Metrics for arccos

start0.0ms (0%)

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

analyze20.0ms (1.4%)

Memory

-43.0MiB live, 11.0MiB allocated; 21ms 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)

sample906.0ms (60%)

Memory

9.0MiB live, 1 264.8MiB allocated; 220ms collecting garbage

Samples

644.0ms	8 256×	0	valid
1.0ms	24×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 397.0ms

ival-add!: 105.0ms (26.4% of total)

ival-atan: 74.0ms (18.6% of total)

ival-div!: 68.0ms (17.1% of total)

ival-sqrt: 66.0ms (16.6% of total)

ival-mult!: 45.0ms (11.3% of total)

ival-sub!: 36.0ms (9.1% of total)

adjust: 2.0ms (0.5% of total)

Bogosity

preprocess60.0ms (4%)

Memory

-19.9MiB live, 26.7MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	37
1	37	37
2	57	37
3	132	33
4	466	33
5	2862	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)

series5.0ms (0.3%)

Memory

7.9MiB live, 7.9MiB allocated; 0ms collecting garbage

Counts

9 → 34

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))
#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 (- 1 x) #s(hole binary64 1))
#s(approx (- 1 x) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx x #s(hole binary64 x))
#s(approx (+ 1 x) #s(hole binary64 1))
#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))
#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))
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	@	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))

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

((* 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 (4.4%)

Memory

3.9MiB live, 57.9MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	154	685
0	161	587
0	953	578

Stop Event

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

Counts

43 → 54

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

eval5.0ms (0.3%)

Memory: 8.0MiB live, 8.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 503 to 278 computations (44.7% saved)

prune2.0ms (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	46	4	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	4	51

Accuracy

100.0%

Counts

51 → 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))
▶	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
▶	98.9%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (neg.f64 x) #s(literal 1 binary64)))))
▶	98.4%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))

Compiler

Compiled 43 to 43 computations (0% saved)

series7.0ms (0.5%)

Memory

8.1MiB live, 8.1MiB allocated; 0ms collecting garbage

Counts

22 → 92

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

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 (+ (neg x) 1) #s(hole binary64 1))
#s(approx (+ (neg x) 1) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* 2 (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1))))) #s(hole binary64 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))))
#s(approx (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) #s(hole binary64 (atan (sqrt (/ (- 1 x) (+ 1 x))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 1))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ 1 (* x (- (* 1/2 x) 1)))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 1))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* -1/2 x))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* x (- (* -1/8 x) 1/2)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))))
#s(approx (- 1 x) #s(hole binary64 1))
#s(approx (- 1 x) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 1))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (+ x 1) #s(hole binary64 1))
#s(approx (+ x 1) #s(hole binary64 (+ 1 x)))
#s(approx (* (atan (sqrt (/ (- 1 x) (+ x 1)))) 2) #s(hole binary64 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))))
#s(approx (atan (sqrt (/ (- 1 x) (+ x 1)))) #s(hole binary64 (atan (sqrt (/ (- 1 x) (+ 1 x))))))
#s(approx (sqrt (/ (- 1 x) (+ x 1))) #s(hole binary64 1))
#s(approx (sqrt (/ (- 1 x) (+ x 1))) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (sqrt (/ (- 1 x) (+ x 1))) #s(hole binary64 (+ 1 (* x (- (* 1/2 x) 1)))))
#s(approx (sqrt (/ (- 1 x) (+ x 1))) #s(hole binary64 (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
#s(approx (/ (- 1 x) (+ x 1)) #s(hole binary64 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 (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 (+ (neg x) 1) #s(hole binary64 (* -1 x)))
#s(approx (+ (neg x) 1) #s(hole binary64 (* x (- (/ 1 x) 1))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (sqrt -1)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ (sqrt -1) (/ 1 (* x (sqrt -1))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #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)) (sqrt (+ x 1))) #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 (sqrt (- 1 x)) #s(hole binary64 (* (sqrt x) (sqrt -1))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 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 (sqrt (+ x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))))
#s(approx (+ x 1) #s(hole binary64 x))
#s(approx (+ x 1) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (sqrt (/ (- 1 x) (+ x 1))) #s(hole binary64 (sqrt -1)))
#s(approx (sqrt (/ (- 1 x) (+ x 1))) #s(hole binary64 (+ (sqrt -1) (/ 1 (* x (sqrt -1))))))
#s(approx (sqrt (/ (- 1 x) (+ x 1))) #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) (+ x 1))) #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) (+ x 1)) #s(hole binary64 -1))
#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 (* 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 (+ (neg x) 1) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))
#s(approx (* 2 (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1))))) #s(hole binary64 (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))))
#s(approx (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) #s(hole binary64 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #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)) (sqrt (+ x 1))) #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 (sqrt (- 1 x)) #s(hole binary64 (* -1 (* (sqrt x) (sqrt -1)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))))
#s(approx (- 1 x) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
#s(approx (* (atan (sqrt (/ (- 1 x) (+ x 1)))) 2) #s(hole binary64 (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))))
#s(approx (atan (sqrt (/ (- 1 x) (+ x 1)))) #s(hole binary64 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))))
#s(approx (sqrt (/ (- 1 x) (+ x 1))) #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) (+ x 1))) #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) (+ 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
3.0ms	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))) (+ (neg x) 1) (neg x) x (* 2 (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1))))) (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (sqrt (- 1 x)) (- 1 x) (sqrt (+ x 1)) (+ x 1) (* (atan (sqrt (/ (- 1 x) (+ x 1)))) 2) (atan (sqrt (/ (- 1 x) (+ x 1)))) (sqrt (/ (- 1 x) (+ x 1))) (/ (- 1 x) (+ x 1)))
2.0ms	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))) (+ (neg x) 1) (neg x) x (* 2 (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1))))) (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (sqrt (- 1 x)) (- 1 x) (sqrt (+ x 1)) (+ x 1) (* (atan (sqrt (/ (- 1 x) (+ x 1)))) 2) (atan (sqrt (/ (- 1 x) (+ x 1)))) (sqrt (/ (- 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 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (neg x) 1) (neg x) x (* 2 (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1))))) (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (sqrt (- 1 x)) (- 1 x) (sqrt (+ x 1)) (+ x 1) (* (atan (sqrt (/ (- 1 x) (+ x 1)))) 2) (atan (sqrt (/ (- 1 x) (+ x 1)))) (sqrt (/ (- 1 x) (+ x 1))) (/ (- 1 x) (+ x 1)))

Time

Variable

Point

Expression

3.0ms

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

2.0ms

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

rewrite74.0ms (4.9%)

Memory

-7.2MiB live, 40.2MiB allocated; 1ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	337	2250
0	361	1866
0	1808	1819

Stop Event

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

Counts

114 → 149

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 (neg.f64 x) #s(literal 1 binary64)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (neg.f64 x) #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (neg.f64 x) #s(literal 1 binary64)))
(+.f64 (neg.f64 x) #s(literal 1 binary64))
(neg.f64 x)
x
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 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))
(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)))
#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 (+ (neg x) 1) #s(hole binary64 1))
#s(approx (+ (neg x) 1) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* 2 (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1))))) #s(hole binary64 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))))
#s(approx (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) #s(hole binary64 (atan (sqrt (/ (- 1 x) (+ 1 x))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 1))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ 1 (* x (- (* 1/2 x) 1)))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 1))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* -1/2 x))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* x (- (* -1/8 x) 1/2)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))))
#s(approx (- 1 x) #s(hole binary64 1))
#s(approx (- 1 x) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 1))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (+ x 1) #s(hole binary64 1))
#s(approx (+ x 1) #s(hole binary64 (+ 1 x)))
#s(approx (* (atan (sqrt (/ (- 1 x) (+ x 1)))) 2) #s(hole binary64 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))))
#s(approx (atan (sqrt (/ (- 1 x) (+ x 1)))) #s(hole binary64 (atan (sqrt (/ (- 1 x) (+ 1 x))))))
#s(approx (sqrt (/ (- 1 x) (+ x 1))) #s(hole binary64 1))
#s(approx (sqrt (/ (- 1 x) (+ x 1))) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (sqrt (/ (- 1 x) (+ x 1))) #s(hole binary64 (+ 1 (* x (- (* 1/2 x) 1)))))
#s(approx (sqrt (/ (- 1 x) (+ x 1))) #s(hole binary64 (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
#s(approx (/ (- 1 x) (+ x 1)) #s(hole binary64 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 (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 (+ (neg x) 1) #s(hole binary64 (* -1 x)))
#s(approx (+ (neg x) 1) #s(hole binary64 (* x (- (/ 1 x) 1))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (sqrt -1)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ (sqrt -1) (/ 1 (* x (sqrt -1))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #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)) (sqrt (+ x 1))) #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 (sqrt (- 1 x)) #s(hole binary64 (* (sqrt x) (sqrt -1))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 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 (sqrt (+ x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))))
#s(approx (+ x 1) #s(hole binary64 x))
#s(approx (+ x 1) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (sqrt (/ (- 1 x) (+ x 1))) #s(hole binary64 (sqrt -1)))
#s(approx (sqrt (/ (- 1 x) (+ x 1))) #s(hole binary64 (+ (sqrt -1) (/ 1 (* x (sqrt -1))))))
#s(approx (sqrt (/ (- 1 x) (+ x 1))) #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) (+ x 1))) #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) (+ x 1)) #s(hole binary64 -1))
#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 (* 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 (+ (neg x) 1) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))
#s(approx (* 2 (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1))))) #s(hole binary64 (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))))
#s(approx (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) #s(hole binary64 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #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)) (sqrt (+ x 1))) #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 (sqrt (- 1 x)) #s(hole binary64 (* -1 (* (sqrt x) (sqrt -1)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))))
#s(approx (- 1 x) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
#s(approx (* (atan (sqrt (/ (- 1 x) (+ x 1)))) 2) #s(hole binary64 (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))))
#s(approx (atan (sqrt (/ (- 1 x) (+ x 1)))) #s(hole binary64 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))))
#s(approx (sqrt (/ (- 1 x) (+ x 1))) #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) (+ x 1))) #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) (+ 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)) (sqrt (+ x 1))) #s(literal 1 binary64))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(literal 1 binary64))))
(+.f64 (atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(literal 1 binary64))) (atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(literal 1 binary64))))
#s(literal 2 binary64)
(atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(literal 1 binary64)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(literal 1 binary64))
#s(literal 1 binary64)
(*.f64 (atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.f64 (neg.f64 x) #s(literal 1 binary64)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.f64 (neg.f64 x) #s(literal 1 binary64)))))
(+.f64 (atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.f64 (neg.f64 x) #s(literal 1 binary64)))) (atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.f64 (neg.f64 x) #s(literal 1 binary64)))))
(atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.f64 (neg.f64 x) #s(literal 1 binary64))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.f64 (neg.f64 x) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) (neg.f64 x))) (-.f64 #s(literal 1 binary64) (neg.f64 x)))
(/.f64 (-.f64 (*.f64 (neg.f64 x) (neg.f64 x)) #s(literal 1 binary64)) (-.f64 (neg.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 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (neg.f64 x) (neg.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (neg.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) (*.f64 #s(literal 1 binary64) x))
(+.f64 (neg.f64 x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (neg.f64 x))
(*.f64 #s(literal -1 binary64) x)
(*.f64 x #s(literal -1 binary64))
(neg.f64 x)
x
(*.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 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 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))))
(pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 x #s(literal 1 binary64)))
(/.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))))
(-.f64 #s(literal 1 binary64) x)
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x 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 (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 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
(*.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 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 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))))
(/.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 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 x (+.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)) (sqrt (+ x 1))) #s(literal 1 binary64))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.f64 (neg.f64 x) #s(literal 1 binary64)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (fma.f64 (-.f64 (*.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 (+ (neg x) 1) #s(literal 1 binary64))
#s(approx (+ (neg x) 1) (+.f64 (neg.f64 x) #s(literal 1 binary64)))
#s(approx (neg x) (neg.f64 x))
#s(approx x 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)) (sqrt (+ x 1))) #s(literal 1 binary64))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.f64 (neg.f64 x) #s(literal 1 binary64)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (fma.f64 (-.f64 (*.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 (sqrt (- 1 x)) #s(literal 1 binary64))
#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
#s(approx (sqrt (- 1 x)) (fma.f64 (-.f64 (*.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (sqrt (- 1 x)) (fma.f64 (-.f64 (.f64 (-.f64 (.f64 #s(literal -1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (- 1 x) #s(literal 1 binary64))
#s(approx (- 1 x) (+.f64 (neg.f64 x) #s(literal 1 binary64)))
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
#s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
#s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (+ x 1) #s(literal 1 binary64))
#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)) (sqrt (+ x 1))) #s(literal 1 binary64))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.f64 (neg.f64 x) #s(literal 1 binary64)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (fma.f64 (-.f64 (*.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) (+ x 1)) #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 (-.f64 (+.f64 x x) #s(literal 2 binary64)) x #s(literal 1 binary64)))
#s(approx (/ (- 1 x) (+ x 1)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x) #s(literal 2 binary64)) x #s(literal 1 binary64)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (sqrt.f64 #s(literal -1 binary64)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.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)) (sqrt (+ x 1))) (+.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)) (sqrt (+ x 1))) (+.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 (+ (neg x) 1) (neg.f64 x))
#s(approx (+ (neg x) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (sqrt.f64 #s(literal -1 binary64)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.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)) (sqrt (+ x 1))) (+.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)) (sqrt (+ x 1))) (+.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 (sqrt (- 1 x)) (sqrt.f64 (neg.f64 x)))
#s(approx (sqrt (- 1 x)) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)))) #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))) x))
#s(approx (sqrt (- 1 x)) (.f64 (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)))) #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))))) x))
#s(approx (sqrt (- 1 x)) (.f64 (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -7 binary64))) #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -5 binary64)) (fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)))) #s(literal 1/2 binary64) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))))) 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 (sqrt (+ x 1)) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) (.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (sqrt (+ x 1)) (.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (sqrt (+ x 1)) (.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (pow.f64 x #s(literal -7 binary64))) #s(literal 1/16 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (+ x 1) x)
#s(approx (+ x 1) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (sqrt.f64 #s(literal -1 binary64)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.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)) (sqrt (+ x 1))) (+.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)) (sqrt (+ x 1))) (+.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) (+ x 1)) #s(literal -1 binary64))
#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 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (*.f64 (atan.f64 (sqrt.f64 (/.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 x))))) #s(literal 2 binary64)))
#s(approx (atan (sqrt (/ (- 1 x) (+ 1 x)))) (atan.f64 (sqrt.f64 (/.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 x))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.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)) (sqrt (+ x 1))) (+.f64 (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (/.f64 #s(literal -1/2 binary64) (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 (+ (neg x) 1) (*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))
#s(approx (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (*.f64 (atan.f64 (sqrt.f64 (/.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 x))))) #s(literal 2 binary64)))
#s(approx (atan (sqrt (/ (- 1 x) (+ 1 x)))) (atan.f64 (sqrt.f64 (/.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 x))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.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)) (sqrt (+ x 1))) (+.f64 (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (/.f64 #s(literal -1/2 binary64) (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)) (neg.f64 (sqrt.f64 (neg.f64 x))))
#s(approx (sqrt (- 1 x)) (.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)) #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))))))
#s(approx (sqrt (- 1 x)) (.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal -5 binary64)) #s(literal -1 binary64))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)) #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))))))
#s(approx (sqrt (- 1 x)) (.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal -5 binary64)) #s(literal -1 binary64))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal -7 binary64)) #s(literal -1 binary64))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)) #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 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))))
#s(approx (sqrt (+ x 1)) (neg.f64 (*.f64 (sqrt.f64 x) #s(literal -1 binary64))))
#s(approx (sqrt (+ x 1)) (.f64 (neg.f64 x) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64)))))
#s(approx (sqrt (+ x 1)) (.f64 (neg.f64 x) (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal 1/2 binary64))))))
#s(approx (sqrt (+ x 1)) (.f64 (neg.f64 x) (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -7 binary64))) #s(literal 1/16 binary64)) #s(literal 1 binary64) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64)))))))
#s(approx (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (*.f64 (atan.f64 (sqrt.f64 (/.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 x))))) #s(literal 2 binary64)))
#s(approx (atan (sqrt (/ (- 1 x) (+ 1 x)))) (atan.f64 (sqrt.f64 (/.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 x))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.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)) (sqrt (+ x 1))) (+.f64 (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (/.f64 #s(literal -1/2 binary64) (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 (/ (- 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)))

eval26.0ms (1.7%)

Memory: -24.7MiB live, 22.5MiB allocated; 2ms collecting garbage
Compiler: Compiled 1 250 to 653 computations (47.8% saved)

prune3.0ms (0.2%)

Memory

8.0MiB live, 8.0MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	118	5	123

Accuracy

100.0%

Counts

123 → 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))
▶	98.4%	(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
✓	98.9%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (neg.f64 x) #s(literal 1 binary64)))))
▶	98.9%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (neg x) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))))
✓	98.4%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))

Compiler

Compiled 62 to 62 computations (0% saved)

series5.0ms (0.3%)

Memory

8.8MiB live, 8.8MiB allocated; 0ms collecting garbage

Counts

16 → 72

Calls

Call 1

Inputs
(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (neg x) 1) (.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 (+ (neg x) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (neg x) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))
#s(approx (+ (neg x) 1) (*.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 #s(literal 2 binary64) (atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
(sqrt.f64 (+.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 (+ (neg x) 1) #s(hole binary64 1))
#s(approx (+ (neg x) 1) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (* (- (/ 1 x) 1) x) #s(hole binary64 1))
#s(approx (* (- (/ 1 x) 1) x) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (- (/ 1 x) 1) #s(hole binary64 (/ 1 x)))
#s(approx (- (/ 1 x) 1) #s(hole binary64 (/ (+ 1 (* -1 x)) x)))
#s(approx (/ 1 x) #s(hole binary64 (/ 1 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* 2 (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1))))) #s(hole binary64 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))))
#s(approx (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) #s(hole binary64 (atan (sqrt (/ (- 1 x) (+ 1 x))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 1))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ 1 (* x (- (* 1/2 x) 1)))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 1))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* -1/2 x))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* x (- (* -1/8 x) 1/2)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 1))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (+ x 1) #s(hole binary64 1))
#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 (+ (neg x) 1) #s(hole binary64 (* -1 x)))
#s(approx (+ (neg x) 1) #s(hole binary64 (* x (- (/ 1 x) 1))))
#s(approx (* (- (/ 1 x) 1) x) #s(hole binary64 (* -1 x)))
#s(approx (* (- (/ 1 x) 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 (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (sqrt -1)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ (sqrt -1) (/ 1 (* x (sqrt -1))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #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)) (sqrt (+ x 1))) #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 (sqrt (- 1 x)) #s(hole binary64 (* (sqrt x) (sqrt -1))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))))
#s(approx (+ x 1) #s(hole binary64 x))
#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 (+ (neg x) 1) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))
#s(approx (* (- (/ 1 x) 1) x) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))
#s(approx (* 2 (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1))))) #s(hole binary64 (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))))
#s(approx (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) #s(hole binary64 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #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)) (sqrt (+ x 1))) #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 (sqrt (- 1 x)) #s(hole binary64 (* -1 (* (sqrt x) (sqrt -1)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

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

rewrite73.0ms (4.8%)

Memory

23.5MiB live, 68.1MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	281	1727
0	294	1441
0	1533	1403

Stop Event

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

Counts

88 → 104

Calls

Call 1

Inputs
(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (neg x) 1) (.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 (+ (neg x) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (neg x) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))
#s(approx (+ (neg x) 1) (*.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 #s(literal 2 binary64) (atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
(sqrt.f64 (+.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 (+ (neg x) 1) #s(hole binary64 1))
#s(approx (+ (neg x) 1) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (* (- (/ 1 x) 1) x) #s(hole binary64 1))
#s(approx (* (- (/ 1 x) 1) x) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (- (/ 1 x) 1) #s(hole binary64 (/ 1 x)))
#s(approx (- (/ 1 x) 1) #s(hole binary64 (/ (+ 1 (* -1 x)) x)))
#s(approx (/ 1 x) #s(hole binary64 (/ 1 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* 2 (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1))))) #s(hole binary64 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))))
#s(approx (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) #s(hole binary64 (atan (sqrt (/ (- 1 x) (+ 1 x))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 1))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ 1 (* x (- (* 1/2 x) 1)))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 1))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* -1/2 x))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* x (- (* -1/8 x) 1/2)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 1))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (+ x 1) #s(hole binary64 1))
#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 (+ (neg x) 1) #s(hole binary64 (* -1 x)))
#s(approx (+ (neg x) 1) #s(hole binary64 (* x (- (/ 1 x) 1))))
#s(approx (* (- (/ 1 x) 1) x) #s(hole binary64 (* -1 x)))
#s(approx (* (- (/ 1 x) 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 (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (sqrt -1)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ (sqrt -1) (/ 1 (* x (sqrt -1))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #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)) (sqrt (+ x 1))) #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 (sqrt (- 1 x)) #s(hole binary64 (* (sqrt x) (sqrt -1))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))))
#s(approx (+ x 1) #s(hole binary64 x))
#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 (+ (neg x) 1) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))
#s(approx (* (- (/ 1 x) 1) x) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))
#s(approx (* 2 (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1))))) #s(hole binary64 (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))))
#s(approx (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) #s(hole binary64 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #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)) (sqrt (+ x 1))) #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 (sqrt (- 1 x)) #s(hole binary64 (* -1 (* (sqrt x) (sqrt -1)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))

Outputs
(.f64 (atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(approx (+ (neg x) 1) (.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)) (sqrt (+ x 1))) #s(approx (+ (neg x) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))))
(+.f64 (atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(approx (+ (neg x) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))) (atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(approx (+ (neg x) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))))
#s(literal 2 binary64)
(atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(approx (+ (neg x) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(approx (+ (neg x) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))
#s(approx (+ (neg x) 1) (*.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 (*.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)))))
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(pow.f64 x #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 (atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(+.f64 (atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (neg.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x 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 (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 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
#s(approx (* 2 (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1))))) (*.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)) (sqrt (+ x 1)))) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(literal 1 binary64))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.f64 (neg.f64 x) #s(literal 1 binary64)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (fma.f64 (-.f64 (*.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 (+ (neg x) 1) #s(literal 1 binary64))
#s(approx (+ (neg x) 1) (+.f64 (neg.f64 x) #s(literal 1 binary64)))
#s(approx (* (- (/ 1 x) 1) x) #s(literal 1 binary64))
#s(approx (* (- (/ 1 x) 1) x) (+.f64 (neg.f64 x) #s(literal 1 binary64)))
#s(approx (- (/ 1 x) 1) (/.f64 #s(literal 1 binary64) x))
#s(approx (- (/ 1 x) 1) (/.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64)) x))
#s(approx (/ 1 x) (/.f64 #s(literal 1 binary64) x))
#s(approx x x)
#s(approx (* 2 (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1))))) (*.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)) (sqrt (+ x 1)))) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(literal 1 binary64))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.f64 (neg.f64 x) #s(literal 1 binary64)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (fma.f64 (-.f64 (*.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 (sqrt (- 1 x)) #s(literal 1 binary64))
#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
#s(approx (sqrt (- 1 x)) (fma.f64 (-.f64 (*.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (sqrt (- 1 x)) (fma.f64 (-.f64 (.f64 (-.f64 (.f64 #s(literal -1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
#s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
#s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (+ x 1) #s(literal 1 binary64))
#s(approx (+ x 1) (+.f64 x #s(literal 1 binary64)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (sqrt.f64 #s(literal -1 binary64)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.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)) (sqrt (+ x 1))) (+.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)) (sqrt (+ x 1))) (+.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 (+ (neg x) 1) (neg.f64 x))
#s(approx (+ (neg x) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x))
#s(approx (* (- (/ 1 x) 1) x) (neg.f64 x))
#s(approx (* (- (/ 1 x) 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 (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (sqrt.f64 #s(literal -1 binary64)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.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)) (sqrt (+ x 1))) (+.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)) (sqrt (+ x 1))) (+.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 (sqrt (- 1 x)) (sqrt.f64 (neg.f64 x)))
#s(approx (sqrt (- 1 x)) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)))) #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))) x))
#s(approx (sqrt (- 1 x)) (.f64 (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)))) #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))))) x))
#s(approx (sqrt (- 1 x)) (.f64 (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -7 binary64))) #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -5 binary64)) (fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)))) #s(literal 1/2 binary64) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))))) x))
#s(approx (sqrt (+ x 1)) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) (.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (sqrt (+ x 1)) (.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (sqrt (+ x 1)) (.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (pow.f64 x #s(literal -7 binary64))) #s(literal 1/16 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (+ x 1) 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)) (sqrt (+ x 1))))) (*.f64 (atan.f64 (sqrt.f64 (/.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 x))))) #s(literal 2 binary64)))
#s(approx (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) (atan.f64 (sqrt.f64 (/.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 x))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.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)) (sqrt (+ x 1))) (+.f64 (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (/.f64 #s(literal -1/2 binary64) (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 (+ (neg x) 1) (*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))
#s(approx (* (- (/ 1 x) 1) x) (*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))
#s(approx (* 2 (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1))))) (*.f64 (atan.f64 (sqrt.f64 (/.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 x))))) #s(literal 2 binary64)))
#s(approx (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) (atan.f64 (sqrt.f64 (/.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 x))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.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)) (sqrt (+ x 1))) (+.f64 (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (/.f64 #s(literal -1/2 binary64) (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)) (neg.f64 (sqrt.f64 (neg.f64 x))))
#s(approx (sqrt (- 1 x)) (.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)) #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))))))
#s(approx (sqrt (- 1 x)) (.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal -5 binary64)) #s(literal -1 binary64))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)) #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))))))
#s(approx (sqrt (- 1 x)) (.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal -5 binary64)) #s(literal -1 binary64))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal -7 binary64)) #s(literal -1 binary64))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)) #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))))))))
#s(approx (sqrt (+ x 1)) (neg.f64 (*.f64 (sqrt.f64 x) #s(literal -1 binary64))))
#s(approx (sqrt (+ x 1)) (.f64 (neg.f64 x) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64)))))
#s(approx (sqrt (+ x 1)) (.f64 (neg.f64 x) (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal 1/2 binary64))))))
#s(approx (sqrt (+ x 1)) (.f64 (neg.f64 x) (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -7 binary64))) #s(literal 1/16 binary64)) #s(literal 1 binary64) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64)))))))

eval27.0ms (1.8%)

Memory: -19.4MiB live, 29.6MiB allocated; 5ms collecting garbage
Compiler: Compiled 962 to 494 computations (48.6% saved)

prune3.0ms (0.2%)

Memory

7.6MiB live, 7.6MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	0	0	0
Picked	2	0	2
Done	0	3	3
Total	77	5	82

Accuracy

100.0%

Counts

82 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.4%	(*.f64 (atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
✓	100.0%	(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
▶	98.9%	(.f64 (atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(approx (+ (neg x) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))) #s(literal 2 binary64))
✓	98.9%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (neg.f64 x) #s(literal 1 binary64)))))
✓	98.4%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))

Compiler

Compiled 63 to 63 computations (0% saved)

series4.0ms (0.3%)

Memory

7.6MiB live, 7.6MiB allocated; 0ms collecting garbage

Counts

16 → 58

Calls

Call 1

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

Outputs
#s(approx (* (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) 2) #s(hole binary64 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))))
#s(approx (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) #s(hole binary64 (atan (sqrt (/ (- 1 x) (+ 1 x))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 1))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ 1 (* x (- (* 1/2 x) 1)))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
#s(approx (+ (neg x) 1) #s(hole binary64 1))
#s(approx (+ (neg x) 1) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (* (- (/ 1 x) 1) x) #s(hole binary64 1))
#s(approx (* (- (/ 1 x) 1) x) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (- (/ 1 x) 1) #s(hole binary64 (/ 1 x)))
#s(approx (- (/ 1 x) 1) #s(hole binary64 (/ (+ 1 (* -1 x)) x)))
#s(approx (/ 1 x) #s(hole binary64 (/ 1 x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- 1 x)) #s(hole binary64 1))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* -1/2 x))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* x (- (* -1/8 x) 1/2)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 1))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (+ x 1) #s(hole binary64 1))
#s(approx (+ x 1) #s(hole binary64 (+ 1 x)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (sqrt -1)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ (sqrt -1) (/ 1 (* x (sqrt -1))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #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)) (sqrt (+ x 1))) #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 (+ (neg x) 1) #s(hole binary64 (* -1 x)))
#s(approx (+ (neg x) 1) #s(hole binary64 (* x (- (/ 1 x) 1))))
#s(approx (* (- (/ 1 x) 1) x) #s(hole binary64 (* -1 x)))
#s(approx (* (- (/ 1 x) 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 (sqrt (- 1 x)) #s(hole binary64 (* (sqrt x) (sqrt -1))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))))
#s(approx (+ x 1) #s(hole binary64 x))
#s(approx (+ x 1) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (* (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) 2) #s(hole binary64 (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))))
#s(approx (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) #s(hole binary64 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #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)) (sqrt (+ x 1))) #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 (+ (neg x) 1) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))
#s(approx (* (- (/ 1 x) 1) x) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* (sqrt x) (sqrt -1)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

rewrite72.0ms (4.8%)

Memory

-13.3MiB live, 78.2MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	267	1347
0	280	1138
0	1519	1104

Stop Event

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

Counts

74 → 88

Calls

Call 1

Inputs
(.f64 (atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(approx (+ (neg x) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))) #s(literal 2 binary64))
(atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(approx (+ (neg x) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(approx (+ (neg x) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))
#s(approx (+ (neg x) 1) (*.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)
(*.f64 (atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
#s(approx (* (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) 2) #s(hole binary64 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))))
#s(approx (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) #s(hole binary64 (atan (sqrt (/ (- 1 x) (+ 1 x))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 1))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ 1 (* x (- (* 1/2 x) 1)))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))))
#s(approx (+ (neg x) 1) #s(hole binary64 1))
#s(approx (+ (neg x) 1) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (* (- (/ 1 x) 1) x) #s(hole binary64 1))
#s(approx (* (- (/ 1 x) 1) x) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (- (/ 1 x) 1) #s(hole binary64 (/ 1 x)))
#s(approx (- (/ 1 x) 1) #s(hole binary64 (/ (+ 1 (* -1 x)) x)))
#s(approx (/ 1 x) #s(hole binary64 (/ 1 x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- 1 x)) #s(hole binary64 1))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* -1/2 x))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* x (- (* -1/8 x) 1/2)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 1))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (+ x 1) #s(hole binary64 1))
#s(approx (+ x 1) #s(hole binary64 (+ 1 x)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (sqrt -1)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(hole binary64 (+ (sqrt -1) (/ 1 (* x (sqrt -1))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #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)) (sqrt (+ x 1))) #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 (+ (neg x) 1) #s(hole binary64 (* -1 x)))
#s(approx (+ (neg x) 1) #s(hole binary64 (* x (- (/ 1 x) 1))))
#s(approx (* (- (/ 1 x) 1) x) #s(hole binary64 (* -1 x)))
#s(approx (* (- (/ 1 x) 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 (sqrt (- 1 x)) #s(hole binary64 (* (sqrt x) (sqrt -1))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))))
#s(approx (+ x 1) #s(hole binary64 x))
#s(approx (+ x 1) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (* (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) 2) #s(hole binary64 (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))))
#s(approx (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) #s(hole binary64 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #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)) (sqrt (+ x 1))) #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 (+ (neg x) 1) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))
#s(approx (* (- (/ 1 x) 1) x) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* (sqrt x) (sqrt -1)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))

Outputs
(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(approx (+ (neg x) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))))
(.f64 (atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(approx (+ (neg x) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))) #s(literal 2 binary64))
(atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(approx (+ (neg x) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(approx (+ (neg x) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))
#s(approx (+ (neg x) 1) (*.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 (*.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)))))
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(pow.f64 x #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal 2 binary64)
(*.f64 (atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (neg.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 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 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) (.f64 (.f64 x x) x)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) (.f64 #s(literal 1 binary64) x))))
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
#s(approx (* (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) 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)) (sqrt (+ x 1)))) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(literal 1 binary64))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.f64 (neg.f64 x) #s(literal 1 binary64)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (fma.f64 (-.f64 (*.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 (+ (neg x) 1) #s(literal 1 binary64))
#s(approx (+ (neg x) 1) (+.f64 (neg.f64 x) #s(literal 1 binary64)))
#s(approx (* (- (/ 1 x) 1) x) #s(literal 1 binary64))
#s(approx (* (- (/ 1 x) 1) x) (+.f64 (neg.f64 x) #s(literal 1 binary64)))
#s(approx (- (/ 1 x) 1) (/.f64 #s(literal 1 binary64) x))
#s(approx (- (/ 1 x) 1) (/.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64)) x))
#s(approx (/ 1 x) (/.f64 #s(literal 1 binary64) x))
#s(approx x x)
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
#s(approx (sqrt (- 1 x)) (fma.f64 (-.f64 (*.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (sqrt (- 1 x)) (fma.f64 (-.f64 (.f64 (-.f64 (.f64 #s(literal -1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
#s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
#s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (+ x 1) #s(literal 1 binary64))
#s(approx (+ x 1) (+.f64 x #s(literal 1 binary64)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (sqrt.f64 #s(literal -1 binary64)))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.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)) (sqrt (+ x 1))) (+.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)) (sqrt (+ x 1))) (+.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 (+ (neg x) 1) (neg.f64 x))
#s(approx (+ (neg x) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x))
#s(approx (* (- (/ 1 x) 1) x) (neg.f64 x))
#s(approx (* (- (/ 1 x) 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 (sqrt (- 1 x)) (sqrt.f64 (neg.f64 x)))
#s(approx (sqrt (- 1 x)) (.f64 (fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)))) #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))) x))
#s(approx (sqrt (- 1 x)) (.f64 (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)))) #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))))) x))
#s(approx (sqrt (- 1 x)) (.f64 (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -7 binary64))) #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -5 binary64)) (fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)))) #s(literal 1/2 binary64) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))))) x))
#s(approx (sqrt (+ x 1)) (sqrt.f64 x))
#s(approx (sqrt (+ x 1)) (.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (sqrt (+ x 1)) (.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (sqrt (+ x 1)) (.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (pow.f64 x #s(literal -7 binary64))) #s(literal 1/16 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (+ x 1) x)
#s(approx (+ x 1) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x))
#s(approx (* (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) 2) (*.f64 (atan.f64 (sqrt.f64 (/.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 x))))) #s(literal 2 binary64)))
#s(approx (atan (/ (sqrt (- 1 x)) (sqrt (+ x 1)))) (atan.f64 (sqrt.f64 (/.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 x))))))
#s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) (+.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)) (sqrt (+ x 1))) (+.f64 (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (/.f64 #s(literal -1/2 binary64) (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 (+ (neg x) 1) (*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))
#s(approx (* (- (/ 1 x) 1) x) (*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))
#s(approx (sqrt (- 1 x)) (neg.f64 (sqrt.f64 (neg.f64 x))))
#s(approx (sqrt (- 1 x)) (.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)) #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))))))
#s(approx (sqrt (- 1 x)) (.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal -5 binary64)) #s(literal -1 binary64))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)) #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))))))
#s(approx (sqrt (- 1 x)) (.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal -5 binary64)) #s(literal -1 binary64))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal -7 binary64)) #s(literal -1 binary64))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)) #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))))))))
#s(approx (sqrt (+ x 1)) (neg.f64 (*.f64 (sqrt.f64 x) #s(literal -1 binary64))))
#s(approx (sqrt (+ x 1)) (.f64 (neg.f64 x) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64)))))
#s(approx (sqrt (+ x 1)) (.f64 (neg.f64 x) (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal 1/2 binary64))))))
#s(approx (sqrt (+ x 1)) (.f64 (neg.f64 x) (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -7 binary64))) #s(literal 1/16 binary64)) #s(literal 1 binary64) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64)))))))

eval8.0ms (0.5%)

Memory: 25.9MiB live, 25.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 879 to 488 computations (44.5% saved)

prune7.0ms (0.4%)

Memory

-27.7MiB live, 18.4MiB allocated; 4ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	72	5	77

Accuracy

100.0%

Counts

77 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.4%	(*.f64 (atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
✓	100.0%	(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
✓	98.9%	(.f64 (atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(approx (+ (neg x) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))) #s(literal 2 binary64))
✓	98.9%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (neg.f64 x) #s(literal 1 binary64)))))
✓	98.4%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))

Compiler

Compiled 140 to 116 computations (17.1% saved)

regimes19.0ms (1.3%)

Memory

-2.5MiB live, 55.0MiB allocated; 10ms 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 (neg.f64 x) #s(literal 1 binary64)))))
(*.f64 (atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(.f64 (atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(approx (+ (neg x) 1) (.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 (+ (neg x) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))))
(*.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)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))

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

Calls

5 calls:

10.0ms	(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	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
2.0ms	(atan.f64 (sqrt.f64 (/.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)

regimes11.0ms (0.7%)

Memory

-6.6MiB live, 40.8MiB allocated; 2ms collecting garbage

Counts

8 → 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 (neg.f64 x) #s(literal 1 binary64)))))
(*.f64 (atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(.f64 (atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(approx (+ (neg x) 1) (.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 (+ (neg x) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))))
(*.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:

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

25.8MiB live, 25.8MiB 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 (neg.f64 x) #s(literal 1 binary64)))))
(*.f64 (atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(.f64 (atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(approx (+ (neg x) 1) (.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 (+ (neg x) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))))

Outputs
(.f64 (atan.f64 #s(approx (/ (sqrt (- 1 x)) (sqrt (+ x 1))) #s(approx (+ (neg x) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))) #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	(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
98.9%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`
98.9%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
98.9%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
98.9%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
98.9%	1	`x`

Compiler

Compiled 32 to 28 computations (12.5% saved)

regimes8.0ms (0.5%)

Memory

-26.9MiB live, 19.6MiB allocated; 2ms 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 (neg.f64 x) #s(literal 1 binary64)))))
(*.f64 (atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 (/.f64 #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))

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

Calls

5 calls:

3.0ms	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
2.0ms	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
98.9%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`
98.9%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
98.9%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
98.9%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
98.9%	1	`x`

Compiler

Compiled 32 to 28 computations (12.5% saved)

regimes4.0ms (0.3%)

Memory

14.6MiB live, 14.6MiB allocated; 0ms 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	(*.f64 #s(literal 2 binary64) (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))
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))))

Results

Accuracy	Segments	Branch
98.4%	1	`x`
98.4%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`
98.4%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
98.4%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
98.4%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`

Compiler

Compiled 32 to 28 computations (12.5% saved)

derivations16.0ms (1.1%)

Memory

-22.7MiB live, 24.5MiB allocated; 1ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 47 to 40 computations (14.9% saved)

preprocess68.0ms (4.5%)

Memory: 24.2MiB live, 73.1MiB allocated; 4ms collecting garbage
Compiler: Compiled 57 to 49 computations (14% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze20.0ms (1.4%)

sample906.0ms (60%)

preprocess60.0ms (4%)

series5.0ms (0.3%)

rewrite66.0ms (4.4%)

eval5.0ms (0.3%)

prune2.0ms (0.2%)

series7.0ms (0.5%)

rewrite74.0ms (4.9%)

eval26.0ms (1.7%)

prune3.0ms (0.2%)

series5.0ms (0.3%)

rewrite73.0ms (4.8%)

eval27.0ms (1.8%)

prune3.0ms (0.2%)

series4.0ms (0.3%)

rewrite72.0ms (4.8%)

eval8.0ms (0.5%)

prune7.0ms (0.4%)

regimes19.0ms (1.3%)

regimes11.0ms (0.7%)

regimes8.0ms (0.6%)

regimes8.0ms (0.5%)

regimes4.0ms (0.3%)

derivations16.0ms (1.1%)

preprocess68.0ms (4.5%)

end0.0ms (0%)

Profiling