Metrics for arccos

start10.0ms (0.6%)

Memory: -47.9MiB live, 0.1MiB allocated; 13ms collecting garbage

analyze4.0ms (0.3%)

Memory

9.7MiB live, 9.7MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	100%	0%	0%	0%	0%	3
33.3%	25%	50%	0%	0%	25%	0%	4
60%	37.5%	25%	0%	0%	37.5%	0%	5
77.8%	43.7%	12.5%	0%	0%	43.7%	0%	6
88.2%	46.9%	6.2%	0%	0%	46.9%	0%	7
93.9%	48.4%	3.1%	0%	0%	48.4%	0%	8
96.9%	49.2%	1.6%	0%	0%	49.2%	0%	9
98.4%	49.6%	0.8%	0%	0%	49.6%	0%	10
99.2%	49.8%	0.4%	0%	0%	49.8%	0%	11
99.6%	49.9%	0.2%	0%	0%	49.9%	0%	12

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample959.0ms (58.4%)

Memory

50.5MiB live, 1 412.6MiB allocated; 254ms collecting garbage

Samples

676.0ms	8 256×	0	valid
1.0ms	23×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 472.0ms

ival-sqrt: 151.0ms (32% of total)

ival-mult!: 139.0ms (29.4% of total)

ival-atan: 77.0ms (16.3% of total)

ival-div!: 43.0ms (9.1% of total)

ival-add!: 32.0ms (6.8% of total)

ival-sub!: 29.0ms (6.1% of total)

adjust: 2.0ms (0.4% of total)

Bogosity

explain96.0ms (5.8%)

Memory

-6.2MiB live, 195.8MiB allocated; 27ms collecting garbage

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	1

Precision?

0/0

Recall?

0/0

Samples

31.0ms

512×

valid

Compiler

Compiled 103 to 31 computations (69.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-atan: 5.0ms (30% of total)

ival-sqrt: 4.0ms (24% of total)

ival-sub!: 2.0ms (12% of total)

ival-add!: 2.0ms (12% of total)

ival-div!: 2.0ms (12% of total)

ival-mult!: 2.0ms (12% of total)

adjust: 0.0ms (0% of total)

preprocess59.0ms (3.6%)

Memory

-30.6MiB live, 16.3MiB allocated; 3ms 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 22 to 18 computations (18.2% saved)

series5.0ms (0.3%)

Memory

7.2MiB live, 7.2MiB 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))
1.0ms	x	@	-inf	((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (- 1 x) (+ 1 x)) (- 1 x) 1 x (+ 1 x))
1.0ms	x	@	0	((* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (- 1 x) (+ 1 x)) (- 1 x) 1 x (+ 1 x))

Time

Variable

Point

Expression

2.0ms

inf

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

1.0ms

-inf

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

1.0ms

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

rewrite72.0ms (4.4%)

Memory

-5.5MiB live, 89.4MiB allocated; 10ms 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) (pow.f64 x #s(literal 3 binary64))) (+.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) (pow.f64 x #s(literal 3 binary64))) (+.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))) (fma.f64 #s(literal -1 binary64) 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 #s(literal 2 binary64)) #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) (fma.f64 #s(literal -1 binary64) 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 (pow.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) #s(literal -1 binary64)) (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))))) (pow.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) #s(literal -1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -3 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (pow.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) #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 (fma.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal 2 binary64) (/.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 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) x))
#s(approx (+ 1 x) x)
#s(approx (+ 1 x) (*.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) x))
#s(approx (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (*.f64 (atan.f64 (sqrt.f64 (/.f64 (fma.f64 #s(literal -1 binary64) 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 (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 x))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) x) #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.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)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) x) #s(literal -1 binary64) (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) (pow.f64 x #s(literal -1 binary64)))))

eval6.0ms (0.4%)

Memory: 17.3MiB live, 17.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 996 to 281 computations (71.8% saved)

prune4.0ms (0.3%)

Memory

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

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	52	5	57
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	52	6	58

Accuracy

100.0%

Counts

58 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)))))
✓	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
▶	99.7%	(.f64 #s(literal 2 binary64) (atan.f64 #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)))))
▶	99.5%	(.f64 #s(literal 2 binary64) (atan.f64 #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)))))
▶	99.1%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)))))
▶	98.2%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))

Compiler

Compiled 189 to 145 computations (23.3% saved)

series15.0ms (0.9%)

Memory

-15.7MiB live, 31.1MiB allocated; 3ms collecting garbage

Counts

35 → 104

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
5.0ms	x	@	inf	((* 2 (atan (sqrt (/ (/ (- 1 (* x x)) (+ x 1)) (+ 1 x))))) 2 (atan (sqrt (/ (/ (- 1 (* x x)) (+ x 1)) (+ 1 x)))) (sqrt (/ (/ (- 1 (* x x)) (+ x 1)) (+ 1 x))) (/ (/ (- 1 (* x x)) (+ x 1)) (+ 1 x)) (/ (- 1 (* x x)) (+ x 1)) (- 1 (* x x)) 1 (* x x) x (+ x 1) (+ 1 x) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* -1 x) 1) -1 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (- (* 1/2 x) 1) x) 1) (- (* 1/2 x) 1) (* 1/2 x) 1/2 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (- (* (+ (* -1/2 x) 1/2) x) 1) x) 1) (- (* (+ (* -1/2 x) 1/2) x) 1) (* (+ (* -1/2 x) 1/2) x) (+ (* -1/2 x) 1/2) -1/2)
4.0ms	x	@	-inf	((* 2 (atan (sqrt (/ (/ (- 1 (* x x)) (+ x 1)) (+ 1 x))))) 2 (atan (sqrt (/ (/ (- 1 (* x x)) (+ x 1)) (+ 1 x)))) (sqrt (/ (/ (- 1 (* x x)) (+ x 1)) (+ 1 x))) (/ (/ (- 1 (* x x)) (+ x 1)) (+ 1 x)) (/ (- 1 (* x x)) (+ x 1)) (- 1 (* x x)) 1 (* x x) x (+ x 1) (+ 1 x) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* -1 x) 1) -1 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (- (* 1/2 x) 1) x) 1) (- (* 1/2 x) 1) (* 1/2 x) 1/2 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (- (* (+ (* -1/2 x) 1/2) x) 1) x) 1) (- (* (+ (* -1/2 x) 1/2) x) 1) (* (+ (* -1/2 x) 1/2) x) (+ (* -1/2 x) 1/2) -1/2)
3.0ms	x	@	0	((* 2 (atan (sqrt (/ (/ (- 1 (* x x)) (+ x 1)) (+ 1 x))))) 2 (atan (sqrt (/ (/ (- 1 (* x x)) (+ x 1)) (+ 1 x)))) (sqrt (/ (/ (- 1 (* x x)) (+ x 1)) (+ 1 x))) (/ (/ (- 1 (* x x)) (+ x 1)) (+ 1 x)) (/ (- 1 (* x x)) (+ x 1)) (- 1 (* x x)) 1 (* x x) x (+ x 1) (+ 1 x) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* -1 x) 1) -1 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (- (* 1/2 x) 1) x) 1) (- (* 1/2 x) 1) (* 1/2 x) 1/2 (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (+ (* (- (* (+ (* -1/2 x) 1/2) x) 1) x) 1) (- (* (+ (* -1/2 x) 1/2) x) 1) (* (+ (* -1/2 x) 1/2) x) (+ (* -1/2 x) 1/2) -1/2)

Time

Variable

Point

Expression

5.0ms

inf

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

4.0ms

-inf

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

3.0ms

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

rewrite108.0ms (6.5%)

Memory

19.1MiB live, 116.2MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	356	2390
0	393	1985
0	1863	1974

Stop Event

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

Counts

139 → 220

Calls

Call 1

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

eval63.0ms (3.8%)

Memory: -22.0MiB live, 70.0MiB allocated; 9ms collecting garbage
Compiler: Compiled 5 827 to 1 120 computations (80.8% saved)

prune6.0ms (0.4%)

Memory

20.0MiB live, 20.0MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	230	2	232
Fresh	0	0	0
Picked	2	3	5
Done	0	1	1
Total	232	6	238

Accuracy

100.0%

Counts

238 → 6

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)))))
✓	99.7%	(.f64 #s(literal 2 binary64) (atan.f64 #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)))))
✓	99.5%	(.f64 #s(literal 2 binary64) (atan.f64 #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)))))
▶	99.2%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
▶	99.1%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (neg.f64 x) #s(literal 1 binary64)))))
✓	98.2%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))

Compiler

Compiled 105 to 81 computations (22.9% saved)

series4.0ms (0.3%)

Memory

12.2MiB live, 12.2MiB allocated; 0ms collecting garbage

Counts

15 → 35

Calls

Call 1

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

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

rewrite48.0ms (2.9%)

Memory

2.4MiB live, 48.4MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	144	746
0	158	600
0	818	595

Stop Event

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

Counts

50 → 87

Calls

Call 1

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

Outputs
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)))))
(+.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)))) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)))))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x 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 x x (-.f64 #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 x x) (.f64 #s(literal 1 binary64) (neg.f64 x)))))
(/.f64 (neg.f64 (expm1.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))) (neg.f64 (-.f64 (neg.f64 x) #s(literal 1 binary64))))
(/.f64 (expm1.f64 (*.f64 (log.f64 x) #s(literal 2 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 (/.f64 (*.f64 x x) (-.f64 (neg.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (neg.f64 x) #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
#s(literal 1 binary64)
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)))))
(+.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)))) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x 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 x x (-.f64 #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 x x) (.f64 #s(literal 1 binary64) (neg.f64 x)))))
(/.f64 (neg.f64 (expm1.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))) (neg.f64 (-.f64 (neg.f64 x) #s(literal 1 binary64))))
(/.f64 (expm1.f64 (*.f64 (log.f64 x) #s(literal 2 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 (/.f64 (*.f64 x x) (-.f64 (neg.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (neg.f64 x) #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 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 x x) (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1 binary64)))))
(expm1.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(-.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) #s(literal 1 binary64)))))
(/.f64 (expm1.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)))
(-.f64 (neg.f64 x) #s(literal 1 binary64))
#s(approx (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64)))
#s(approx (atan (sqrt (/ (- 1 x) (+ 1 x)))) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 #s(literal -1 binary64) 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 (+ (neg x) 1) #s(literal 1 binary64))
#s(approx (+ (neg x) 1) (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)))
#s(approx (neg x) (neg.f64 x))
#s(approx x x)
#s(approx (+ (neg x) 1) #s(literal 1 binary64))
#s(approx (+ (neg x) 1) (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)))
#s(approx (- (* x x) 1) #s(literal -1 binary64))
#s(approx (- (* x x) 1) (expm1.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))))
#s(approx (* x x) (*.f64 x x))
#s(approx (- (neg x) 1) #s(literal -1 binary64))
#s(approx (- (neg x) 1) (-.f64 (neg.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 (pow.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64) (pow.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 #s(literal -1 binary64))))) (pow.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) #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 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) x))
#s(approx (+ (neg x) 1) (neg.f64 x))
#s(approx (+ (neg x) 1) (*.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) x))
#s(approx (- (* x x) 1) (*.f64 x x))
#s(approx (- (* x x) 1) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))) (.f64 x x)))
#s(approx (- (neg x) 1) (neg.f64 x))
#s(approx (- (neg x) 1) (*.f64 (neg.f64 x) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))))
#s(approx (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (*.f64 (atan.f64 (sqrt.f64 (/.f64 (fma.f64 #s(literal -1 binary64) 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 (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 x))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) x) #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.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)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) x) #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (+ (neg x) 1) (*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64)))))
#s(approx (+ (neg x) 1) (*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64)))))

eval14.0ms (0.8%)

Memory: -23.2MiB live, 28.3MiB allocated; 6ms collecting garbage
Compiler: Compiled 1 788 to 367 computations (79.5% saved)

prune4.0ms (0.2%)

Memory

10.5MiB live, 10.5MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	0	0
Picked	1	1	2
Done	0	4	4
Total	78	6	84

Accuracy

100.0%

Counts

84 → 6

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)))))
✓	99.7%	(.f64 #s(literal 2 binary64) (atan.f64 #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)))))
✓	99.5%	(.f64 #s(literal 2 binary64) (atan.f64 #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)))))
▶	99.2%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 #s(approx (- ( x x) 1) #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
✓	99.1%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (neg.f64 x) #s(literal 1 binary64)))))
✓	98.2%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))

Compiler

Compiled 107 to 83 computations (22.4% saved)

series3.0ms (0.2%)

Memory

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

Counts

11 → 29

Calls

Call 1

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

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

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

1.0ms

inf

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

1.0ms

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

rewrite47.0ms (2.8%)

Memory

4.1MiB live, 49.8MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	131	650
0	137	561
0	786	556

Stop Event

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

Counts

40 → 47

Calls

Call 1

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

Outputs
(.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 #s(approx (- ( x x) 1) #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 #s(approx (- ( x x) 1) #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
(+.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 #s(approx (- (* x x) 1) #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 #s(approx (- (* x x) 1) #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 #s(approx (- (* x x) 1) #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 #s(approx (- (* x x) 1) #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 #s(approx (- (* x x) 1) #s(literal -1 binary64))) (neg.f64 (-.f64 (neg.f64 x) #s(literal 1 binary64))))
(/.f64 #s(approx (- (* x x) 1) #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))
#s(approx (- (* x x) 1) #s(literal -1 binary64))
#s(literal -1 binary64)
(/.f64 (-.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) #s(literal 1 binary64)))))
(/.f64 (expm1.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)))
(-.f64 (neg.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) x)
(*.f64 x #s(literal -1 binary64))
(neg.f64 x)
x
#s(literal 1 binary64)
#s(approx (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64)))
#s(approx (atan (sqrt (/ (- 1 x) (+ 1 x)))) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 #s(literal -1 binary64) 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 (/ (- (* x x) 1) (- (neg x) 1)) #s(literal 1 binary64))
#s(approx (/ (- (* x x) 1) (- (neg x) 1)) (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)))
#s(approx (- (* x x) 1) #s(literal -1 binary64))
#s(approx (- (* x x) 1) (expm1.f64 (*.f64 (log.f64 x) #s(literal 2 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 (sqrt (/ (- 1 x) (+ 1 x))) (sqrt.f64 #s(literal -1 binary64)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (pow.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64) (pow.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 #s(literal -1 binary64))))) (pow.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (/ (- (* x x) 1) (- (neg x) 1)) (neg.f64 x))
#s(approx (/ (- (* x x) 1) (- (neg x) 1)) (*.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) x))
#s(approx (- (* x x) 1) (*.f64 x x))
#s(approx (- (* x x) 1) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))) (.f64 x x)))
#s(approx (- (neg x) 1) (neg.f64 x))
#s(approx (- (neg x) 1) (*.f64 (neg.f64 x) (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))))
#s(approx (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (*.f64 (atan.f64 (sqrt.f64 (/.f64 (fma.f64 #s(literal -1 binary64) 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 (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 x))))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) x) #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.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)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) x) #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (/ (- (* x x) 1) (- (neg x) 1)) (*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64)))))

eval6.0ms (0.4%)

Memory: -32.2MiB live, 14.7MiB allocated; 1ms collecting garbage
Compiler: Compiled 1 198 to 225 computations (81.2% saved)

prune4.0ms (0.3%)

Memory

12.6MiB live, 12.6MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	46	6	52

Accuracy

100.0%

Counts

52 → 6

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)))))
✓	99.7%	(.f64 #s(literal 2 binary64) (atan.f64 #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)))))
✓	99.5%	(.f64 #s(literal 2 binary64) (atan.f64 #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)))))
✓	99.2%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 #s(approx (- ( x x) 1) #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
✓	99.1%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (neg.f64 x) #s(literal 1 binary64)))))
✓	98.2%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))

Compiler

Compiled 269 to 146 computations (45.7% saved)

regimes13.0ms (0.8%)

Memory

-12.1MiB live, 34.4MiB allocated; 2ms 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 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)))))
(.f64 #s(literal 2 binary64) (atan.f64 #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)))))
(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 #s(approx (- ( x x) 1) #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
(.f64 #s(literal 2 binary64) (atan.f64 #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)))))
(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 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 (sqrt.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)))))

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

Calls

5 calls:

4.0ms	(/.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	(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)))

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 36 to 28 computations (22.2% saved)

regimes10.0ms (0.6%)

Memory

31.6MiB live, 31.6MiB allocated; 0ms collecting garbage

Counts

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

Outputs

(*.f64 #s(literal 2 binary64) (atan.f64 #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)))))

Calls

5 calls:

2.0ms	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
99.7%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`
99.7%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
99.7%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
99.7%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
99.7%	1	`x`

Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes16.0ms (0.9%)

Memory

-24.1MiB live, 29.9MiB allocated; 10ms collecting garbage

Counts

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

Outputs
(.f64 #s(literal 2 binary64) (atan.f64 #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)))))

Calls

5 calls:

9.0ms	(*.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
2.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
1.0ms	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
99.5%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`
99.5%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
99.5%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
99.5%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
99.5%	1	`x`

Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes6.0ms (0.4%)

Memory

19.6MiB live, 19.7MiB allocated; 0ms collecting garbage

Counts

3 → 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 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 #s(literal -1 binary64) 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:

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

Results

Accuracy	Segments	Branch
99.1%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`
99.1%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
99.1%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
99.1%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
99.1%	1	`x`

Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes6.0ms (0.4%)

Memory

-30.7MiB live, 16.1MiB allocated; 3ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

5 calls:

3.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
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	(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
98.2%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`
98.2%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
98.2%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
98.2%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
98.2%	1	`x`

Compiler

Compiled 36 to 28 computations (22.2% saved)

derivations12.0ms (0.8%)

Memory

38.5MiB live, 38.5MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 83 to 37 computations (55.4% saved)

preprocess42.0ms (2.6%)

Memory: 2.9MiB live, 87.7MiB allocated; 21ms collecting garbage
Compiler: Compiled 188 to 92 computations (51.1% saved)

end0.0ms (0%)

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

start10.0ms (0.6%)

analyze4.0ms (0.3%)

sample959.0ms (58.4%)

explain96.0ms (5.8%)

preprocess59.0ms (3.6%)

series5.0ms (0.3%)

rewrite72.0ms (4.4%)

eval6.0ms (0.4%)

prune4.0ms (0.3%)

series15.0ms (0.9%)

rewrite108.0ms (6.5%)

eval63.0ms (3.8%)

prune6.0ms (0.4%)

series4.0ms (0.3%)

rewrite48.0ms (2.9%)

eval14.0ms (0.8%)

prune4.0ms (0.2%)

series3.0ms (0.2%)

rewrite47.0ms (2.8%)

eval6.0ms (0.4%)

prune4.0ms (0.3%)

regimes13.0ms (0.8%)

regimes10.0ms (0.6%)

regimes16.0ms (0.9%)

regimes6.0ms (0.4%)

regimes6.0ms (0.4%)

derivations12.0ms (0.8%)

preprocess42.0ms (2.6%)

end0.0ms (0%)

Profiling