Metrics for Ian Simplification

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze4.0ms (0%)

Memory

7.1MiB live, 7.1MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 15 to 13 computations (13.3% saved)

sample4.7s (38.9%)

Memory

-134.0MiB live, 4 688.6MiB allocated

Samples

2.8s	3 187×	2	valid
1.3s	4 802×	1	valid
22.0ms	267×	0	valid
0.0ms	6×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 3.7s

ival-asin: 1.3s (35.1% of total)

ival-sub: 1.3s (34.2% of total)

ival-div: 367.0ms (9.8% of total)

adjust: 282.0ms (7.5% of total)

ival-sqrt: 204.0ms (5.4% of total)

ival-mult: 150.0ms (4% of total)

ival-pi: 125.0ms (3.3% of total)

exact: 9.0ms (0.2% of total)

ival-true: 7.0ms (0.2% of total)

ival-assert: 4.0ms (0.1% of total)

Bogosity

explain403.0ms (3.3%)

Memory

37.1MiB live, 503.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
253	-	-	`(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))`
0	-	-	`(/.f64 (PI.f64) #s(literal 2 binary64))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(-.f64 #s(literal 1 binary64) x)`
0	-	-	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))`
0	-	-	`(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))`
0	-	-	`(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))`
0	-	-	`x`
0	-	-	`(PI.f64)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))`	cancellation	253	0

Confusion

	Predicted +	Predicted -
+	253	0
-	0	3

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	253	0	0
-	0	0	3

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	3
1	253

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

127.0ms	200×	2	valid
102.0ms	300×	1	valid
1.0ms	12×	0	valid

Compiler

Compiled 117 to 37 computations (68.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 169.0ms

ival-asin: 73.0ms (43.2% of total)

ival-sub: 36.0ms (21.3% of total)

ival-div: 17.0ms (10.1% of total)

adjust: 16.0ms (9.5% of total)

ival-sqrt: 10.0ms (5.9% of total)

ival-mult: 9.0ms (5.3% of total)

ival-pi: 7.0ms (4.1% of total)

ival-true: 1.0ms (0.6% of total)

exact: 1.0ms (0.6% of total)

ival-assert: 0.0ms (0% of total)

preprocess37.0ms (0.3%)

Memory

-29.4MiB live, 17.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	29
1	26	29
2	39	26
3	56	26
4	71	26
5	80	26
6	84	26
0	11	13
0	19	13
1	32	13
2	40	13
3	48	13
4	57	13
5	61	13
6	62	13
0	62	12

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

Outputs

(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))

(fma.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64)))

Compiler

Compiled 13 to 11 computations (15.4% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.2%	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))

Compiler

Compiled 13 to 11 computations (15.4% saved)

simplify5.0ms (0%)

Memory

4.5MiB live, 4.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
cost-diff	0	(PI.f64)
cost-diff	0	(/.f64 (PI.f64) #s(literal 2 binary64))
cost-diff	1	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	50
0	19	50
1	32	50
2	40	50
3	48	50
4	57	50
5	61	50
6	62	50
0	62	49

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize177.0ms (1.5%)

Memory

-9.6MiB live, 79.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(PI.f64)
accuracy	0.00390625	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
accuracy	0.97265625	(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
accuracy	59.03079891096031	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))

Samples

128.0ms	100×	2	valid
36.0ms	150×	1	valid
1.0ms	6×	0	valid

Compiler

Compiled 52 to 13 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 150.0ms

ival-div: 88.0ms (58.6% of total)

ival-asin: 35.0ms (23.3% of total)

adjust: 8.0ms (5.3% of total)

ival-sub: 6.0ms (4% of total)

ival-sqrt: 5.0ms (3.3% of total)

ival-mult: 5.0ms (3.3% of total)

ival-pi: 3.0ms (2% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series27.0ms (0.2%)

Memory

-35.7MiB live, 7.3MiB allocated

Counts

6 → 18

Calls

Call 1

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

Outputs
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* -1/8 (* x (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* x (+ (* -1/8 (sqrt 1/2)) (* -1/16 (* x (sqrt 1/2))))))))
(* (sqrt x) (* (sqrt -1) (sqrt 1/2)))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt 1/2) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))

Calls

3 calls:

Time	Variable		Point	Expression
23.0ms	x	@	0	((- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2))))) (/ (PI) 2) (PI) (* 2 (asin (sqrt (/ (- 1 x) 2)))) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)))
2.0ms	x	@	inf	((- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2))))) (/ (PI) 2) (PI) (* 2 (asin (sqrt (/ (- 1 x) 2)))) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)))
1.0ms	x	@	-inf	((- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2))))) (/ (PI) 2) (PI) (* 2 (asin (sqrt (/ (- 1 x) 2)))) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)))

Time

Variable

Point

Expression

23.0ms

((- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2))))) (/ (PI) 2) (PI) (* 2 (asin (sqrt (/ (- 1 x) 2)))) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)))

2.0ms

inf

((- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2))))) (/ (PI) 2) (PI) (* 2 (asin (sqrt (/ (- 1 x) 2)))) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)))

1.0ms

-inf

((- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2))))) (/ (PI) 2) (PI) (* 2 (asin (sqrt (/ (- 1 x) 2)))) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)))

simplify166.0ms (1.4%)

Memory

40.4MiB live, 130.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	94	392
1	287	361
2	1116	345
3	5123	339
0	8450	322

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 18

Calls

Call 1

Inputs
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* -1/8 (* x (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* x (+ (* -1/8 (sqrt 1/2)) (* -1/16 (* x (sqrt 1/2))))))))
(* (sqrt x) (* (sqrt -1) (sqrt 1/2)))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt 1/2) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))

Outputs
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(fma.f64 #s(literal -2 binary64) (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 (PI.f64) #s(literal 1/2 binary64)))
(* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(.f64 (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* -1/8 (* x (sqrt 1/2))))))
(fma.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* x (+ (* -1/8 (sqrt 1/2)) (* -1/16 (* x (sqrt 1/2))))))))
(fma.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 (.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/8 binary64)) x) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt x) (* (sqrt -1) (sqrt 1/2)))
(.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 x))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))
(.f64 (fma.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)))) x)
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1 binary64))) #s(literal -1/8 binary64) (.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) (sqrt.f64 #s(literal -1 binary64)))) x)
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt 1/2) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1 binary64))) #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) (sqrt.f64 #s(literal -1 binary64))))) x)
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(fma.f64 #s(literal -2 binary64) (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 (PI.f64) #s(literal 1/2 binary64)))
(* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(.f64 (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))
(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(.f64 (.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(.f64 (neg.f64 x) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))
(.f64 (neg.f64 x) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))

rewrite479.0ms (3.9%)

Memory

-20.7MiB live, 309.6MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	39
0	19	35
1	81	35
2	513	23
3	6339	23
0	8483	23

Stop Event

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

Counts

6 → 4 030

Calls

Call 1

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

Outputs
(.f64 (.f64 (neg.f64 (PI.f64)) #s(literal 2 binary64)) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(.f64 (.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(.f64 (.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) #s(literal 2 binary64)) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(.f64 (.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64))) #s(literal 8 binary64))
(.f64 (.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) #s(literal 8 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64)))
(.f64 (.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(literal 4 binary64))
(.f64 (.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)))
(.f64 (.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(.f64 (.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(.f64 (.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))
(.f64 (.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal -2 binary64)) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(.f64 (.f64 (neg.f64 (PI.f64)) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))) #s(literal 2 binary64))
(.f64 (.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (PI.f64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))) #s(literal 2 binary64))
(.f64 (.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))) #s(literal 2 binary64))
(*.f64 (+.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3/2 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3/2 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(.f64 (.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3/2 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (*.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3/2 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(.f64 (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 3/4 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 3/4 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 (.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 4 binary64))
(.f64 (.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64))) #s(literal 64 binary64))
(.f64 (.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))) #s(literal 16 binary64))
(.f64 #s(literal 16 binary64) (.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))))
(*.f64 (fabs.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))) #s(literal 2 binary64))
(*.f64 (pow.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64)) #s(literal 3 binary64)) #s(literal 512 binary64))
(*.f64 #s(literal 512 binary64) (pow.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3/2 binary64)))
(.f64 (pow.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64)))
(.f64 (pow.f64 (.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3 binary64)) #s(literal 8 binary64))
(*.f64 (pow.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) #s(literal 3 binary64)) #s(literal 64 binary64))
(.f64 #s(literal 64 binary64) (.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64))))
(*.f64 #s(literal 64 binary64) (pow.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) #s(literal 3 binary64)))
(.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(.f64 (.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -2 binary64))
(.f64 (.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(.f64 (.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64))
(.f64 (neg.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (.f64 (cbrt.f64 (PI.f64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(*.f64 (asin.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))) #s(literal 2 binary64))
(.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3/2 binary64)) (.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3/2 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(*.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (/.f64 #s(literal 4 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(*.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) #s(literal 4 binary64))
(*.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(*.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 4 binary64) (/.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(*.f64 #s(literal 4 binary64) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)))
(*.f64 #s(literal 4 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(*.f64 #s(literal 4 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(*.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(.f64 (neg.f64 (sqrt.f64 (PI.f64))) (.f64 (neg.f64 (sqrt.f64 (PI.f64))) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(.f64 (neg.f64 (sqrt.f64 (PI.f64))) (.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(*.f64 #s(literal -8 binary64) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64)) (/.f64 #s(literal 8 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(*.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64)) #s(literal -8 binary64))
(*.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64)) #s(literal 8 binary64))
(*.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(*.f64 #s(literal 8 binary64) (/.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(*.f64 #s(literal 8 binary64) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64)))
(*.f64 #s(literal 8 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(*.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(*.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(*.f64 #s(literal -2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(*.f64 #s(literal -2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(*.f64 (neg.f64 (PI.f64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (neg.f64 (sqrt.f64 (PI.f64))) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (.f64 (neg.f64 (cbrt.f64 (PI.f64))) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (.f64 (cbrt.f64 (PI.f64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(*.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(*.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(*.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(*.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (-.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)))
(*.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 4 binary64))
(*.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 (PI.f64) #s(literal -2 binary64)))
(*.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64)))
(*.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 8 binary64))
(*.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)))
(*.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)))
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(/.f64 (sin.f64 (acos.f64 x)) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (sin.f64 (acos.f64 x)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 2 binary64))))
(/.f64 (sin.f64 (acos.f64 (pow.f64 x #s(literal 3/2 binary64)))) (*.f64 (sqrt.f64 (+.f64 (fma.f64 x x x) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (sin.f64 (acos.f64 (pow.f64 x #s(literal 3/2 binary64)))) (sqrt.f64 (*.f64 (+.f64 (fma.f64 x x x) #s(literal 1 binary64)) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 #s(literal -2 binary64)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))) (sinh.f64 (log.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))

eval218.0ms (1.8%)

Memory: 18.5MiB live, 236.1MiB allocated
Compiler: Compiled 38 880 to 3 030 computations (92.2% saved)

prune81.0ms (0.7%)

Memory

-5.5MiB live, 152.1MiB allocated

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	2 079	14	2 093
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	2 080	14	2 094

Accuracy

9.3%

Counts

2 094 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	3.9%	(fma.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
	6.2%	(fma.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
	6.2%	(/.f64 (-.f64 (pow.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))))
	6.2%	(/.f64 (-.f64 (pow.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))) (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
	6.2%	(/.f64 (-.f64 (.f64 (PI.f64) (+.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64))))) (.f64 #s(literal 2 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)))))
▶	0.0%	(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
▶	7.8%	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))))
	6.4%	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))))
▶	4.0%	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (sqrt.f64 #s(literal 1/2 binary64))))))
	6.2%	(-.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
▶	7.7%	(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
	3.8%	(*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))
	3.8%	(*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
	6.2%	#s(approx (- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2))))) (fma.f64 #s(literal -2 binary64) (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 (PI.f64) #s(literal 1/2 binary64))))

Compiler

Compiled 576 to 356 computations (38.2% saved)

simplify7.0ms (0.1%)

Memory

13.0MiB live, 13.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(PI.f64)
cost-diff	0	(/.f64 (PI.f64) #s(literal 2 binary64))
cost-diff	0	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal -2 binary64))))
cost-diff	0	(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
cost-diff	0	(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
cost-diff	0	(fma.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
cost-diff	0	(*.f64 #s(literal 2 binary64) (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (sqrt.f64 #s(literal 1/2 binary64)))))
cost-diff	0	(PI.f64)
cost-diff	0	(/.f64 (PI.f64) #s(literal 2 binary64))
cost-diff	0	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (sqrt.f64 #s(literal 1/2 binary64))))))
cost-diff	0	(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
cost-diff	0	(*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
cost-diff	0	(PI.f64)
cost-diff	0	(/.f64 (PI.f64) #s(literal 2 binary64))
cost-diff	0	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	257
0	51	257

Stop Event

1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Calls

Call 1

Inputs
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))))
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
#s(literal 0 binary64)
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (sqrt.f64 #s(literal 1/2 binary64))))))
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(*.f64 #s(literal 2 binary64) (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (sqrt.f64 #s(literal 1/2 binary64)))))
(asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (sqrt (/ (- 1 x) 2)) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(fma.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal 2 binary64)
(/.f64 (PI.f64) #s(literal -2 binary64))
(PI.f64)
#s(literal -2 binary64)
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal -2 binary64))))
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(-.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal -2 binary64)))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(/.f64 (PI.f64) #s(literal -2 binary64))
#s(literal -2 binary64)
(acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))

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

localize78.0ms (0.6%)

Memory

16.3MiB live, 158.0MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.0	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
accuracy	0.0	(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
accuracy	0.0	(acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
accuracy	61.99849058512738	(PI.f64)
accuracy	0.0	(-.f64 #s(literal 1 binary64) x)
accuracy	0.0	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
accuracy	0.0	(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
accuracy	61.99849058512738	(PI.f64)
accuracy	0.0	(sqrt.f64 #s(literal 1/2 binary64))
accuracy	0.0	(asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (sqrt.f64 #s(literal 1/2 binary64))))
accuracy	0.0	#s(approx (sqrt (/ (- 1 x) 2)) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	61.99849058512738	(PI.f64)
accuracy	0.0	(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
accuracy	0.0	(*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
accuracy	0.0	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
accuracy	0.0	(acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
accuracy	61.99849058512738	(PI.f64)

Samples

56.0ms

256×

invalid

Compiler

Compiled 248 to 28 computations (88.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-sub: 9.0ms (23.7% of total)

ival-div: 6.0ms (15.8% of total)

ival-mult: 6.0ms (15.8% of total)

ival-acos: 5.0ms (13.2% of total)

ival-asin: 4.0ms (10.5% of total)

ival-sqrt: 3.0ms (7.9% of total)

ival-add: 2.0ms (5.3% of total)

ival-pi: 1.0ms (2.6% of total)

exact: 1.0ms (2.6% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series9.0ms (0.1%)

Memory

-28.8MiB live, 15.8MiB allocated

Counts

18 → 40

Calls

Call 1

Inputs
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))))
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
(*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (sqrt.f64 #s(literal 1/2 binary64))))))
(*.f64 #s(literal 2 binary64) (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal -2 binary64))))
(acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
#s(approx (sqrt (/ (- 1 x) 2)) (sqrt.f64 #s(literal 1/2 binary64)))
(asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt.f64 #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) x)

Outputs
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(+ (* -1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* -1/8 (* x (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* x (+ (* -1/8 (sqrt 1/2)) (* -1/16 (* x (sqrt 1/2))))))))
1/2
(+ 1/2 (* -1/2 x))
(- (+ (acos (* (sqrt 1/2) (sqrt (- 1 x)))) (+ (* -1/2 (PI)) (* 1/2 (PI)))) (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(- (+ (* -1/2 (PI)) (* 1/2 (PI))) (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
1
(+ 1 (* -1 x))
(* (sqrt x) (* (sqrt -1) (sqrt 1/2)))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt 1/2) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1/2 x)
(* x (- (* 1/2 (/ 1 x)) 1/2))
(* -1 x)
(* x (- (/ 1 x) 1))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(+ (* -1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))
(* -1 (* x (- 1/2 (* 1/2 (/ 1 x)))))
(- (+ (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (+ (* -1/2 (PI)) (* 1/2 (PI)))) (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(- (+ (* -1/2 (PI)) (* 1/2 (PI))) (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(* -1 (* x (- 1 (/ 1 x))))

Calls

3 calls:

Time	Variable		Point	Expression
5.0ms	x	@	0	((- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/ (PI) 2) (PI) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2))))) (/ 0 0) (- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2))))) (* 2 (asin (sqrt (/ (- 1 x) 2)))) (+ (* (asin (sqrt (/ (- 1 x) 2))) 2) (/ (PI) -2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (/ (- 1 x) 2) (+ (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (acos (sqrt (/ (- 1 x) 2)))) (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (acos (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt 1/2) (- 1 x))
2.0ms	x	@	inf	((- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/ (PI) 2) (PI) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2))))) (/ 0 0) (- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2))))) (* 2 (asin (sqrt (/ (- 1 x) 2)))) (+ (* (asin (sqrt (/ (- 1 x) 2))) 2) (/ (PI) -2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (/ (- 1 x) 2) (+ (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (acos (sqrt (/ (- 1 x) 2)))) (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (acos (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt 1/2) (- 1 x))
2.0ms	x	@	-inf	((- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/ (PI) 2) (PI) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2))))) (/ 0 0) (- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2))))) (* 2 (asin (sqrt (/ (- 1 x) 2)))) (+ (* (asin (sqrt (/ (- 1 x) 2))) 2) (/ (PI) -2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (/ (- 1 x) 2) (+ (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (acos (sqrt (/ (- 1 x) 2)))) (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (acos (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt 1/2) (- 1 x))

Time

Variable

Point

Expression

5.0ms

((- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/ (PI) 2) (PI) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2))))) (/ 0 0) (- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2))))) (* 2 (asin (sqrt (/ (- 1 x) 2)))) (+ (* (asin (sqrt (/ (- 1 x) 2))) 2) (/ (PI) -2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (/ (- 1 x) 2) (+ (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (acos (sqrt (/ (- 1 x) 2)))) (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (acos (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt 1/2) (- 1 x))

2.0ms

inf

((- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/ (PI) 2) (PI) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2))))) (/ 0 0) (- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2))))) (* 2 (asin (sqrt (/ (- 1 x) 2)))) (+ (* (asin (sqrt (/ (- 1 x) 2))) 2) (/ (PI) -2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (/ (- 1 x) 2) (+ (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (acos (sqrt (/ (- 1 x) 2)))) (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (acos (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt 1/2) (- 1 x))

2.0ms

-inf

((- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/ (PI) 2) (PI) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2))))) (/ 0 0) (- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2))))) (* 2 (asin (sqrt (/ (- 1 x) 2)))) (+ (* (asin (sqrt (/ (- 1 x) 2))) 2) (/ (PI) -2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (/ (- 1 x) 2) (+ (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (acos (sqrt (/ (- 1 x) 2)))) (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (acos (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt 1/2) (- 1 x))

simplify214.0ms (1.8%)

Memory

34.1MiB live, 266.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	125	612
1	366	572
2	1334	550
3	5565	547
0	8150	523

Stop Event

1×	iter limit
1×	node limit

Counts

40 → 40

Calls

Call 1

Inputs
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(+ (* -1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* -1/8 (* x (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* x (+ (* -1/8 (sqrt 1/2)) (* -1/16 (* x (sqrt 1/2))))))))
1/2
(+ 1/2 (* -1/2 x))
(- (+ (acos (* (sqrt 1/2) (sqrt (- 1 x)))) (+ (* -1/2 (PI)) (* 1/2 (PI)))) (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(- (+ (* -1/2 (PI)) (* 1/2 (PI))) (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
1
(+ 1 (* -1 x))
(* (sqrt x) (* (sqrt -1) (sqrt 1/2)))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt 1/2) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1/2 x)
(* x (- (* 1/2 (/ 1 x)) 1/2))
(* -1 x)
(* x (- (/ 1 x) 1))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(+ (* -1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))
(* -1 (* x (- 1/2 (* 1/2 (/ 1 x)))))
(- (+ (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (+ (* -1/2 (PI)) (* 1/2 (PI)))) (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(- (+ (* -1/2 (PI)) (* 1/2 (PI))) (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(* -1 (* x (- 1 (/ 1 x))))

Outputs
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(fma.f64 #s(literal -2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(fma.f64 #s(literal -2 binary64) (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 (PI.f64) #s(literal 1/2 binary64)))
(* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(.f64 (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(+ (* -1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(fma.f64 (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64) (.f64 #s(literal -1/2 binary64) (PI.f64)))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* -1/8 (* x (sqrt 1/2))))))
(fma.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* x (+ (* -1/8 (sqrt 1/2)) (* -1/16 (* x (sqrt 1/2))))))))
(fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/8 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) x (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x (sqrt.f64 #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
(- (+ (acos (* (sqrt 1/2) (sqrt (- 1 x)))) (+ (* -1/2 (PI)) (* 1/2 (PI)))) (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(-.f64 (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))
(- (+ (* -1/2 (PI)) (* 1/2 (PI))) (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(neg.f64 (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(* (sqrt x) (* (sqrt -1) (sqrt 1/2)))
(.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 x))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))
(.f64 (fma.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)))) x)
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1 binary64))) #s(literal -1/8 binary64) (.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) (sqrt.f64 #s(literal -1 binary64)))) x)
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt 1/2) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1 binary64))) #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) (sqrt.f64 #s(literal -1 binary64))))) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* x (- (* 1/2 (/ 1 x)) 1/2))
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) x)
(* -1 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))
(fma.f64 #s(literal -2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(- (* 1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(fma.f64 #s(literal -2 binary64) (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 (PI.f64) #s(literal 1/2 binary64)))
(* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(.f64 (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(+ (* -1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(fma.f64 (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64) (.f64 #s(literal -1/2 binary64) (PI.f64)))
(asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))
(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(.f64 (.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(.f64 (neg.f64 x) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))
(.f64 (neg.f64 x) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (- 1/2 (* 1/2 (/ 1 x)))))
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1/2 binary64)) x)
(- (+ (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (+ (* -1/2 (PI)) (* 1/2 (PI)))) (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(-.f64 (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))
(- (+ (* -1/2 (PI)) (* 1/2 (PI))) (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(neg.f64 (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (- 1 (/ 1 x))))
(*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))

rewrite40.0ms (0.3%)

Memory

-10.1MiB live, 45.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	164
0	51	164

Stop Event

1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

18 → 19

Calls

Call 1

Inputs
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))))
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
(*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (sqrt.f64 #s(literal 1/2 binary64))))))
(*.f64 #s(literal 2 binary64) (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal -2 binary64))))
(acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
#s(approx (sqrt (/ (- 1 x) 2)) (sqrt.f64 #s(literal 1/2 binary64)))
(asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt.f64 #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) x)

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

eval38.0ms (0.3%)

Memory: -10.3MiB live, 33.9MiB allocated
Compiler: Compiled 3 941 to 419 computations (89.4% saved)

prune46.0ms (0.4%)

Memory

-16.1MiB live, 30.8MiB allocated

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	129	7	136
Fresh	1	8	9
Picked	3	2	5
Done	0	0	0
Total	133	17	150

Accuracy

9.3%

Counts

150 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	6.2%	(fma.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
▶	2.6%	(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
▶	4.1%	(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
	6.2%	(/.f64 (-.f64 (pow.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))))
	6.2%	(/.f64 (-.f64 (pow.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))) (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
	6.2%	(/.f64 (-.f64 (.f64 (PI.f64) (+.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64))))) (.f64 #s(literal 2 binary64) (+.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)))))
✓	0.0%	(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
▶	5.3%	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))))))
✓	4.0%	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (sqrt.f64 #s(literal 1/2 binary64))))))
	6.2%	(-.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
	7.7%	(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))))))
	7.5%	(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) x)))))
▶	6.8%	(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
	3.8%	(*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))
	3.8%	(*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
▶	7.7%	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (fma.f64 #s(literal -2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
	6.2%	#s(approx (- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2))))) (fma.f64 #s(literal -2 binary64) (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 (PI.f64) #s(literal 1/2 binary64))))

Compiler

Compiled 773 to 526 computations (32% saved)

simplify243.0ms (2%)

Memory

-12.8MiB live, 234.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	1	(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
cost-diff	1	(-.f64 (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))
cost-diff	1	(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
cost-diff	6	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64))))
cost-diff	0	(PI.f64)
cost-diff	0	(/.f64 (PI.f64) #s(literal 2 binary64))
cost-diff	2	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))))))
cost-diff	3	(*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))))))
cost-diff	0	#s(approx (/ (- 1 x) 2) (*.f64 #s(literal -1/2 binary64) x))
cost-diff	0	(sqrt.f64 #s(approx (/ (- 1 x) 2) (*.f64 #s(literal -1/2 binary64) x)))
cost-diff	0	(asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (*.f64 #s(literal -1/2 binary64) x))))
cost-diff	0	(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
cost-diff	0	#s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))
cost-diff	0	(sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))
cost-diff	0	(asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))))
cost-diff	0	(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
cost-diff	0	(*.f64 (PI.f64) #s(literal 1/2 binary64))
cost-diff	0	(-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))
cost-diff	0	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (fma.f64 #s(literal -2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
cost-diff	4	(fma.f64 #s(literal -2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (PI.f64) #s(literal 1/2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	424
0	87	424
1	121	424
2	191	424
3	306	424
4	492	424
5	770	409
6	1549	401
7	3930	393
8	5471	393
9	7649	393
0	8279	363

Stop Event

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

Calls

Call 1

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

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

localize453.0ms (3.7%)

Memory

13.1MiB live, 640.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.04201127930532605	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64))))
accuracy	0.5557094409913033	#s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
accuracy	0.97265625	(asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
accuracy	58.983928692450874	(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
accuracy	0.0234375	(acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))))
accuracy	0.02734375	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))))
accuracy	1.1027715122768347	#s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))
accuracy	59.03079891096031	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))))))
accuracy	0.00390625	(sqrt.f64 #s(approx (/ (- 1 x) 2) (*.f64 #s(literal -1/2 binary64) x)))
accuracy	0.97265625	(asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (*.f64 #s(literal -1/2 binary64) x))))
accuracy	59.03079891096031	(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
accuracy	61.57287481373716	#s(approx (/ (- 1 x) 2) (*.f64 #s(literal -1/2 binary64) x))
accuracy	0.00390625	(sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))
accuracy	0.97265625	(asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))))
accuracy	1.1027715122768347	#s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))
accuracy	59.03079891096031	(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
accuracy	0.021816259768442016	(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	0.0234375	(acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))
accuracy	0.02734375	(-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))
accuracy	59.03079891096031	(fma.f64 #s(literal -2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (PI.f64) #s(literal 1/2 binary64)))

Samples

241.0ms	98×	2	valid
140.0ms	151×	1	valid
2.0ms	7×	0	valid

Compiler

Compiled 337 to 35 computations (89.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 332.0ms

ival-mult: 97.0ms (29.3% of total)

ival-acos: 87.0ms (26.2% of total)

adjust: 33.0ms (10% of total)

ival-asin: 27.0ms (8.1% of total)

exact: 25.0ms (7.5% of total)

ival-sqrt: 18.0ms (5.4% of total)

ival-sub: 17.0ms (5.1% of total)

ival-div: 12.0ms (3.6% of total)

ival-add: 11.0ms (3.3% of total)

ival-pi: 3.0ms (0.9% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

8.4MiB live, 8.4MiB allocated

Counts

26 → 37

Calls

Call 1

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

Outputs
(+ (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (* 1/2 (PI)))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))
(+ (* -1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* -1/8 (* x (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* x (+ (* -1/8 (sqrt 1/2)) (* -1/16 (* x (sqrt 1/2))))))))
1/2
(+ 1/2 (* -1/2 x))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(- (+ (* -1/2 (PI)) (* 1/2 (PI))) (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(- (+ (acos (* (sqrt 1/2) (sqrt (- 1 x)))) (+ (* -1/2 (PI)) (* 1/2 (PI)))) (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(- (asin (* (sqrt 1/2) (sqrt (- 1 x)))) (* -1/2 (PI)))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(* (sqrt x) (* (sqrt -1) (sqrt 1/2)))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt 1/2) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1/2 x)
(* x (- (* 1/2 (/ 1 x)) 1/2))
(+ (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))) (* 1/2 (PI)))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(+ (* -1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))
(* -1 (* x (- 1/2 (* 1/2 (/ 1 x)))))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(- (+ (* -1/2 (PI)) (* 1/2 (PI))) (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(- (+ (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (+ (* -1/2 (PI)) (* 1/2 (PI)))) (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(- (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (* -1/2 (PI)))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

-inf

((+ (* -2 (- (* (PI) 1/2) (acos (* (sqrt (- 1 x)) (sqrt 1/2))))) (* (PI) 1/2)) (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (- (* (PI) 1/2) (acos (* (sqrt (- 1 x)) (sqrt 1/2)))) (* (PI) 1/2) (+ (* (asin (sqrt (/ (- 1 x) 2))) 2) (/ (PI) -2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (/ (- 1 x) 2) (+ (* (asin (sqrt (/ (- 1 x) 2))) 2) (/ (PI) -2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (/ (- 1 x) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2))))) (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/ (PI) 2) (PI) (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (+ (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (acos (sqrt (/ (- 1 x) 2)))) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (/ (- 1 x) 2) (acos (* (sqrt (- 1 x)) (sqrt 1/2))) (* (sqrt (- 1 x)) (sqrt 1/2)) (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))) (acos (sqrt (/ (- 1 x) 2))) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)))

2.0ms

inf

((+ (* -2 (- (* (PI) 1/2) (acos (* (sqrt (- 1 x)) (sqrt 1/2))))) (* (PI) 1/2)) (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (- (* (PI) 1/2) (acos (* (sqrt (- 1 x)) (sqrt 1/2)))) (* (PI) 1/2) (+ (* (asin (sqrt (/ (- 1 x) 2))) 2) (/ (PI) -2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (/ (- 1 x) 2) (+ (* (asin (sqrt (/ (- 1 x) 2))) 2) (/ (PI) -2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (/ (- 1 x) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2))))) (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/ (PI) 2) (PI) (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (+ (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (acos (sqrt (/ (- 1 x) 2)))) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (/ (- 1 x) 2) (acos (* (sqrt (- 1 x)) (sqrt 1/2))) (* (sqrt (- 1 x)) (sqrt 1/2)) (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))) (acos (sqrt (/ (- 1 x) 2))) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)))

2.0ms

((+ (* -2 (- (* (PI) 1/2) (acos (* (sqrt (- 1 x)) (sqrt 1/2))))) (* (PI) 1/2)) (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (- (* (PI) 1/2) (acos (* (sqrt (- 1 x)) (sqrt 1/2)))) (* (PI) 1/2) (+ (* (asin (sqrt (/ (- 1 x) 2))) 2) (/ (PI) -2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (/ (- 1 x) 2) (+ (* (asin (sqrt (/ (- 1 x) 2))) 2) (/ (PI) -2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (/ (- 1 x) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2))))) (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/ (PI) 2) (PI) (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (+ (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (acos (sqrt (/ (- 1 x) 2)))) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (/ (- 1 x) 2) (acos (* (sqrt (- 1 x)) (sqrt 1/2))) (* (sqrt (- 1 x)) (sqrt 1/2)) (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))) (acos (sqrt (/ (- 1 x) 2))) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)))

simplify191.0ms (1.6%)

Memory

29.2MiB live, 324.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	125	626
1	362	587
2	1324	565
3	5524	562
0	8106	536

Stop Event

1×	iter limit
1×	node limit

Counts

37 → 37

Calls

Call 1

Inputs
(+ (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (* 1/2 (PI)))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))
(+ (* -1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* -1/8 (* x (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* x (+ (* -1/8 (sqrt 1/2)) (* -1/16 (* x (sqrt 1/2))))))))
1/2
(+ 1/2 (* -1/2 x))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(- (+ (* -1/2 (PI)) (* 1/2 (PI))) (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(- (+ (acos (* (sqrt 1/2) (sqrt (- 1 x)))) (+ (* -1/2 (PI)) (* 1/2 (PI)))) (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(- (asin (* (sqrt 1/2) (sqrt (- 1 x)))) (* -1/2 (PI)))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(* (sqrt x) (* (sqrt -1) (sqrt 1/2)))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt 1/2) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1/2 x)
(* x (- (* 1/2 (/ 1 x)) 1/2))
(+ (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))) (* 1/2 (PI)))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(+ (* -1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))
(* -1 (* x (- 1/2 (* 1/2 (/ 1 x)))))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(- (+ (* -1/2 (PI)) (* 1/2 (PI))) (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(- (+ (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (+ (* -1/2 (PI)) (* 1/2 (PI)))) (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(- (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (* -1/2 (PI)))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))

Outputs
(+ (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))) (* 1/2 (PI)))
(fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal -2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64)))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal -2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64)))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))
(-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (* -1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))))
(fma.f64 (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64) (.f64 #s(literal -1/2 binary64) (PI.f64)))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* -1/8 (* x (sqrt 1/2))))))
(fma.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* x (+ (* -1/8 (sqrt 1/2)) (* -1/16 (* x (sqrt 1/2))))))))
(fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/8 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) x (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x (sqrt.f64 #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))
(.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(- (+ (* -1/2 (PI)) (* 1/2 (PI))) (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(neg.f64 (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))
(- (+ (acos (* (sqrt 1/2) (sqrt (- 1 x)))) (+ (* -1/2 (PI)) (* 1/2 (PI)))) (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(-.f64 (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))
(- (asin (* (sqrt 1/2) (sqrt (- 1 x)))) (* -1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))
(* (sqrt x) (* (sqrt -1) (sqrt 1/2)))
(.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 x))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))
(.f64 (fma.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)))) x)
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1 binary64))) #s(literal -1/8 binary64) (.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) (sqrt.f64 #s(literal -1 binary64)))) x)
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt 1/2) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1 binary64))) #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) (sqrt.f64 #s(literal -1 binary64))))) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* x (- (* 1/2 (/ 1 x)) 1/2))
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) x)
(+ (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))) (* 1/2 (PI)))
(fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal -2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64)))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))
(fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal -2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64)))
(- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (* -1/2 (PI)) (* 2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(fma.f64 (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64) (.f64 #s(literal -1/2 binary64) (PI.f64)))
(asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))
(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(.f64 (.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(.f64 (neg.f64 x) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))
(.f64 (neg.f64 x) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (- 1/2 (* 1/2 (/ 1 x)))))
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1/2 binary64)) x)
(* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))
(.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(- (+ (* -1/2 (PI)) (* 1/2 (PI))) (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(neg.f64 (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))
(- (+ (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (+ (* -1/2 (PI)) (* 1/2 (PI)))) (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(-.f64 (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))
(- (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (* -1/2 (PI)))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))

rewrite264.0ms (2.2%)

Memory

28.2MiB live, 314.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	333
0	87	312
1	304	304
2	2275	304
0	9609	302

Stop Event

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

Counts

26 → 463

Calls

Call 1

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

Outputs
(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64)) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64)) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))) (/.f64 (.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64)) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))) (-.f64 (.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))) (/.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64))))))) (.f64 (/.f64 (.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64)) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))) (/.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64))))))))))
(/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (pow.f64 (.f64 (neg.f64 (neg.f64 (PI.f64))) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (-.f64 (.f64 (.f64 (neg.f64 (neg.f64 (PI.f64))) #s(literal 1/2 binary64)) (.f64 (neg.f64 (neg.f64 (PI.f64))) #s(literal 1/2 binary64))) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (*.f64 (neg.f64 (neg.f64 (PI.f64))) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) (PI.f64))) (.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64)))) (neg.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))
(/.f64 (neg.f64 (-.f64 (.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64)) (.f64 (pow.f64 (neg.f64 (PI.f64)) #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) (PI.f64)) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) (PI.f64)))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64) (.f64 #s(literal -1/2 binary64) (PI.f64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64))))))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) (PI.f64))) (.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64))) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64))))
(/.f64 (-.f64 (.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64)) (.f64 (pow.f64 (neg.f64 (PI.f64)) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) (PI.f64)) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)) (.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (-.f64 (.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) (PI.f64))))) (neg.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64) (.f64 #s(literal -1/2 binary64) (PI.f64)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64))))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) (PI.f64)) (-.f64 (.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (.f64 #s(literal 1/2 binary64) (PI.f64))))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64))))) (neg.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))))
(/.f64 (-.f64 (.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) (PI.f64)))) (fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64) (.f64 #s(literal -1/2 binary64) (PI.f64))))
(/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) (PI.f64)) (-.f64 (.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) (.f64 #s(literal -2 binary64) (.f64 #s(literal 1/2 binary64) (PI.f64)))))))
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(-.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (pow.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))))))) (/.f64 (pow.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (pow.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))))))))
(-.f64 (/.f64 (.f64 (neg.f64 (PI.f64)) (+.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 #s(literal -2 binary64) (+.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))))) (/.f64 (.f64 #s(literal -2 binary64) (.f64 (+.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))) (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))))) (*.f64 #s(literal -2 binary64) (+.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))))))
(-.f64 (/.f64 (.f64 (neg.f64 (PI.f64)) (fma.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (+.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)))) (.f64 #s(literal -2 binary64) (fma.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (+.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))))) (/.f64 (.f64 #s(literal -2 binary64) (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 3 binary64)))) (.f64 #s(literal -2 binary64) (fma.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (+.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))))))
(-.f64 (/.f64 (.f64 (PI.f64) (+.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (+.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))))) (/.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))) (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))))) (*.f64 #s(literal 2 binary64) (+.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))))))
(-.f64 (/.f64 (.f64 (PI.f64) (fma.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (+.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (fma.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (+.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))))) (/.f64 (.f64 #s(literal 2 binary64) (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 3 binary64)))) (.f64 #s(literal 2 binary64) (fma.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (+.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))))
(+.f64 (/.f64 (-.f64 (PI.f64) (PI.f64)) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))))
(acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))))
(asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)))) (neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))))))
(-.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))))) (/.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))))))
(-.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))))))) (/.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))))))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))

eval206.0ms (1.7%)

Memory: -25.0MiB live, 227.6MiB allocated
Compiler: Compiled 38 217 to 2 881 computations (92.5% saved)

prune69.0ms (0.6%)

Memory

-7.6MiB live, 93.4MiB allocated

Pruning

24 alts after pruning (21 fresh and 3 done)

	Pruned	Kept	Total
New	843	12	855
Fresh	1	9	10
Picked	3	2	5
Done	1	1	2
Total	848	24	872

Accuracy

9.4%

Counts

872 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.2%	(fma.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
✓	2.6%	(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
✓	4.1%	(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
▶	4.0%	(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
	6.9%	(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (-.f64 (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))))
	4.1%	(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #s(literal 4 binary64))) (-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64))))
	6.9%	(/.f64 (-.f64 (pow.f64 (+.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64))) #s(literal 2 binary64)) (pow.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))) (+.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))))
	6.2%	(/.f64 (-.f64 (pow.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))))
	6.2%	(/.f64 (-.f64 (pow.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))) (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
✓	0.0%	(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
	6.2%	(-.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
	4.0%	(-.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))))
▶	6.9%	(+.f64 (/.f64 (-.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
	4.2%	(+.f64 (/.f64 (.f64 (pow.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #s(literal 4 binary64)) (-.f64 (.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal -2 binary64)))) (/.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal -2 binary64))) (-.f64 (.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal -2 binary64)))))
	7.7%	(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))))))
	7.5%	(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) x)))))
▶	7.7%	(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
	3.8%	(*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))
	3.8%	(*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
	7.8%	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64))))
	6.2%	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64))))
▶	7.8%	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))))
	7.7%	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (-.f64 (.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) (PI.f64)))) (fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64) (.f64 #s(literal -1/2 binary64) (PI.f64)))))
	6.2%	#s(approx (- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2))))) (fma.f64 #s(literal -2 binary64) (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 (PI.f64) #s(literal 1/2 binary64))))

Compiler

Compiled 1 547 to 932 computations (39.8% saved)

simplify167.0ms (1.4%)

Memory

4.8MiB live, 194.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64))
cost-diff	1	(-.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)))
cost-diff	1	(+.f64 (/.f64 (-.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
cost-diff	14	(/.f64 (-.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64))))
cost-diff	0	(PI.f64)
cost-diff	0	(/.f64 (PI.f64) #s(literal 2 binary64))
cost-diff	0	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))))
cost-diff	0	(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
cost-diff	0	(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
cost-diff	0	(fma.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
cost-diff	0	#s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))
cost-diff	0	(sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))
cost-diff	0	(asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))))
cost-diff	0	(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
cost-diff	0	(/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64))))))
cost-diff	0	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))))
cost-diff	1	(-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))
cost-diff	4	(.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	784
0	122	784
1	181	784
2	356	784
3	989	776
4	2871	724
5	5296	724
0	8509	716

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))))
(/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64))))))
(fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (*.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64))))
(pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64))
(-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(*.f64 #s(literal 1/2 binary64) (PI.f64))
#s(literal 1/2 binary64)
(PI.f64)
(acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal 3 binary64)
#s(literal -8 binary64)
(*.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))
#s(literal 1/8 binary64)
(pow.f64 (PI.f64) #s(literal 3 binary64))
(fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))
(pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 4 binary64)
(.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64))))
(-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))
(.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
#s(literal -2 binary64)
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
(asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(literal -2 binary64)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(fma.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal 2 binary64)
#s(literal -2 binary64)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))))
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
#s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(literal 1/2 binary64)
(asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(sqrt.f64 #s(literal 1/2 binary64))
(acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(+.f64 (/.f64 (-.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64))))
(-.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)))
(pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
#s(literal -1/2 binary64)
x
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(literal 2 binary64)
(pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
(-.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))
(/.f64 (PI.f64) #s(literal -2 binary64))
#s(literal -2 binary64)
(acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) x)

Outputs
#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))))
#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) (.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 #s(literal 4 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (.f64 (fma.f64 #s(literal 1/4 binary64) (PI.f64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))) (PI.f64)))))
(/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64))))))
(/.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) (.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 #s(literal 4 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (.f64 (fma.f64 #s(literal 1/4 binary64) (PI.f64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))) (PI.f64))))
(fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (*.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64))))
(fma.f64 #s(literal -8 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/8 binary64)))
(pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64))
(pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64))
(-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(*.f64 #s(literal 1/2 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(PI.f64)
(acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal 3 binary64)
#s(literal -8 binary64)
(*.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
(pow.f64 (PI.f64) #s(literal 3 binary64))
(fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))
(fma.f64 #s(literal 4 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (.f64 (fma.f64 #s(literal 1/4 binary64) (PI.f64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))) (PI.f64)))
(pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 4 binary64)
(.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64))))
(.f64 (fma.f64 #s(literal 1/4 binary64) (PI.f64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))) (PI.f64))
(-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))
(fma.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))
#s(literal -2 binary64)
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
(asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(literal -2 binary64)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(fma.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal 2 binary64)
#s(literal -2 binary64)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(-.f64 (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))))
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
#s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
#s(literal 1/2 binary64)
(asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))
(asin.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(sqrt.f64 #s(literal 1/2 binary64))
(acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(+.f64 (/.f64 (-.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(fma.f64 (+.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))) #s(literal 1 binary64) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64))))
(.f64 (+.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))) #s(literal 1 binary64))
(-.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)))
(fma.f64 (/.f64 (PI.f64) #s(literal -4 binary64)) (PI.f64) (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)))
(pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
#s(literal -1/2 binary64)
x
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(literal 2 binary64)
(pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
(-.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))
(/.f64 (PI.f64) #s(literal -2 binary64))
#s(literal -2 binary64)
(acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) x)

localize751.0ms (6.2%)

Memory

-19.5MiB live, 458.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.5557094409913033	#s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
accuracy	0.98046875	(/.f64 (-.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64))))
accuracy	0.98046875	(-.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)))
accuracy	58.983928692450874	(+.f64 (/.f64 (-.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
accuracy	0.0234375	(acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
accuracy	0.04201127930532605	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))))
accuracy	0.97265625	(asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))
accuracy	58.983928692450874	(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
accuracy	0.0	(PI.f64)
accuracy	0.00390625	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
accuracy	0.97265625	(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
accuracy	59.03079891096031	(fma.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	0.00390625	(sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))
accuracy	0.97265625	(asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))))
accuracy	1.1027715122768347	#s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))
accuracy	59.03079891096031	(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	0.96484375	(fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))
accuracy	0.984375	(pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64))
accuracy	1.0	(pow.f64 (PI.f64) #s(literal 3 binary64))
accuracy	58.962235457570536	(fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (*.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64))))

Samples

348.0ms	98×	2	valid
306.0ms	151×	1	valid
3.0ms	7×	0	valid

Compiler

Compiled 621 to 59 computations (90.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 573.0ms

ival-mult: 98.0ms (17.1% of total)

ival-sub: 82.0ms (14.3% of total)

ival-asin: 78.0ms (13.6% of total)

ival-pow: 76.0ms (13.3% of total)

adjust: 73.0ms (12.7% of total)

ival-acos: 67.0ms (11.7% of total)

ival-pow2: 41.0ms (7.2% of total)

ival-div: 20.0ms (3.5% of total)

ival-add: 17.0ms (3% of total)

ival-sqrt: 16.0ms (2.8% of total)

ival-pi: 3.0ms (0.5% of total)

exact: 1.0ms (0.2% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series31.0ms (0.3%)

Memory

24.3MiB live, 24.3MiB allocated

Counts

27 → 49

Calls

Call 1

Inputs
(.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64))))
(-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))
#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))))
(/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64))))))
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
(asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))
(fma.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))))
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
(/.f64 (-.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64))))
(+.f64 (/.f64 (-.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(-.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)))
(pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (*.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64))))
(pow.f64 (PI.f64) #s(literal 3 binary64))
(pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64))
(fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))
(asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))
(acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
#s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))

Outputs
(* 1/2 (* (PI) (- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))))
(- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(/ (+ (* -8 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))) 3)) (* 1/8 (pow (PI) 3))) (+ (* 1/2 (* (PI) (- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))))) (* 4 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))) 2))))
(+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* -1/8 (* x (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* x (+ (* -1/8 (sqrt 1/2)) (* -1/16 (* x (sqrt 1/2))))))))
1/2
(+ 1/2 (* -1/2 x))
(- (+ (acos (* (sqrt 1/2) (sqrt (- 1 x)))) (+ (* -1/2 (PI)) (* 1/2 (PI)))) (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(- (+ (* -1/2 (PI)) (* 1/2 (PI))) (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(/ (- (pow (acos (* (sqrt 1/2) (sqrt (- 1 x)))) 2) (* 1/4 (pow (PI) 2))) (- (acos (* (sqrt 1/2) (sqrt (- 1 x)))) (* -1/2 (PI))))
(- (+ (acos (* (sqrt 1/2) (sqrt (- 1 x)))) (/ (pow (acos (* (sqrt 1/2) (sqrt (- 1 x)))) 2) (- (acos (* (sqrt 1/2) (sqrt (- 1 x)))) (* -1/2 (PI))))) (* 1/4 (/ (pow (PI) 2) (- (acos (* (sqrt 1/2) (sqrt (- 1 x)))) (* -1/2 (PI))))))
(- (pow (acos (* (sqrt 1/2) (sqrt (- 1 x)))) 2) (* 1/4 (pow (PI) 2)))
(pow (acos (* (sqrt 1/2) (sqrt (- 1 x)))) 2)
(+ (* -8 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))) 3)) (* 1/8 (pow (PI) 3)))
(pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))) 3)
(+ (* 1/2 (* (PI) (- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))))) (* 4 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))) 2)))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(* (sqrt x) (* (sqrt -1) (sqrt 1/2)))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt 1/2) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1/2 x)
(* x (- (* 1/2 (/ 1 x)) 1/2))
(* 1/2 (* (PI) (- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))))
(- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))
(/ (+ (* -8 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) 3)) (* 1/8 (pow (PI) 3))) (+ (* 1/2 (* (PI) (- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))))) (* 4 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) 2))))
(+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))
(asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))
(* -1 (* x (- 1/2 (* 1/2 (/ 1 x)))))
(- (+ (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (+ (* -1/2 (PI)) (* 1/2 (PI)))) (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(- (+ (* -1/2 (PI)) (* 1/2 (PI))) (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(/ (- (pow (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) 2) (* 1/4 (pow (PI) 2))) (- (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (* -1/2 (PI))))
(- (+ (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (/ (pow (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) 2) (- (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (* -1/2 (PI))))) (* 1/4 (/ (pow (PI) 2) (- (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (* -1/2 (PI))))))
(- (pow (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) 2) (* 1/4 (pow (PI) 2)))
(pow (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) 2)
(+ (* -8 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) 3)) (* 1/8 (pow (PI) 3)))
(pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) 3)
(+ (* 1/2 (* (PI) (- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))))) (* 4 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) 2)))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))

Calls

3 calls:

Time

Variable

Point

Expression

12.0ms

inf

((* (* 1/2 (PI)) (- (* 1/2 (PI)) (* (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) -2))) (- (* 1/2 (PI)) (* (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) -2)) (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/ (+ (* (pow (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) 3) -8) (* 1/8 (pow (PI) 3))) (+ (* (pow (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) 2) 4) (* (* 1/2 (PI)) (- (* 1/2 (PI)) (* (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) -2))))) (+ (* (asin (sqrt (/ (- 1 x) 2))) -2) (/ (PI) 2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (/ (- 1 x) 2) (+ (* (asin (sqrt (/ (- 1 x) 2))) -2) (/ (PI) 2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (/ (- 1 x) 2) (+ (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (acos (sqrt (/ (- 1 x) 2)))) (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (/ (PI) 2) (PI) (/ (- (pow (acos (sqrt (/ (- 1 x) 2))) 2) (pow (/ (PI) 2) 2)) (- (acos (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (+ (/ (- (pow (acos (sqrt (/ (- 1 x) 2))) 2) (pow (/ (PI) 2) 2)) (- (acos (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (acos (sqrt (/ (- 1 x) 2)))) (- (pow (acos (sqrt (/ (- 1 x) 2))) 2) (pow (/ (PI) 2) 2)) (pow (acos (sqrt (/ (- 1 x) 2))) 2) (+ (* (pow (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) 3) -8) (* 1/8 (pow (PI) 3))) (pow (PI) 3) (pow (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) 3) (+ (* (pow (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) 2) 4) (* (* 1/2 (PI)) (- (* 1/2 (PI)) (* (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) -2)))) (asin (* (sqrt (- 1 x)) (sqrt 1/2))) (acos (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)))

8.0ms

((* (* 1/2 (PI)) (- (* 1/2 (PI)) (* (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) -2))) (- (* 1/2 (PI)) (* (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) -2)) (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/ (+ (* (pow (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) 3) -8) (* 1/8 (pow (PI) 3))) (+ (* (pow (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) 2) 4) (* (* 1/2 (PI)) (- (* 1/2 (PI)) (* (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) -2))))) (+ (* (asin (sqrt (/ (- 1 x) 2))) -2) (/ (PI) 2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (/ (- 1 x) 2) (+ (* (asin (sqrt (/ (- 1 x) 2))) -2) (/ (PI) 2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (/ (- 1 x) 2) (+ (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (acos (sqrt (/ (- 1 x) 2)))) (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (/ (PI) 2) (PI) (/ (- (pow (acos (sqrt (/ (- 1 x) 2))) 2) (pow (/ (PI) 2) 2)) (- (acos (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (+ (/ (- (pow (acos (sqrt (/ (- 1 x) 2))) 2) (pow (/ (PI) 2) 2)) (- (acos (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (acos (sqrt (/ (- 1 x) 2)))) (- (pow (acos (sqrt (/ (- 1 x) 2))) 2) (pow (/ (PI) 2) 2)) (pow (acos (sqrt (/ (- 1 x) 2))) 2) (+ (* (pow (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) 3) -8) (* 1/8 (pow (PI) 3))) (pow (PI) 3) (pow (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) 3) (+ (* (pow (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) 2) 4) (* (* 1/2 (PI)) (- (* 1/2 (PI)) (* (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) -2)))) (asin (* (sqrt (- 1 x)) (sqrt 1/2))) (acos (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)))

8.0ms

-inf

((* (* 1/2 (PI)) (- (* 1/2 (PI)) (* (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) -2))) (- (* 1/2 (PI)) (* (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) -2)) (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/ (+ (* (pow (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) 3) -8) (* 1/8 (pow (PI) 3))) (+ (* (pow (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) 2) 4) (* (* 1/2 (PI)) (- (* 1/2 (PI)) (* (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) -2))))) (+ (* (asin (sqrt (/ (- 1 x) 2))) -2) (/ (PI) 2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (/ (- 1 x) 2) (+ (* (asin (sqrt (/ (- 1 x) 2))) -2) (/ (PI) 2)) (asin (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)) (/ (- 1 x) 2) (+ (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (acos (sqrt (/ (- 1 x) 2)))) (- (/ (PI) 2) (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (/ (PI) 2) (PI) (/ (- (pow (acos (sqrt (/ (- 1 x) 2))) 2) (pow (/ (PI) 2) 2)) (- (acos (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (+ (/ (- (pow (acos (sqrt (/ (- 1 x) 2))) 2) (pow (/ (PI) 2) 2)) (- (acos (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (acos (sqrt (/ (- 1 x) 2)))) (- (pow (acos (sqrt (/ (- 1 x) 2))) 2) (pow (/ (PI) 2) 2)) (pow (acos (sqrt (/ (- 1 x) 2))) 2) (+ (* (pow (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) 3) -8) (* 1/8 (pow (PI) 3))) (pow (PI) 3) (pow (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) 3) (+ (* (pow (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) 2) 4) (* (* 1/2 (PI)) (- (* 1/2 (PI)) (* (- (* 1/2 (PI)) (acos (sqrt (* (- 1 x) 1/2)))) -2)))) (asin (* (sqrt (- 1 x)) (sqrt 1/2))) (acos (sqrt (/ (- 1 x) 2))) (sqrt (/ (- 1 x) 2)))

simplify207.0ms (1.7%)

Memory

7.0MiB live, 102.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	167	1054
1	464	1015
2	1664	993
3	6434	991
0	8113	943

Stop Event

1×	iter limit
1×	node limit

Counts

49 → 49

Calls

Call 1

Inputs
(* 1/2 (* (PI) (- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))))
(- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(/ (+ (* -8 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))) 3)) (* 1/8 (pow (PI) 3))) (+ (* 1/2 (* (PI) (- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))))) (* 4 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))) 2))))
(+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* -1/8 (* x (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* x (+ (* -1/8 (sqrt 1/2)) (* -1/16 (* x (sqrt 1/2))))))))
1/2
(+ 1/2 (* -1/2 x))
(- (+ (acos (* (sqrt 1/2) (sqrt (- 1 x)))) (+ (* -1/2 (PI)) (* 1/2 (PI)))) (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(- (+ (* -1/2 (PI)) (* 1/2 (PI))) (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(/ (- (pow (acos (* (sqrt 1/2) (sqrt (- 1 x)))) 2) (* 1/4 (pow (PI) 2))) (- (acos (* (sqrt 1/2) (sqrt (- 1 x)))) (* -1/2 (PI))))
(- (+ (acos (* (sqrt 1/2) (sqrt (- 1 x)))) (/ (pow (acos (* (sqrt 1/2) (sqrt (- 1 x)))) 2) (- (acos (* (sqrt 1/2) (sqrt (- 1 x)))) (* -1/2 (PI))))) (* 1/4 (/ (pow (PI) 2) (- (acos (* (sqrt 1/2) (sqrt (- 1 x)))) (* -1/2 (PI))))))
(- (pow (acos (* (sqrt 1/2) (sqrt (- 1 x)))) 2) (* 1/4 (pow (PI) 2)))
(pow (acos (* (sqrt 1/2) (sqrt (- 1 x)))) 2)
(+ (* -8 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))) 3)) (* 1/8 (pow (PI) 3)))
(pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))) 3)
(+ (* 1/2 (* (PI) (- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))))) (* 4 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))) 2)))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(* (sqrt x) (* (sqrt -1) (sqrt 1/2)))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt 1/2) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1/2 x)
(* x (- (* 1/2 (/ 1 x)) 1/2))
(* 1/2 (* (PI) (- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))))
(- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))
(/ (+ (* -8 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) 3)) (* 1/8 (pow (PI) 3))) (+ (* 1/2 (* (PI) (- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))))) (* 4 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) 2))))
(+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))
(asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))
(* -1 (* x (- 1/2 (* 1/2 (/ 1 x)))))
(- (+ (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (+ (* -1/2 (PI)) (* 1/2 (PI)))) (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(- (+ (* -1/2 (PI)) (* 1/2 (PI))) (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(/ (- (pow (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) 2) (* 1/4 (pow (PI) 2))) (- (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (* -1/2 (PI))))
(- (+ (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (/ (pow (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) 2) (- (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (* -1/2 (PI))))) (* 1/4 (/ (pow (PI) 2) (- (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (* -1/2 (PI))))))
(- (pow (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) 2) (* 1/4 (pow (PI) 2)))
(pow (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) 2)
(+ (* -8 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) 3)) (* 1/8 (pow (PI) 3)))
(pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) 3)
(+ (* 1/2 (* (PI) (- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))))) (* 4 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) 2)))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))

Outputs
(* 1/2 (* (PI) (- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))))
(.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64))) (PI.f64)) #s(literal 1/2 binary64))
(- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64)))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x)))))))
(fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal -2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64)))
(/ (+ (* -8 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))) 3)) (* 1/8 (pow (PI) 3))) (+ (* 1/2 (* (PI) (- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))))) (* 4 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))) 2))))
(/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) (PI.f64))) (PI.f64)) #s(literal 1/2 binary64))))
(+ (* -2 (asin (* (sqrt 1/2) (sqrt (- 1 x))))) (* 1/2 (PI)))
(fma.f64 (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal -2 binary64) (.f64 #s(literal 1/2 binary64) (PI.f64)))
(asin (* (sqrt 1/2) (sqrt (- 1 x))))
(asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/2 (* x (sqrt 1/2))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* -1/8 (* x (sqrt 1/2))))))
(fma.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* x (+ (* -1/2 (sqrt 1/2)) (* x (+ (* -1/8 (sqrt 1/2)) (* -1/16 (* x (sqrt 1/2))))))))
(fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/8 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) x (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x (sqrt.f64 #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
(- (+ (acos (* (sqrt 1/2) (sqrt (- 1 x)))) (+ (* -1/2 (PI)) (* 1/2 (PI)))) (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(-.f64 (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))
(- (+ (* -1/2 (PI)) (* 1/2 (PI))) (asin (* (sqrt 1/2) (sqrt (- 1 x)))))
(neg.f64 (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))
(/ (- (pow (acos (* (sqrt 1/2) (sqrt (- 1 x)))) 2) (* 1/4 (pow (PI) 2))) (- (acos (* (sqrt 1/2) (sqrt (- 1 x)))) (* -1/2 (PI))))
(/.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (PI.f64)) (PI.f64) (pow.f64 (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))))
(- (+ (acos (* (sqrt 1/2) (sqrt (- 1 x)))) (/ (pow (acos (* (sqrt 1/2) (sqrt (- 1 x)))) 2) (- (acos (* (sqrt 1/2) (sqrt (- 1 x)))) (* -1/2 (PI))))) (* 1/4 (/ (pow (PI) 2) (- (acos (* (sqrt 1/2) (sqrt (- 1 x)))) (* -1/2 (PI))))))
(+.f64 (/.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (PI.f64)) (PI.f64) (pow.f64 (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))
(- (pow (acos (* (sqrt 1/2) (sqrt (- 1 x)))) 2) (* 1/4 (pow (PI) 2)))
(fma.f64 (.f64 #s(literal -1/4 binary64) (PI.f64)) (PI.f64) (pow.f64 (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(pow (acos (* (sqrt 1/2) (sqrt (- 1 x)))) 2)
(pow.f64 (acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(+ (* -8 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))) 3)) (* 1/8 (pow (PI) 3)))
(fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (*.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/8 binary64)))
(pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))) 3)
(pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 3 binary64))
(+ (* 1/2 (* (PI) (- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))))))) (* 4 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (- 1 x))))) 2)))
(fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64))) (PI.f64)) #s(literal 1/2 binary64)))
(acos (* (sqrt 1/2) (sqrt (- 1 x))))
(acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))
(* (sqrt x) (* (sqrt -1) (sqrt 1/2)))
(.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 x))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))
(.f64 (fma.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)))) x)
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1 binary64))) #s(literal -1/8 binary64) (.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) (sqrt.f64 #s(literal -1 binary64)))) x)
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt 1/2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt 1/2) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt 1/2) (sqrt -1)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1 binary64))) #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) (sqrt.f64 #s(literal -1 binary64))))) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* x (- (* 1/2 (/ 1 x)) 1/2))
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) x)
(* 1/2 (* (PI) (- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))))
(.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64))) (PI.f64)) #s(literal 1/2 binary64))
(- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))
(fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64)))
(- (* 1/2 (PI)) (* 2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))))
(fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal -2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64)))
(/ (+ (* -8 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) 3)) (* 1/8 (pow (PI) 3))) (+ (* 1/2 (* (PI) (- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))))) (* 4 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) 2))))
(/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) (PI.f64))) (PI.f64)) #s(literal 1/2 binary64))))
(+ (* -2 (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) (* 1/2 (PI)))
(fma.f64 (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal -2 binary64) (.f64 #s(literal 1/2 binary64) (PI.f64)))
(asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt 1/2))))
(.f64 (.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))
(.f64 (.f64 (neg.f64 x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2)))))))
(.f64 (neg.f64 x) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (sqrt 1/2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt 1/2))))))))
(.f64 (neg.f64 x) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (- 1/2 (* 1/2 (/ 1 x)))))
(*.f64 (fma.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) x)
(- (+ (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (+ (* -1/2 (PI)) (* 1/2 (PI)))) (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(-.f64 (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))
(- (+ (* -1/2 (PI)) (* 1/2 (PI))) (asin (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))))
(neg.f64 (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))
(/ (- (pow (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) 2) (* 1/4 (pow (PI) 2))) (- (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (* -1/2 (PI))))
(/.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (PI.f64)) (PI.f64) (pow.f64 (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))))
(- (+ (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (/ (pow (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) 2) (- (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (* -1/2 (PI))))) (* 1/4 (/ (pow (PI) 2) (- (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) (* -1/2 (PI))))))
(+.f64 (/.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (PI.f64)) (PI.f64) (pow.f64 (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))
(- (pow (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) 2) (* 1/4 (pow (PI) 2)))
(fma.f64 (.f64 #s(literal -1/4 binary64) (PI.f64)) (PI.f64) (pow.f64 (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(pow (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x))))) 2)
(pow.f64 (acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(+ (* -8 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) 3)) (* 1/8 (pow (PI) 3)))
(fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (*.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/8 binary64)))
(pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) 3)
(pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 3 binary64))
(+ (* 1/2 (* (PI) (- (* 1/2 (PI)) (* -2 (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))))))) (* 4 (pow (- (* 1/2 (PI)) (acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))) 2)))
(fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64))) (PI.f64)) #s(literal 1/2 binary64)))
(acos (* (sqrt 1/2) (sqrt (+ 1 (* -1 x)))))
(acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))

rewrite287.0ms (2.4%)

Memory

-8.0MiB live, 275.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	539
0	122	531
1	433	483
2	3242	483
0	8212	478

Stop Event

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

Counts

27 → 593

Calls

Call 1

Inputs
(.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64))))
(-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))
#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))))
(/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64))))))
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
(asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))
#s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))
(fma.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))))))
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
(/.f64 (-.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64))))
(+.f64 (/.f64 (-.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(-.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)))
(pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (*.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64))))
(pow.f64 (PI.f64) #s(literal 3 binary64))
(pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64))
(fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))
(asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))
(acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
#s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))

Outputs
(.f64 (.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) #s(literal 1/2 binary64)) (PI.f64))
(.f64 (.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) (PI.f64)) #s(literal 1/2 binary64))
(.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))))
(.f64 (PI.f64) (.f64 #s(literal 1/2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))))))
(.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) (PI.f64)))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 4 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)))) (.f64 (PI.f64) #s(literal 1/2 binary64))) (fma.f64 #s(literal -2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) (.f64 (PI.f64) #s(literal 1/2 binary64))))
(/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) (.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (.f64 (PI.f64) #s(literal 1/2 binary64))) (fma.f64 (.f64 #s(literal -2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))) (fma.f64 #s(literal -2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 #s(literal 1/4 binary64) (*.f64 (PI.f64) (PI.f64)))))
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(+.f64 (/.f64 (.f64 #s(literal 64 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 6 binary64))) (fma.f64 (.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) (.f64 (PI.f64) #s(literal 1/2 binary64))) (-.f64 (.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 #s(literal 4 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)))) (.f64 (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 4 binary64)) #s(literal 16 binary64)))) (/.f64 (pow.f64 (.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) (.f64 (PI.f64) #s(literal 1/2 binary64))) #s(literal 3 binary64)) (fma.f64 (.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) (.f64 (PI.f64) #s(literal 1/2 binary64))) (-.f64 (.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 #s(literal 4 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)))) (.f64 (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 4 binary64)) #s(literal 16 binary64)))))
(+.f64 (.f64 #s(literal 4 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64))) (.f64 (neg.f64 (.f64 #s(literal -1/2 binary64) (PI.f64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))))))
(+.f64 (.f64 #s(literal 4 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64))) (.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) (.f64 (PI.f64) #s(literal 1/2 binary64))))
(+.f64 (.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 #s(literal 4 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64))))
(asin.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) #s(literal 3 binary64)) (pow.f64 (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (pow.f64 (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))) (asin.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) #s(literal 3 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))))
(/.f64 (-.f64 (.f64 (neg.f64 (PI.f64)) (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 #s(literal -2 binary64) (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))))) (*.f64 #s(literal -2 binary64) (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(/.f64 (-.f64 (.f64 (neg.f64 (PI.f64)) (fma.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)))) (.f64 #s(literal -2 binary64) (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) #s(literal 3 binary64)) (pow.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64))))) (*.f64 #s(literal -2 binary64) (fma.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (.f64 (PI.f64) (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))))) (*.f64 #s(literal 2 binary64) (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(/.f64 (-.f64 (.f64 (PI.f64) (fma.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) #s(literal 3 binary64)) (pow.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64))))) (*.f64 #s(literal 2 binary64) (fma.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
#s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))

eval408.0ms (3.3%)

Memory: 0.6MiB live, 421.0MiB allocated
Compiler: Compiled 83 665 to 5 292 computations (93.7% saved)

prune146.0ms (1.2%)

Memory

-13.2MiB live, 181.3MiB allocated

Pruning

35 alts after pruning (30 fresh and 5 done)

	Pruned	Kept	Total
New	1 332	21	1 353
Fresh	7	9	16
Picked	3	2	5
Done	0	3	3
Total	1 342	35	1 377

Accuracy

9.5%

Counts

1 377 → 35

Alt Table

Click to see full alt table

Status	Accuracy	Program
	6.2%	(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
✓	2.6%	(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
✓	4.1%	(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
✓	4.0%	(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
	6.3%	(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) #s(literal 4 binary64))) (fma.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))))
	6.9%	(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))) #s(literal 2 binary64)) (pow.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))) (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
	6.2%	(/.f64 (-.f64 (pow.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))) (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
	7.7%	(/.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) #s(literal 3 binary64)) (pow.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (-.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))))) (pow.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) #s(literal 2 binary64))))
✓	0.0%	(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
	5.6%	(-.f64 (/.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (-.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (-.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
	6.2%	(-.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
	4.0%	(-.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))))
	7.5%	(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) x)))))
	7.7%	(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
	6.2%	(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))))) (/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))))
	6.4%	(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))))) (acos.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))))
✓	7.7%	(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
	7.8%	(+.f64 #s(approx (/ (- (pow (acos (sqrt (/ (- 1 x) 2))) 2) (pow (/ (PI) 2) 2)) (- (acos (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (/.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (PI.f64)) (PI.f64) (pow.f64 (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
	3.8%	(*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))
	3.8%	(*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
	6.2%	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (fma.f64 (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) (/.f64 #s(literal -8 binary64) (fma.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) (.f64 (PI.f64) #s(literal 1/2 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64))))) (/.f64 (.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) (.f64 (PI.f64) #s(literal 1/2 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)))))))
	7.8%	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64))))
	6.2%	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64))))
	7.7%	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 (pow.f64 (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 3/2 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))))
	6.2%	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 (pow.f64 (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))))
	6.2%	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -8 binary64)) (.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))))
	6.2%	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3/2 binary64)) (.f64 (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3/2 binary64)) #s(literal -8 binary64)) (.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))))
	6.4%	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 2 binary64)))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))))
	6.1%	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 9 binary64)))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))))
	7.8%	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)))) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))))
	2.6%	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (/.f64 (.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 4 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)))) (.f64 (PI.f64) #s(literal 1/2 binary64))) (fma.f64 #s(literal -2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) (*.f64 (PI.f64) #s(literal 1/2 binary64)))))))
	7.8%	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (PI.f64) (PI.f64)) (PI.f64)))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))))
	7.7%	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 (exp.f64 (.f64 (log.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))) #s(literal 3 binary64))) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))))
	7.7%	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 #s(literal -512 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 9 binary64)) (pow.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 9 binary64))) (.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 6 binary64)) (pow.f64 (.f64 (.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal -2 binary64)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))) #s(literal 3 binary64)))) (fma.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) (.f64 (PI.f64) #s(literal 1/2 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)))))))
	7.7%	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (-.f64 (.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) (PI.f64)))) (fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64) (.f64 #s(literal -1/2 binary64) (PI.f64)))))

Compiler

Compiled 4 359 to 1 300 computations (70.2% saved)

regimes134.0ms (1.1%)

Memory

2.5MiB live, 99.6MiB allocated

Counts

55 → 1

Calls

Call 1

Inputs
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
(*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (sqrt.f64 #s(literal 1/2 binary64))))))
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64))))
#s(approx (- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2))))) (fma.f64 #s(literal -2 binary64) (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 (PI.f64) #s(literal 1/2 binary64))))
(fma.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
(fma.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))))))
#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (fma.f64 #s(literal -2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))))
#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64))))
(-.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))))
(-.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
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#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)))) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))))
#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3/2 binary64)) (.f64 (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3/2 binary64)) #s(literal -8 binary64)) (.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64)))))))
#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) #s(literal -8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64) (/.f64 (.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) (PI.f64))) (.f64 #s(literal 4 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)))) (.f64 (PI.f64) #s(literal 1/2 binary64))) (fma.f64 #s(literal -2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) (*.f64 (PI.f64) #s(literal 1/2 binary64)))))))
(/.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) #s(literal 3 binary64)) (pow.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (-.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))))) (pow.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) #s(literal 2 binary64))))
#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (fma.f64 (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 3 binary64)) (/.f64 #s(literal -8 binary64) (fma.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) (.f64 (PI.f64) #s(literal 1/2 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64))))) (/.f64 (.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) (.f64 (PI.f64) #s(literal 1/2 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)))))))
(/.f64 (-.f64 (pow.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (*.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))))
#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 #s(literal -512 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 9 binary64)) (pow.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 9 binary64))) (.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal 6 binary64)) (pow.f64 (.f64 (.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) #s(literal -2 binary64)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))) #s(literal 3 binary64)))) (fma.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) (.f64 (PI.f64) #s(literal 1/2 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)))))))

Outputs

(+.f64 #s(approx (/ (- (pow (acos (sqrt (/ (- 1 x) 2))) 2) (pow (/ (PI) 2) 2)) (- (acos (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (/.f64 (fma.f64 (*.f64 #s(literal -1/4 binary64) (PI.f64)) (PI.f64) (pow.f64 (acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))

Calls

7 calls:

31.0ms	(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
14.0ms	x
11.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
10.0ms	(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
10.0ms	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))

Results

Accuracy	Segments	Branch
7.8%	1	`(-.f64 #s(literal 1 binary64) x)`
7.8%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))`
7.8%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))`
7.8%	1	`(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))`
7.8%	1	`(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))`
7.8%	1	`(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))`
7.8%	1	`x`

Compiler

Compiled 44 to 41 computations (6.8% saved)

regimes70.0ms (0.6%)

Memory

38.2MiB live, 84.7MiB allocated

Counts

30 → 1

Calls

Call 1

Inputs
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
(*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (sqrt.f64 #s(literal 1/2 binary64))))))
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64))))
#s(approx (- (/ (PI) 2) (* 2 (asin (sqrt (/ (- 1 x) 2))))) (fma.f64 #s(literal -2 binary64) (asin.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 (PI.f64) #s(literal 1/2 binary64))))
(fma.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
(fma.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))))))
#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (fma.f64 #s(literal -2 binary64) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64))))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))))
#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64))))
(-.f64 (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))))
(-.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))))))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) x)))))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(approx (- (asin (sqrt (/ (- 1 x) 2))) (/ (PI) -2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))))) (acos.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (-.f64 (.f64 (pow.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 (PI.f64) (PI.f64)))) (fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64) (.f64 #s(literal -1/2 binary64) (PI.f64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #s(literal 4 binary64))) (-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) #s(literal 4 binary64))) (fma.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))))

Outputs

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

Calls

7 calls:

29.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
8.0ms	x
6.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
6.0ms	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
6.0ms	(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))

Results

Accuracy	Segments	Branch
7.8%	1	`(-.f64 #s(literal 1 binary64) x)`
7.8%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))`
7.8%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))`
7.8%	1	`(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))`
7.8%	1	`(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))`
7.8%	1	`(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))`
7.8%	1	`x`

Compiler

Compiled 44 to 41 computations (6.8% saved)

regimes23.0ms (0.2%)

Memory

-7.6MiB live, 39.7MiB allocated

Counts

8 → 1

Calls

Call 1

Inputs
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
(*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (sqrt.f64 #s(literal 1/2 binary64))))))
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))

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

Calls

7 calls:

9.0ms	x
2.0ms	(-.f64 #s(literal 1 binary64) x)
2.0ms	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
2.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
2.0ms	(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))

Results

Accuracy	Segments	Branch
6.2%	1	`(-.f64 #s(literal 1 binary64) x)`
6.2%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))`
6.2%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))`
6.2%	1	`(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))`
6.2%	1	`(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))`
6.2%	1	`(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))`
6.2%	1	`x`

Compiler

Compiled 44 to 41 computations (6.8% saved)

regimes31.0ms (0.3%)

Memory

-16.7MiB live, 31.2MiB allocated

Counts

7 → 2

Calls

Call 1

Inputs
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))
(*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 #s(approx (sqrt (/ (- 1 x) 2)) (sqrt.f64 #s(literal 1/2 binary64))))))
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (*.f64 #s(literal -1/2 binary64) x)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64)))

Outputs

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

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

Calls

7 calls:

18.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
2.0ms	x
2.0ms	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
2.0ms	(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
2.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
5.8%	2	`x`
4.1%	1	`(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))`
4.1%	1	`(-.f64 #s(literal 1 binary64) x)`
4.1%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))`
4.1%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))`
4.1%	1	`(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))`
4.1%	1	`(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))`

Compiler

Compiled 44 to 41 computations (6.8% saved)

regimes8.0ms (0.1%)

Memory

27.9MiB live, 27.9MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))

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

Calls

7 calls:

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

Results

Accuracy	Segments	Branch
4.0%	1	`(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))`
4.0%	1	`(-.f64 #s(literal 1 binary64) x)`
4.0%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))`
4.0%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))`
4.0%	1	`(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))`
4.0%	1	`(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))`
4.0%	1	`x`

Compiler

Compiled 44 to 41 computations (6.8% saved)

regimes19.0ms (0.2%)

Memory

-14.2MiB live, 29.7MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))

Outputs
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))

Calls

7 calls:

13.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
1.0ms	x
1.0ms	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))
1.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
1.0ms	(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))

Results

Accuracy	Segments	Branch
0.0%	1	`(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))))`
0.0%	1	`x`
0.0%	1	`(-.f64 #s(literal 1 binary64) x)`
0.0%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))`
0.0%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))`
0.0%	1	`(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))`
0.0%	1	`(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))`

Compiler

Compiled 44 to 41 computations (6.8% saved)

bsearch102.0ms (0.8%)

Memory

10.3MiB live, 102.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
97.0ms	-2.039748644198372e-296	1.019124371982211e-307

Samples

89.0ms

160×

valid

Compiler

Compiled 296 to 315 computations (-6.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 82.0ms

ival-asin: 41.0ms (50.2% of total)

ival-sub: 17.0ms (20.8% of total)

ival-div: 7.0ms (8.6% of total)

adjust: 7.0ms (8.6% of total)

ival-sqrt: 4.0ms (4.9% of total)

ival-mult: 4.0ms (4.9% of total)

ival-pi: 2.0ms (2.5% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

simplify12.0ms (0.1%)

Memory

15.7MiB live, 15.7MiB allocated

Algorithm

1×	egg-herbie

Stop Event

1×	iter limit
1×	unsound

Calls

Call 1

Inputs
(+.f64 #s(approx (/ (- (pow (acos (sqrt (/ (- 1 x) 2))) 2) (pow (/ (PI) 2) 2)) (- (acos (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (/.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (PI.f64)) (PI.f64) (pow.f64 (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64))))
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
(if (<=.f64 x #s(literal -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 binary64)) (fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64))))
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))

Outputs
(+.f64 #s(approx (/ (- (pow (acos (sqrt (/ (- 1 x) 2))) 2) (pow (/ (PI) 2) 2)) (- (acos (sqrt (/ (- 1 x) 2))) (/ (PI) -2))) (/.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (PI.f64)) (PI.f64) (pow.f64 (acos.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))))) (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64))))
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
(if (<=.f64 x #s(literal -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 binary64)) (fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64) (/.f64 (PI.f64) #s(literal -2 binary64))))
(fma.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))

soundness1.5s (12.6%)

Memory

7.8MiB live, 1 075.9MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	1054
1	464	1015
2	1664	993
3	6434	991
0	8113	943
0	50	333
0	87	312
1	304	304
2	2275	304
0	9609	302
0	125	612
1	366	572
2	1334	550
3	5565	547
0	8150	523
0	11	39
0	19	35
1	81	35
2	513	23
3	6339	23
0	8483	23

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit

Compiler

Compiled 614 to 328 computations (46.6% saved)

preprocess49.0ms (0.4%)

Memory: -30.0MiB live, 94.9MiB allocated
Compiler: Compiled 356 to 156 computations (56.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	13	29
1	26	29
2	39	26
3	56	26
4	71	26
5	80	26
6	84	26
0	11	13
0	19	13
1	32	13
2	40	13
3	48	13
4	57	13
5	61	13
6	62	13
0	62	12

Iter	Nodes	Cost
0	13	29
1	26	29
2	39	26
3	56	26
4	71	26
5	80	26
6	84	26
0	11	13
0	19	13
1	32	13
2	40	13
3	48	13
4	57	13
5	61	13
6	62	13
0	62	12

start0.0ms (0%)

analyze4.0ms (0%)

sample4.7s (38.9%)

explain403.0ms (3.3%)

preprocess37.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify5.0ms (0%)

localize177.0ms (1.5%)

series27.0ms (0.2%)

simplify166.0ms (1.4%)

rewrite479.0ms (3.9%)

eval218.0ms (1.8%)

prune81.0ms (0.7%)

simplify7.0ms (0.1%)

localize78.0ms (0.6%)

series9.0ms (0.1%)

simplify214.0ms (1.8%)

rewrite40.0ms (0.3%)

eval38.0ms (0.3%)

prune46.0ms (0.4%)

simplify243.0ms (2%)

localize453.0ms (3.7%)

series6.0ms (0.1%)

simplify191.0ms (1.6%)

rewrite264.0ms (2.2%)

eval206.0ms (1.7%)

prune69.0ms (0.6%)

simplify167.0ms (1.4%)

localize751.0ms (6.2%)

series31.0ms (0.3%)

simplify207.0ms (1.7%)

rewrite287.0ms (2.4%)

eval408.0ms (3.3%)

prune146.0ms (1.2%)

regimes134.0ms (1.1%)

regimes70.0ms (0.6%)

regimes23.0ms (0.2%)

regimes31.0ms (0.3%)

regimes8.0ms (0.1%)

regimes19.0ms (0.2%)

bsearch102.0ms (0.8%)

simplify12.0ms (0.1%)

soundness1.5s (12.6%)

preprocess49.0ms (0.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	13	29
1	26	29
2	39	26
3	56	26
4	71	26
5	80	26
6	84	26
0	11	13
0	19	13
1	32	13
2	40	13
3	48	13
4	57	13
5	61	13
6	62	13
0	62	12