9%)

Memory

48.4MiB live, 974.1MiB allocated; 250ms collecting garbage

Samples

488.0ms	8 256×	0	valid
1.0ms	21×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 326.0ms

ival-atan: 79.0ms (24.3% of total)

ival-sub!: 65.0ms (20% of total)

ival-sqrt: 61.0ms (18.7% of total)

ival-mult!: 45.0ms (13.8% of total)

ival-add!: 39.0ms (12% of total)

ival-div!: 36.0ms (11.1% of total)

adjust: 2.0ms (0.6% of total)

Bogosity

preprocess46.0ms (3.3%)

Memory

-26.0MiB live, 18.8MiB allocated; 21ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	33
1	64	33
2	214	33
3	817	33

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))

Compiler

Compiled 20 to 18 computations (10% saved)

series4.0ms (0.3%)

Memory

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

Counts

9 → 29

Calls

Call 1

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

Outputs
#s(approx (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) #s(hole binary64 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))))
#s(approx (atan (sqrt (/ (- 1 x) (+ 1 x)))) #s(hole binary64 (atan (sqrt (/ (- 1 x) (+ 1 x))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 1))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* x (- (* 1/2 x) 1)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
#s(approx (/ (- 1 x) (+ 1 x)) #s(hole binary64 (+ 1 (* -2 x))))
#s(approx (/ (- 1 x) (+ 1 x)) #s(hole binary64 (+ 1 (* x (- (* 2 x) 2)))))
#s(approx (/ (- 1 x) (+ 1 x)) #s(hole binary64 (+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))))
#s(approx x #s(hole binary64 x))
#s(approx (+ 1 x) #s(hole binary64 (+ 1 x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (sqrt -1)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (/ 1 (* x (sqrt -1))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))))
#s(approx (/ (- 1 x) (+ 1 x)) #s(hole binary64 -1))
#s(approx (/ (- 1 x) (+ 1 x)) #s(hole binary64 (- (* 2 (/ 1 x)) 1)))
#s(approx (/ (- 1 x) (+ 1 x)) #s(hole binary64 (- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))))
#s(approx (/ (- 1 x) (+ 1 x)) #s(hole binary64 (- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))))
#s(approx (- 1 x) #s(hole binary64 (* -1 x)))
#s(approx (- 1 x) #s(hole binary64 (* x (- (/ 1 x) 1))))
#s(approx (+ 1 x) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) #s(hole binary64 (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))))
#s(approx (atan (sqrt (/ (- 1 x) (+ 1 x)))) #s(hole binary64 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))))
#s(approx (/ (- 1 x) (+ 1 x)) #s(hole binary64 (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)))
#s(approx (/ (- 1 x) (+ 1 x)) #s(hole binary64 (- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)))
#s(approx (- 1 x) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (- 1 x) (+ 1 x)) (- 1 x) 1 x (+ 1 x))
1.0ms	x	@	-inf	((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (- 1 x) (+ 1 x)) (- 1 x) 1 x (+ 1 x))
1.0ms	x	@	0	((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (- 1 x) (+ 1 x)) (- 1 x) 1 x (+ 1 x))

Time

Variable

Point

Expression

2.0ms

inf

((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (- 1 x) (+ 1 x)) (- 1 x) 1 x (+ 1 x))

1.0ms

-inf

((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (- 1 x) (+ 1 x)) (- 1 x) 1 x (+ 1 x))

1.0ms

((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (- 1 x) (+ 1 x)) (- 1 x) 1 x (+ 1 x))

rewrite66.0ms (4.7%)

Memory

6.0MiB live, 52.6MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	149	652
0	156	550
0	1283	537

Stop Event

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

Counts

38 → 72

Calls

Call 1

Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
#s(literal 2 binary64)
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(+.f64 #s(literal 1 binary64) x)
#s(approx (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) #s(hole binary64 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))))
#s(approx (atan (sqrt (/ (- 1 x) (+ 1 x)))) #s(hole binary64 (atan (sqrt (/ (- 1 x) (+ 1 x))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 1))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* x (- (* 1/2 x) 1)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
#s(approx (/ (- 1 x) (+ 1 x)) #s(hole binary64 (+ 1 (* -2 x))))
#s(approx (/ (- 1 x) (+ 1 x)) #s(hole binary64 (+ 1 (* x (- (* 2 x) 2)))))
#s(approx (/ (- 1 x) (+ 1 x)) #s(hole binary64 (+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))))
#s(approx x #s(hole binary64 x))
#s(approx (+ 1 x) #s(hole binary64 (+ 1 x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (sqrt -1)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (/ 1 (* x (sqrt -1))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))))
#s(approx (/ (- 1 x) (+ 1 x)) #s(hole binary64 -1))
#s(approx (/ (- 1 x) (+ 1 x)) #s(hole binary64 (- (* 2 (/ 1 x)) 1)))
#s(approx (/ (- 1 x) (+ 1 x)) #s(hole binary64 (- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))))
#s(approx (/ (- 1 x) (+ 1 x)) #s(hole binary64 (- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))))
#s(approx (- 1 x) #s(hole binary64 (* -1 x)))
#s(approx (- 1 x) #s(hole binary64 (* x (- (/ 1 x) 1))))
#s(approx (+ 1 x) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) #s(hole binary64 (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))))
#s(approx (atan (sqrt (/ (- 1 x) (+ 1 x)))) #s(hole binary64 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))))
#s(approx (/ (- 1 x) (+ 1 x)) #s(hole binary64 (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)))
#s(approx (/ (- 1 x) (+ 1 x)) #s(hole binary64 (- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)))
#s(approx (- 1 x) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))

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

eval7.0ms (0.5%)

Memory: 8.8MiB live, 8.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 609 to 369 computations (39.4% saved)

prune3.0ms (0.2%)

Memory

3.2MiB live, 3.2MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	61	4	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	4	66

Accuracy

100.0%

Counts

66 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
▶	99.4%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
▶	99.3%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
▶	98.6%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))

Compiler

Compiled 47 to 47 computations (0% saved)

series5.0ms (0.3%)

Memory

4.6MiB live, 4.6MiB allocated; 0ms collecting garbage

Counts

22 → 37

Calls

Call 1

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

Outputs
#s(approx (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) #s(hole binary64 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))))
#s(approx (atan (sqrt (/ (- 1 x) (+ 1 x)))) #s(hole binary64 (atan (sqrt (/ (- 1 x) (+ 1 x))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 1))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* x (- (* 1/2 x) 1)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
#s(approx x #s(hole binary64 x))
#s(approx (+ (* 1/2 x) -1) #s(hole binary64 -1))
#s(approx (+ (* 1/2 x) -1) #s(hole binary64 (- (* 1/2 x) 1)))
#s(approx (/ (- 1 x) (+ x 1)) #s(hole binary64 (+ 1 (* -2 x))))
#s(approx (/ (- 1 x) (+ x 1)) #s(hole binary64 (+ 1 (* x (- (* 2 x) 2)))))
#s(approx (/ (- 1 x) (+ x 1)) #s(hole binary64 (+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))))
#s(approx (+ x 1) #s(hole binary64 (+ 1 x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (sqrt -1)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (/ 1 (* x (sqrt -1))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))))
#s(approx (- 1 x) #s(hole binary64 (* -1 x)))
#s(approx (- 1 x) #s(hole binary64 (* x (- (/ 1 x) 1))))
#s(approx (+ (* (+ (* 1/2 x) -1) x) 1) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (+ (* (+ (* 1/2 x) -1) x) 1) #s(hole binary64 (* (pow x 2) (- 1/2 (/ 1 x)))))
#s(approx (+ (* (+ (* 1/2 x) -1) x) 1) #s(hole binary64 (* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))))
#s(approx (+ (* 1/2 x) -1) #s(hole binary64 (* 1/2 x)))
#s(approx (+ (* 1/2 x) -1) #s(hole binary64 (* x (- 1/2 (/ 1 x)))))
#s(approx (/ (- 1 x) (+ x 1)) #s(hole binary64 (- (* 2 (/ 1 x)) 1)))
#s(approx (/ (- 1 x) (+ x 1)) #s(hole binary64 (- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))))
#s(approx (/ (- 1 x) (+ x 1)) #s(hole binary64 (- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))))
#s(approx (+ x 1) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) #s(hole binary64 (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))))
#s(approx (atan (sqrt (/ (- 1 x) (+ 1 x)))) #s(hole binary64 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))))
#s(approx (- 1 x) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))
#s(approx (+ (* (+ (* 1/2 x) -1) x) 1) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))))
#s(approx (+ (* 1/2 x) -1) #s(hole binary64 (* -1 (* x (- (/ 1 x) 1/2)))))
#s(approx (/ (- 1 x) (+ x 1)) #s(hole binary64 (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)))
#s(approx (/ (- 1 x) (+ x 1)) #s(hole binary64 (- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)))

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) 1 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (- 1 x) x (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (+ (* 1/2 x) -1) x) 1) (+ (* 1/2 x) -1) 1/2 -1 (* (atan (sqrt (/ (- 1 x) (+ x 1)))) 2) (atan (sqrt (/ (- 1 x) (+ x 1)))) (sqrt (/ (- 1 x) (+ x 1))) (/ (- 1 x) (+ x 1)) (+ x 1))

1.0ms

inf

((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) 1 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (- 1 x) x (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (+ (* 1/2 x) -1) x) 1) (+ (* 1/2 x) -1) 1/2 -1 (* (atan (sqrt (/ (- 1 x) (+ x 1)))) 2) (atan (sqrt (/ (- 1 x) (+ x 1)))) (sqrt (/ (- 1 x) (+ x 1))) (/ (- 1 x) (+ x 1)) (+ x 1))

1.0ms

-inf

((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) 1 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (- 1 x) x (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (+ (* 1/2 x) -1) x) 1) (+ (* 1/2 x) -1) 1/2 -1 (* (atan (sqrt (/ (- 1 x) (+ x 1)))) 2) (atan (sqrt (/ (- 1 x) (+ x 1)))) (sqrt (/ (- 1 x) (+ x 1))) (/ (- 1 x) (+ x 1)) (+ x 1))

rewrite66.0ms (4.7%)

Memory

-8.4MiB live, 38.2MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	187	908
0	202	795
0	1509	780

Stop Event

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

Counts

59 → 131

Calls

Call 1

Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))
#s(literal 1 binary64)
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
x
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
#s(literal 1/2 binary64)
#s(literal -1 binary64)
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
#s(approx (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) #s(hole binary64 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))))
#s(approx (atan (sqrt (/ (- 1 x) (+ 1 x)))) #s(hole binary64 (atan (sqrt (/ (- 1 x) (+ 1 x))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 1))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* x (- (* 1/2 x) 1)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
#s(approx x #s(hole binary64 x))
#s(approx (+ (* 1/2 x) -1) #s(hole binary64 -1))
#s(approx (+ (* 1/2 x) -1) #s(hole binary64 (- (* 1/2 x) 1)))
#s(approx (/ (- 1 x) (+ x 1)) #s(hole binary64 (+ 1 (* -2 x))))
#s(approx (/ (- 1 x) (+ x 1)) #s(hole binary64 (+ 1 (* x (- (* 2 x) 2)))))
#s(approx (/ (- 1 x) (+ x 1)) #s(hole binary64 (+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))))
#s(approx (+ x 1) #s(hole binary64 (+ 1 x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (sqrt -1)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (/ 1 (* x (sqrt -1))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))))
#s(approx (- 1 x) #s(hole binary64 (* -1 x)))
#s(approx (- 1 x) #s(hole binary64 (* x (- (/ 1 x) 1))))
#s(approx (+ (* (+ (* 1/2 x) -1) x) 1) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (+ (* (+ (* 1/2 x) -1) x) 1) #s(hole binary64 (* (pow x 2) (- 1/2 (/ 1 x)))))
#s(approx (+ (* (+ (* 1/2 x) -1) x) 1) #s(hole binary64 (* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))))
#s(approx (+ (* 1/2 x) -1) #s(hole binary64 (* 1/2 x)))
#s(approx (+ (* 1/2 x) -1) #s(hole binary64 (* x (- 1/2 (/ 1 x)))))
#s(approx (/ (- 1 x) (+ x 1)) #s(hole binary64 (- (* 2 (/ 1 x)) 1)))
#s(approx (/ (- 1 x) (+ x 1)) #s(hole binary64 (- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))))
#s(approx (/ (- 1 x) (+ x 1)) #s(hole binary64 (- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))))
#s(approx (+ x 1) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) #s(hole binary64 (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))))
#s(approx (atan (sqrt (/ (- 1 x) (+ 1 x)))) #s(hole binary64 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))))
#s(approx (- 1 x) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))
#s(approx (+ (* (+ (* 1/2 x) -1) x) 1) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))))
#s(approx (+ (* 1/2 x) -1) #s(hole binary64 (* -1 (* x (- (/ 1 x) 1/2)))))
#s(approx (/ (- 1 x) (+ x 1)) #s(hole binary64 (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)))
#s(approx (/ (- 1 x) (+ x 1)) #s(hole binary64 (- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)))

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

eval14.0ms (1%)

Memory: 17.2MiB live, 17.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 145 to 676 computations (41% saved)

prune4.0ms (0.3%)

Memory

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

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	0	0	0
Picked	2	2	4
Done	0	0	0
Total	124	5	129

Accuracy

100.0%

Counts

129 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
▶	99.4%	(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64))
✓	99.3%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
▶	99.0%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (- 1 x) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))))
✓	98.6%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))

Compiler

Compiled 64 to 63 computations (1.6% saved)

series15.0ms (1%)

Memory

-39.1MiB live, 12.7MiB allocated; 8ms collecting garbage

Counts

23 → 40

Calls

Call 1

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

Outputs
#s(approx (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) #s(hole binary64 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))))
#s(approx (atan (sqrt (/ (- 1 x) (+ 1 x)))) #s(hole binary64 (atan (sqrt (/ (- 1 x) (+ 1 x))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 1))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* x (- (* 1/2 x) 1)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
#s(approx (- (/ 1 x) 1) #s(hole binary64 (/ 1 x)))
#s(approx (- (/ 1 x) 1) #s(hole binary64 (/ (+ 1 (* -1 x)) x)))
#s(approx x #s(hole binary64 x))
#s(approx (+ (* 1/2 x) -1) #s(hole binary64 -1))
#s(approx (+ (* 1/2 x) -1) #s(hole binary64 (- (* 1/2 x) 1)))
#s(approx (/ (- 1 x) (- x -1)) #s(hole binary64 (+ 1 (* -2 x))))
#s(approx (/ (- 1 x) (- x -1)) #s(hole binary64 (+ 1 (* x (- (* 2 x) 2)))))
#s(approx (/ (- 1 x) (- x -1)) #s(hole binary64 (+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))))
#s(approx (- x -1) #s(hole binary64 (+ 1 x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (sqrt -1)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (/ 1 (* x (sqrt -1))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))))
#s(approx (- 1 x) #s(hole binary64 (* -1 x)))
#s(approx (- 1 x) #s(hole binary64 (* x (- (/ 1 x) 1))))
#s(approx (- (/ 1 x) 1) #s(hole binary64 (- (/ 1 x) 1)))
#s(approx (+ (* (+ (* 1/2 x) -1) x) 1) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (+ (* (+ (* 1/2 x) -1) x) 1) #s(hole binary64 (* (pow x 2) (- 1/2 (/ 1 x)))))
#s(approx (+ (* (+ (* 1/2 x) -1) x) 1) #s(hole binary64 (* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))))
#s(approx (+ (* 1/2 x) -1) #s(hole binary64 (* 1/2 x)))
#s(approx (+ (* 1/2 x) -1) #s(hole binary64 (* x (- 1/2 (/ 1 x)))))
#s(approx (/ (- 1 x) (- x -1)) #s(hole binary64 (- (* 2 (/ 1 x)) 1)))
#s(approx (/ (- 1 x) (- x -1)) #s(hole binary64 (- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))))
#s(approx (/ (- 1 x) (- x -1)) #s(hole binary64 (- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))))
#s(approx (- x -1) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) #s(hole binary64 (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))))
#s(approx (atan (sqrt (/ (- 1 x) (+ 1 x)))) #s(hole binary64 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))))
#s(approx (- 1 x) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))
#s(approx (+ (* (+ (* 1/2 x) -1) x) 1) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))))
#s(approx (+ (* 1/2 x) -1) #s(hole binary64 (* -1 (* x (- (/ 1 x) 1/2)))))
#s(approx (/ (- 1 x) (- x -1)) #s(hole binary64 (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)))
#s(approx (/ (- 1 x) (- x -1)) #s(hole binary64 (- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)))

Calls

3 calls:

Time	Variable		Point	Expression
11.0ms	x	@	-inf	((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (- 1 x) (* (- (/ 1 x) 1) x) (- (/ 1 x) 1) (/ 1 x) 1 x (* (atan (sqrt (/ (- 1 x) (+ 1 x)))) 2) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (+ (* 1/2 x) -1) x) 1) (+ (* 1/2 x) -1) 1/2 -1 (* (atan (sqrt (/ (- 1 x) (- x -1)))) 2) (atan (sqrt (/ (- 1 x) (- x -1)))) (sqrt (/ (- 1 x) (- x -1))) (/ (- 1 x) (- x -1)) (- 1 x) (- x -1))
1.0ms	x	@	inf	((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (- 1 x) (* (- (/ 1 x) 1) x) (- (/ 1 x) 1) (/ 1 x) 1 x (* (atan (sqrt (/ (- 1 x) (+ 1 x)))) 2) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (+ (* 1/2 x) -1) x) 1) (+ (* 1/2 x) -1) 1/2 -1 (* (atan (sqrt (/ (- 1 x) (- x -1)))) 2) (atan (sqrt (/ (- 1 x) (- x -1)))) (sqrt (/ (- 1 x) (- x -1))) (/ (- 1 x) (- x -1)) (- 1 x) (- x -1))
1.0ms	x	@	0	((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (- 1 x) (* (- (/ 1 x) 1) x) (- (/ 1 x) 1) (/ 1 x) 1 x (* (atan (sqrt (/ (- 1 x) (+ 1 x)))) 2) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (+ (* 1/2 x) -1) x) 1) (+ (* 1/2 x) -1) 1/2 -1 (* (atan (sqrt (/ (- 1 x) (- x -1)))) 2) (atan (sqrt (/ (- 1 x) (- x -1)))) (sqrt (/ (- 1 x) (- x -1))) (/ (- 1 x) (- x -1)) (- 1 x) (- x -1))

Time

Variable

Point

Expression

11.0ms

-inf

((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (- 1 x) (* (- (/ 1 x) 1) x) (- (/ 1 x) 1) (/ 1 x) 1 x (* (atan (sqrt (/ (- 1 x) (+ 1 x)))) 2) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (+ (* 1/2 x) -1) x) 1) (+ (* 1/2 x) -1) 1/2 -1 (* (atan (sqrt (/ (- 1 x) (- x -1)))) 2) (atan (sqrt (/ (- 1 x) (- x -1)))) (sqrt (/ (- 1 x) (- x -1))) (/ (- 1 x) (- x -1)) (- 1 x) (- x -1))

1.0ms

inf

((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (- 1 x) (* (- (/ 1 x) 1) x) (- (/ 1 x) 1) (/ 1 x) 1 x (* (atan (sqrt (/ (- 1 x) (+ 1 x)))) 2) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (+ (* 1/2 x) -1) x) 1) (+ (* 1/2 x) -1) 1/2 -1 (* (atan (sqrt (/ (- 1 x) (- x -1)))) 2) (atan (sqrt (/ (- 1 x) (- x -1)))) (sqrt (/ (- 1 x) (- x -1))) (/ (- 1 x) (- x -1)) (- 1 x) (- x -1))

1.0ms

((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (- 1 x) (* (- (/ 1 x) 1) x) (- (/ 1 x) 1) (/ 1 x) 1 x (* (atan (sqrt (/ (- 1 x) (+ 1 x)))) 2) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (+ (* 1/2 x) -1) x) 1) (+ (* 1/2 x) -1) 1/2 -1 (* (atan (sqrt (/ (- 1 x) (- x -1)))) 2) (atan (sqrt (/ (- 1 x) (- x -1)))) (sqrt (/ (- 1 x) (- x -1))) (/ (- 1 x) (- x -1)) (- 1 x) (- x -1))

rewrite74.0ms (5.2%)

Memory

6.8MiB live, 93.8MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	193	957
0	210	846
0	1531	831

Stop Event

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

Counts

63 → 139

Calls

Call 1

Inputs
(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (- 1 x) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (- 1 x) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (- 1 x) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))
#s(approx (- 1 x) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
#s(literal 1/2 binary64)
#s(literal -1 binary64)
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64)))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) x)
(-.f64 x #s(literal -1 binary64))
#s(approx (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) #s(hole binary64 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))))
#s(approx (atan (sqrt (/ (- 1 x) (+ 1 x)))) #s(hole binary64 (atan (sqrt (/ (- 1 x) (+ 1 x))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 1))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* x (- (* 1/2 x) 1)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
#s(approx (- (/ 1 x) 1) #s(hole binary64 (/ 1 x)))
#s(approx (- (/ 1 x) 1) #s(hole binary64 (/ (+ 1 (* -1 x)) x)))
#s(approx x #s(hole binary64 x))
#s(approx (+ (* 1/2 x) -1) #s(hole binary64 -1))
#s(approx (+ (* 1/2 x) -1) #s(hole binary64 (- (* 1/2 x) 1)))
#s(approx (/ (- 1 x) (- x -1)) #s(hole binary64 (+ 1 (* -2 x))))
#s(approx (/ (- 1 x) (- x -1)) #s(hole binary64 (+ 1 (* x (- (* 2 x) 2)))))
#s(approx (/ (- 1 x) (- x -1)) #s(hole binary64 (+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))))
#s(approx (- x -1) #s(hole binary64 (+ 1 x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (sqrt -1)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (/ 1 (* x (sqrt -1))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))))
#s(approx (- 1 x) #s(hole binary64 (* -1 x)))
#s(approx (- 1 x) #s(hole binary64 (* x (- (/ 1 x) 1))))
#s(approx (- (/ 1 x) 1) #s(hole binary64 (- (/ 1 x) 1)))
#s(approx (+ (* (+ (* 1/2 x) -1) x) 1) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (+ (* (+ (* 1/2 x) -1) x) 1) #s(hole binary64 (* (pow x 2) (- 1/2 (/ 1 x)))))
#s(approx (+ (* (+ (* 1/2 x) -1) x) 1) #s(hole binary64 (* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))))
#s(approx (+ (* 1/2 x) -1) #s(hole binary64 (* 1/2 x)))
#s(approx (+ (* 1/2 x) -1) #s(hole binary64 (* x (- 1/2 (/ 1 x)))))
#s(approx (/ (- 1 x) (- x -1)) #s(hole binary64 (- (* 2 (/ 1 x)) 1)))
#s(approx (/ (- 1 x) (- x -1)) #s(hole binary64 (- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))))
#s(approx (/ (- 1 x) (- x -1)) #s(hole binary64 (- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))))
#s(approx (- x -1) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) #s(hole binary64 (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))))
#s(approx (atan (sqrt (/ (- 1 x) (+ 1 x)))) #s(hole binary64 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))))
#s(approx (- 1 x) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))
#s(approx (+ (* (+ (* 1/2 x) -1) x) 1) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))))
#s(approx (+ (* 1/2 x) -1) #s(hole binary64 (* -1 (* x (- (/ 1 x) 1/2)))))
#s(approx (/ (- 1 x) (- x -1)) #s(hole binary64 (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)))
#s(approx (/ (- 1 x) (- x -1)) #s(hole binary64 (- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)))

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

eval13.0ms (0.9%)

Memory: 33.5MiB live, 33.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 084 to 710 computations (34.5% saved)

prune4.0ms (0.3%)

Memory

9.5MiB live, 9.5MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	0	0
Picked	1	2	3
Done	0	2	2
Total	112	5	117

Accuracy

100.0%

Counts

117 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
✓	99.4%	(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64))
▶	99.0%	(.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (- 1 x) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))) #s(literal 2 binary64))
✓	99.3%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
✓	98.6%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))

Compiler

Compiled 64 to 63 computations (1.6% saved)

series6.0ms (0.4%)

Memory

-39.5MiB live, 5.9MiB allocated; 6ms collecting garbage

Counts

10 → 22

Calls

Call 1

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

Outputs
#s(approx (* (atan (sqrt (/ (- 1 x) (+ 1 x)))) 2) #s(hole binary64 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))))
#s(approx (atan (sqrt (/ (- 1 x) (+ 1 x)))) #s(hole binary64 (atan (sqrt (/ (- 1 x) (+ 1 x))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 1))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* x (- (* 1/2 x) 1)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
#s(approx (- (/ 1 x) 1) #s(hole binary64 (/ 1 x)))
#s(approx (- (/ 1 x) 1) #s(hole binary64 (/ (+ 1 (* -1 x)) x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (sqrt -1)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (/ 1 (* x (sqrt -1))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))))
#s(approx (- 1 x) #s(hole binary64 (* -1 x)))
#s(approx (- 1 x) #s(hole binary64 (* x (- (/ 1 x) 1))))
#s(approx (- (/ 1 x) 1) #s(hole binary64 -1))
#s(approx (- (/ 1 x) 1) #s(hole binary64 (- (/ 1 x) 1)))
#s(approx (* (atan (sqrt (/ (- 1 x) (+ 1 x)))) 2) #s(hole binary64 (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))))
#s(approx (atan (sqrt (/ (- 1 x) (+ 1 x)))) #s(hole binary64 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))))
#s(approx (- 1 x) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	((* (atan (sqrt (/ (- 1 x) (+ 1 x)))) 2) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (- 1 x) (* (- (/ 1 x) 1) x) (- (/ 1 x) 1) (/ 1 x) 1 x 2)
1.0ms	x	@	-inf	((* (atan (sqrt (/ (- 1 x) (+ 1 x)))) 2) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (- 1 x) (* (- (/ 1 x) 1) x) (- (/ 1 x) 1) (/ 1 x) 1 x 2)
1.0ms	x	@	inf	((* (atan (sqrt (/ (- 1 x) (+ 1 x)))) 2) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (- 1 x) (* (- (/ 1 x) 1) x) (- (/ 1 x) 1) (/ 1 x) 1 x 2)

Time

Variable

Point

Expression

4.0ms

((* (atan (sqrt (/ (- 1 x) (+ 1 x)))) 2) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (- 1 x) (* (- (/ 1 x) 1) x) (- (/ 1 x) 1) (/ 1 x) 1 x 2)

1.0ms

-inf

((* (atan (sqrt (/ (- 1 x) (+ 1 x)))) 2) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (- 1 x) (* (- (/ 1 x) 1) x) (- (/ 1 x) 1) (/ 1 x) 1 x 2)

1.0ms

inf

((* (atan (sqrt (/ (- 1 x) (+ 1 x)))) 2) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (- 1 x) (* (- (/ 1 x) 1) x) (- (/ 1 x) 1) (/ 1 x) 1 x 2)

rewrite149.0ms (10.6%)

Memory

1.1MiB live, 75.0MiB allocated; 133ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	114	550
0	121	461
0	922	456

Stop Event

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

Counts

32 → 44

Calls

Call 1

Inputs
(.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (- 1 x) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))) #s(literal 2 binary64))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (- 1 x) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (- 1 x) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))
#s(approx (- 1 x) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal 2 binary64)
#s(approx (* (atan (sqrt (/ (- 1 x) (+ 1 x)))) 2) #s(hole binary64 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))))
#s(approx (atan (sqrt (/ (- 1 x) (+ 1 x)))) #s(hole binary64 (atan (sqrt (/ (- 1 x) (+ 1 x))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 1))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* x (- (* 1/2 x) 1)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
#s(approx (- (/ 1 x) 1) #s(hole binary64 (/ 1 x)))
#s(approx (- (/ 1 x) 1) #s(hole binary64 (/ (+ 1 (* -1 x)) x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (sqrt -1)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (/ 1 (* x (sqrt -1))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))))
#s(approx (- 1 x) #s(hole binary64 (* -1 x)))
#s(approx (- 1 x) #s(hole binary64 (* x (- (/ 1 x) 1))))
#s(approx (- (/ 1 x) 1) #s(hole binary64 -1))
#s(approx (- (/ 1 x) 1) #s(hole binary64 (- (/ 1 x) 1)))
#s(approx (* (atan (sqrt (/ (- 1 x) (+ 1 x)))) 2) #s(hole binary64 (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))))
#s(approx (atan (sqrt (/ (- 1 x) (+ 1 x)))) #s(hole binary64 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(hole binary64 (+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))))
#s(approx (- 1 x) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))

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

eval3.0ms (0.2%)

Memory: 5.2MiB live, 5.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 333 to 216 computations (35.1% saved)

prune3.0ms (0.2%)

Memory

5.6MiB live, 5.6MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	30	0	30
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	30	5	35

Accuracy

100.0%

Counts

35 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
✓	99.4%	(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64))
✓	99.0%	(.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (- 1 x) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))) #s(literal 2 binary64))
✓	99.3%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
✓	98.6%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))

Compiler

Compiled 141 to 109 computations (22.7% saved)

regimes85.0ms (6%)

Memory

-38.0MiB live, 17.9MiB allocated; 17ms collecting garbage

Counts

9 → 1

Calls

Call 1

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

Outputs
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))

Calls

5 calls:

76.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
3.0ms	x
2.0ms	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
2.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
2.0ms	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
100.0%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`
100.0%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
100.0%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
100.0%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
100.0%	1	`x`

Compiler

Compiled 32 to 28 computations (12.5% saved)

regimes8.0ms (0.6%)

Memory

15.3MiB live, 15.3MiB allocated; 0ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

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

Calls

5 calls:

2.0ms	x
1.0ms	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
1.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
99.4%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`
99.4%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
99.4%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
99.4%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
99.4%	1	`x`

Compiler

Compiled 32 to 28 computations (12.5% saved)

regimes7.0ms (0.5%)

Memory

14.3MiB live, 14.3MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

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

Calls

5 calls:

2.0ms	x
1.0ms	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
1.0ms	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
99.3%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`
99.3%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
99.3%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
99.3%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
99.3%	1	`x`

Compiler

Compiled 32 to 28 computations (12.5% saved)

regimes30.0ms (2.2%)

Memory

-37.6MiB live, 9.2MiB allocated; 3ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

5 calls:

1.0ms	x
1.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
1.0ms	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
98.6%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`
98.6%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
98.6%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
98.6%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
98.6%	1	`x`

Compiler

Compiled 32 to 28 computations (12.5% saved)

derivations18.0ms (1.2%)

Memory

22.9MiB live, 23.0MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 36 to 27 computations (25% saved)

preprocess31.0ms (2.2%)

Memory: -4.2MiB live, 41.5MiB allocated; 5ms collecting garbage
Compiler: Compiled 46 to 36 computations (21.7% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze4.0ms (0.3%)

sample743.0ms (52.9%)

preprocess46.0ms (3.3%)

series4.0ms (0.3%)

rewrite66.0ms (4.7%)

eval7.0ms (0.5%)

prune3.0ms (0.2%)

series5.0ms (0.3%)

rewrite66.0ms (4.7%)

eval14.0ms (1%)

prune4.0ms (0.3%)

series15.0ms (1%)

rewrite74.0ms (5.2%)

eval13.0ms (0.9%)

prune4.0ms (0.3%)

series6.0ms (0.4%)

rewrite149.0ms (10.6%)

eval3.0ms (0.2%)

prune3.0ms (0.2%)

regimes85.0ms (6%)

regimes8.0ms (0.6%)

regimes7.0ms (0.5%)

regimes30.0ms (2.2%)

derivations18.0ms (1.2%)

preprocess31.0ms (2.2%)

end0.0ms (0%)

Profiling