Metrics for Ian Simplification

start0.0ms (0%)

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

analyze4.0ms (0%)

Memory

4.8MiB live, 4.8MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 15 to 13 computations (13.3% saved)

sample4.6s (40.4%)

Memory

-158.5MiB live, 4 644.1MiB allocated; 2.3s collecting garbage

Samples

2.2s	4 740×	1	valid
1.8s	3 381×	2	valid
11.0ms	135×	0	valid
0.0ms	5×	0	invalid

Precisions

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

ival-asin: 1.9s (52.3% of total)

adjust: 462.0ms (12.5% of total)

ival-div: 330.0ms (8.9% of total)

ival-mult: 313.0ms (8.4% of total)

ival-sqrt: 288.0ms (7.8% of total)

ival-sub: 251.0ms (6.8% of total)

ival-pi: 105.0ms (2.8% of total)

exact: 10.0ms (0.3% of total)

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

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

Bogosity

explain330.0ms (2.9%)

Memory

5.7MiB live, 266.5MiB allocated; 30ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
255	-	-	`(-.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	255	0

Confusion

	Predicted +	Predicted -
+	255	0
-	0	1

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	255	0	0
-	0	0	1

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	1
1	255

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

140.0ms	230×	2	valid
100.0ms	276×	1	valid
1.0ms	6×	0	valid

Compiler

Compiled 117 to 37 computations (68.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 181.0ms

ival-asin: 62.0ms (34.2% of total)

ival-div: 59.0ms (32.5% of total)

adjust: 20.0ms (11% of total)

ival-sqrt: 11.0ms (6.1% of total)

ival-sub: 11.0ms (6.1% of total)

ival-mult: 9.0ms (5% of total)

ival-pi: 8.0ms (4.4% of total)

exact: 1.0ms (0.6% of total)

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

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

preprocess79.0ms (0.7%)

Memory

-24.2MiB live, 20.5MiB allocated; 7ms collecting garbage

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: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	5.7%	(-.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

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

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

localize128.0ms (1.1%)

Memory

24.4MiB live, 70.4MiB allocated; 4ms collecting garbage

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	0.9765625	(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
accuracy	58.97926763145954	(-.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

81.0ms	115×	2	valid
35.0ms	138×	1	valid
0.0ms	3×	0	valid

Compiler

Compiled 52 to 13 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 100.0ms

ival-sqrt: 38.0ms (38% of total)

ival-asin: 31.0ms (31% of total)

adjust: 10.0ms (10% of total)

ival-div: 8.0ms (8% of total)

ival-sub: 5.0ms (5% of total)

ival-mult: 4.0ms (4% of total)

ival-pi: 3.0ms (3% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0%)

Memory

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

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
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)))
1.0ms	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)))

Time

Variable

Point

Expression

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)))

1.0ms

((- (/ (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)))

simplify251.0ms (2.2%)

Memory

-17.0MiB live, 168.2MiB allocated; 25ms collecting garbage

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))))))))

rewrite372.0ms (3.3%)

Memory

29.9MiB live, 363.1MiB allocated; 32ms collecting garbage

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))))))

eval193.0ms (1.7%)

Memory: -44.2MiB live, 356.4MiB allocated; 89ms collecting garbage
Compiler: Compiled 38 880 to 3 030 computations (92.2% saved)

prune125.0ms (1.1%)

Memory

-13.2MiB live, 180.8MiB allocated; 32ms collecting garbage

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	2 080	13	2 093
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	2 081	13	2 094

Accuracy

9.1%

Counts

2 094 → 13

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)))
	5.7%	(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)))
	5.7%	(/.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))))))
	5.6%	(/.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))
	5.6%	(-.f64 (/.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.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%	(-.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)))))))
▶	3.9%	(-.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))))))
	5.7%	(-.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)))))
▶	7.8%	(+.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))
	3.6%	(*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
	5.6%	#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 472 to 322 computations (31.8% saved)

simplify7.0ms (0.1%)

Memory

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

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))))

localize87.0ms (0.8%)

Memory

2.9MiB live, 142.8MiB allocated; 21ms collecting garbage

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

63.0ms

256×

invalid

Compiler

Compiled 248 to 28 computations (88.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-mult: 8.0ms (22.1% of total)

ival-div: 6.0ms (16.6% of total)

ival-sub: 6.0ms (16.6% of total)

ival-acos: 4.0ms (11% of total)

ival-asin: 3.0ms (8.3% of total)

ival-sqrt: 3.0ms (8.3% of total)

ival-add: 2.0ms (5.5% of total)

ival-pi: 1.0ms (2.8% of total)

exact: 1.0ms (2.8% of total)

adjust: 0.0ms (0% of total)

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

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

series7.0ms (0.1%)

Memory

13.6MiB live, 13.6MiB allocated; 0ms collecting garbage

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
2.0ms	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

2.0ms

((- (/ (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))

simplify220.0ms (1.9%)

Memory

9.7MiB live, 254.7MiB allocated; 41ms collecting garbage

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)))

rewrite15.0ms (0.1%)

Memory

-18.8MiB live, 27.1MiB allocated; 3ms collecting garbage

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)

eval16.0ms (0.1%)

Memory: -3.8MiB live, 41.2MiB allocated; 4ms collecting garbage
Compiler: Compiled 3 941 to 419 computations (89.4% saved)

prune18.0ms (0.2%)

Memory

-16.4MiB live, 41.0MiB allocated; 7ms collecting garbage

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	129	7	136
Fresh	1	7	8
Picked	3	2	5
Done	0	0	0
Total	133	16	149

Accuracy

9.1%

Counts

149 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	5.7%	(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)))
▶	2.4%	(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)))
▶	4.0%	(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)))
	5.7%	(/.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))))))
	5.6%	(/.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))
▶	5.8%	(-.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 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))))))
✓	3.9%	(-.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))))))
	5.7%	(-.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)))))
	7.8%	(+.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))))))
	7.4%	(+.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)))))
▶	7.1%	(+.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)))))
	3.8%	(*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))
	3.6%	(*.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 #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))))
	5.6%	#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 663 to 490 computations (26.1% saved)

simplify197.0ms (1.7%)

Memory

13.7MiB live, 333.7MiB allocated; 41ms collecting garbage

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)

localize452.0ms (4%)

Memory

49.8MiB live, 747.2MiB allocated; 98ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.028007519536884032	(-.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	0.415560418892717	#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	0.9765625	(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	58.95601425116112	(+.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	0.01171875	(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))))
accuracy	0.015625	(acos.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))))
accuracy	0.8905221936718313	#s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))
accuracy	58.97926763145954	(-.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	0.9765625	(asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) (*.f64 #s(literal -1/2 binary64) x))))
accuracy	58.97926763145954	(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	61.690744035441064	#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	0.8905221936718313	#s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))
accuracy	0.9765625	(asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))))
accuracy	58.97926763145954	(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	0.01171875	(-.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	0.015625	(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	0.015625	(acos.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))))
accuracy	58.97926763145954	(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

194.0ms	115×	2	valid
166.0ms	138×	1	valid
1.0ms	3×	0	valid

Compiler

Compiled 337 to 35 computations (89.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 293.0ms

ival-acos: 65.0ms (22.2% of total)

ival-asin: 63.0ms (21.5% of total)

ival-mult: 44.0ms (15% of total)

adjust: 43.0ms (14.7% of total)

ival-sub: 23.0ms (7.8% of total)

ival-div: 15.0ms (5.1% of total)

ival-sqrt: 15.0ms (5.1% of total)

ival-pi: 14.0ms (4.8% of total)

ival-add: 9.0ms (3.1% of total)

exact: 1.0ms (0.3% of total)

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

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

series6.0ms (0.1%)

Memory

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

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

simplify232.0ms (2%)

Memory

-26.6MiB live, 207.8MiB allocated; 60ms collecting garbage

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))))

rewrite356.0ms (3.1%)

Memory

7.6MiB live, 203.9MiB allocated; 51ms collecting garbage

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

eval217.0ms (1.9%)

Memory: 7.3MiB live, 192.5MiB allocated; 30ms collecting garbage
Compiler: Compiled 38 217 to 2 881 computations (92.5% saved)

prune54.0ms (0.5%)

Memory

19.3MiB live, 77.0MiB allocated; 8ms collecting garbage

Pruning

22 alts after pruning (18 fresh and 4 done)

	Pruned	Kept	Total
New	845	10	855
Fresh	1	8	9
Picked	2	3	5
Done	1	1	2
Total	849	22	871

Accuracy

9.2%

Counts

871 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	5.7%	(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)))
✓	2.4%	(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)))
✓	4.0%	(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)))
▶	3.9%	(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)))
	7.2%	(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 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 3 binary64))) (+.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (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))))))))))
	7.2%	(/.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))))))))
	4.0%	(/.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))))
	5.7%	(/.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))))))
	5.6%	(/.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))
	5.7%	(-.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)))))
	3.9%	(-.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)))))
▶	4.0%	(+.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)))))
	7.4%	(+.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)))))
	7.8%	(+.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)))))
▶	7.2%	(+.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)))))
	3.8%	(*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))
	3.6%	(*.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))))
	5.6%	#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)))))) (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))))
	5.6%	#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 1 276 to 767 computations (39.9% saved)

simplify234.0ms (2.1%)

Memory

-4.3MiB live, 184.2MiB allocated; 16ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(*.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))
cost-diff	0	(/.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))))
cost-diff	2	(*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal -2 binary64)))
cost-diff	11	(+.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)))))
cost-diff	0	(/.f64 (PI.f64) #s(literal -2 binary64))
cost-diff	0	(+.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))))))
cost-diff	0	(+.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)))))
cost-diff	1	(/.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	1	(/.f64 (-.f64 #s(literal 1 binary64) x) #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 (.f64 #s(literal 1/2 binary64) (PI.f64)) (acos.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
cost-diff	0	#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))))
cost-diff	1	(*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
cost-diff	4	(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)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	492
0	90	476
1	134	476
2	230	470
3	457	470
4	988	470
5	1900	466
6	3626	460
7	6958	460
0	8099	421

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

localize514.0ms (4.5%)

Memory

-16.8MiB live, 335.4MiB allocated; 103ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.015625	(pow.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
accuracy	0.8905221936718313	#s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))
accuracy	0.9765625	(asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))))
accuracy	58.964276385169796	(+.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)))))
accuracy	0.015625	(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)))))
accuracy	0.01953125	(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	0.415560418892717	#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	58.95601425116112	(+.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)))))
accuracy	0.0	(PI.f64)
accuracy	0.00390625	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
accuracy	0.9765625	(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
accuracy	58.97926763145954	(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	0.8905221936718313	#s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))
accuracy	0.9765625	(asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64))))
accuracy	58.97926763145954	(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	0.00390625	(sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
accuracy	0.01171875	(-.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)))))
accuracy	0.015625	(acos.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
accuracy	58.97926763145954	(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)))

Samples

241.0ms	138×	1	valid
226.0ms	115×	2	valid
1.0ms	3×	0	valid

Compiler

Compiled 416 to 43 computations (89.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 372.0ms

adjust: 107.0ms (28.8% of total)

ival-acos: 104.0ms (27.9% of total)

ival-mult: 33.0ms (8.9% of total)

ival-add: 30.0ms (8.1% of total)

ival-asin: 28.0ms (7.5% of total)

ival-sqrt: 26.0ms (7% of total)

ival-div: 20.0ms (5.4% of total)

ival-sub: 14.0ms (3.8% of total)

ival-pow2: 6.0ms (1.6% of total)

ival-pi: 3.0ms (0.8% of total)

exact: 1.0ms (0.3% of total)

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

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

series20.0ms (0.2%)

Memory

7.2MiB live, 7.2MiB allocated; 0ms collecting garbage

Counts

26 → 44

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

8.0ms

-inf

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

6.0ms

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

5.0ms

inf

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

simplify211.0ms (1.9%)

Memory

-21.8MiB live, 163.5MiB allocated; 24ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	151	782
1	431	721
2	1513	705
3	5998	696
0	8585	660

Stop Event

1×	iter limit
1×	node limit

Counts

44 → 44

Calls

Call 1

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

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

rewrite301.0ms (2.6%)

Memory

18.3MiB live, 505.2MiB allocated; 70ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	346
0	90	321
1	320	301
2	2479	301
0	9718	300

Stop Event

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

Counts

26 → 568

Calls

Call 1

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

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

eval187.0ms (1.6%)

Memory: 17.7MiB live, 341.7MiB allocated; 44ms collecting garbage
Compiler: Compiled 64 111 to 3 746 computations (94.2% saved)

prune74.0ms (0.6%)

Memory

-5.8MiB live, 185.3MiB allocated; 23ms collecting garbage

Pruning

31 alts after pruning (25 fresh and 6 done)

	Pruned	Kept	Total
New	1 101	16	1 117
Fresh	4	9	13
Picked	2	3	5
Done	1	3	4
Total	1 108	31	1 139

Accuracy

9.3%

Counts

1 139 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	4.0%	(fma.f64 (/.f64 (.f64 #s(literal 4 binary64) (pow.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 8 binary64) (pow.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (pow.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) #s(literal 3 binary64)))) (fma.f64 #s(literal 4 binary64) (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)) (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 (.f64 (PI.f64) (/.f64 (PI.f64) #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)))))
	5.2%	(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal -2 binary64)) (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))))))
✓	5.7%	(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)))
✓	2.4%	(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)))
✓	4.0%	(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)))
✓	3.9%	(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)))
	5.0%	(fma.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))))) #s(literal -2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))
	5.1%	(/.f64 (fma.f64 (pow.f64 (+.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))) (/.f64 (PI.f64) #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 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (pow.f64 (+.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64))) #s(literal 2 binary64))) (.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 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (pow.f64 (+.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 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 3 binary64)))) (.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 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (pow.f64 (+.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64))) #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 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (pow.f64 (+.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64))) #s(literal 2 binary64)))))
	5.7%	(/.f64 (fma.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 (PI.f64) (/.f64 (PI.f64) #s(literal -4 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))))
	5.0%	(/.f64 (fma.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)) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 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))))) (-.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 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 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))))) (-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))))))
	5.0%	(/.f64 (fma.f64 (+.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))) #s(literal 3 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) #s(literal 3 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 (fma.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))) (-.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 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) (+.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 (fma.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))) (-.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 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 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))))))
	7.8%	(/.f64 (fma.f64 (.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 2 binary64)))) #s(literal 2 binary64))) #s(literal -2 binary64)) #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))) (PI.f64))) (*.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(literal 2 binary64)))
	5.6%	(/.f64 (fma.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 (-.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))) #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)))))
	7.2%	(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 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 3 binary64))) (+.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (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))))))))))
	7.1%	(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) #s(literal 2 binary64)) (pow.f64 (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))))) #s(literal 2 binary64))) (-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))))))
	5.7%	(/.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))))))
	5.6%	(/.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)))))
	7.2%	(/.f64 (+.f64 (pow.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) #s(literal 3 binary64)) (pow.f64 (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))))) #s(literal 2 binary64)) (.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))))))))
✓	0.0%	(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
	5.7%	(-.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)))))
	3.9%	(-.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)))))
	7.8%	(+.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)))))
	5.2%	(+.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 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))))
✓	7.2%	(+.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)))))
	3.8%	(*.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) #s(literal 2 binary64))
	3.6%	(*.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 #s(approx ( (- 1 x) 1/2) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)))))) #s(literal -2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64))))
	5.8%	#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 #s(approx ( (- 1 x) 1/2) #s(literal 1/2 binary64))))) #s(literal -2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64))))
	5.6%	#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))))
	5.7%	#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 (.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)) #s(literal -8 binary64)) (fma.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (-.f64 (.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 (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 4 binary64))) (.f64 (fma.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (-.f64 (.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 (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 4 binary64))) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64))))) (.f64 (fma.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (-.f64 (.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 (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 4 binary64))) (fma.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (-.f64 (.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 (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 4 binary64))))))
	7.8%	#s(approx (+ (+ (/ (PI) -2) (acos (sqrt (/ (- 1 x) 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 #s(literal -1/2 binary64) (PI.f64))))

Compiler

Compiled 3 746 to 959 computations (74.4% saved)

regimes87.0ms (0.8%)

Memory

3.6MiB live, 142.7MiB allocated; 12ms collecting garbage

Counts

47 → 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)))
#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 #s(approx ( (- 1 x) 1/2) #s(literal 1/2 binary64))))) #s(literal -2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64))))
(*.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)))
#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 #s(approx ( (- 1 x) 1/2) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)))))) #s(literal -2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64))))
#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 #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 (PI.f64) #s(literal 2 binary64)))
#s(approx (+ (+ (/ (PI) -2) (acos (sqrt (/ (- 1 x) 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 #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) (-.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 (/.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.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 (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)) (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)))))
(+.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)) (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 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 #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 (/.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)))))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal -2 binary64)) (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))))))
(/.f64 (fma.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 (PI.f64) (/.f64 (PI.f64) #s(literal -4 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))))
(/.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 (.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)))))
(/.f64 (fma.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 (-.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))) #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 (fma.f64 (.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 2 binary64)))) #s(literal 2 binary64))) #s(literal -2 binary64)) #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))) (PI.f64))) (*.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(literal 2 binary64)))
(/.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)))))
(/.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))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) #s(literal 2 binary64)) (pow.f64 (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))))) #s(literal 2 binary64))) (-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))))))
(/.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))))))))
(fma.f64 (/.f64 (.f64 #s(literal 4 binary64) (pow.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 8 binary64) (pow.f64 (asin.f64 (sqrt.f64 #s(approx (/ (- 1 x) 2) #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (pow.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) #s(literal 3 binary64)))) (fma.f64 #s(literal 4 binary64) (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)) (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 (.f64 (PI.f64) (/.f64 (PI.f64) #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 (pow.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) #s(literal 3 binary64)) (pow.f64 (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))))) #s(literal 2 binary64)) (.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (+.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 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 3 binary64))) (+.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (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))))))))))
(/.f64 (fma.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)) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 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))))) (-.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 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 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))))) (-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))))))
(/.f64 (fma.f64 (+.f64 (pow.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))) #s(literal 3 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) #s(literal 3 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 (fma.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))) (-.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 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) (+.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 (fma.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))) (-.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 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 (acos.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))))))
#s(approx (- (/ (PI) 2) (* 2 (- (/ (PI) 2) (acos (sqrt (/ (- 1 x) 2)))))) (/.f64 (fma.f64 (.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)) #s(literal -8 binary64)) (fma.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (-.f64 (.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 (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 4 binary64))) (.f64 (fma.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (-.f64 (.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 (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 4 binary64))) (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64))))) (.f64 (fma.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (-.f64 (.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 (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 4 binary64))) (fma.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (-.f64 (.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 (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 4 binary64))))))
(/.f64 (fma.f64 (pow.f64 (+.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))) (/.f64 (PI.f64) #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 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (pow.f64 (+.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64))) #s(literal 2 binary64))) (.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 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (pow.f64 (+.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 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 3 binary64)))) (.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 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (pow.f64 (+.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64))) #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 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64)))) (pow.f64 (+.f64 (acos.f64 #s(approx (sqrt (/ (- 1 x) 2)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))) (/.f64 (PI.f64) #s(literal -2 binary64))) #s(literal 2 binary64)))))

Outputs

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

Calls

7 calls:

20.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
15.0ms	x
11.0ms	(-.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))))))
9.0ms	(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
9.0ms	(*.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)

regimes46.0ms (0.4%)

Memory

-27.0MiB live, 36.2MiB allocated; 9ms collecting garbage

Counts

11 → 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)))
#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 #s(approx ( (- 1 x) 1/2) #s(literal 1/2 binary64))))) #s(literal -2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64))))
(*.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)))
#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 #s(approx ( (- 1 x) 1/2) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)))))) #s(literal -2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64))))
#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 #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 (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 #s(approx (* (- 1 x) 1/2) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)))))) #s(literal -2 binary64) (*.f64 #s(literal 1/2 binary64) (PI.f64))))

Calls

7 calls:

28.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
3.0ms	x
3.0ms	(-.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))))))
3.0ms	(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
3.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
7.8%	1	`x`
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))))))`

Compiler

Compiled 44 to 41 computations (6.8% saved)

regimes42.0ms (0.4%)

Memory

-12.8MiB live, 34.8MiB allocated; 2ms collecting garbage

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

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

Calls

7 calls:

28.0ms	(-.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))))))
3.0ms	x
2.0ms	(*.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 1 binary64) x)
2.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))

Results

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

regimes9.0ms (0.1%)

Memory

22.3MiB live, 22.3MiB allocated; 0ms collecting garbage

Counts

3 → 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)))

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:

2.0ms	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	(asin.f64 (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)))))
1.0ms	(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
4.0%	1	`x`
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	`(-.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 44 to 41 computations (6.8% saved)

regimes51.0ms (0.4%)

Memory

-26.5MiB live, 20.3MiB allocated; 3ms collecting garbage

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:

43.0ms	(/.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	(-.f64 #s(literal 1 binary64) x)
1.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
3.9%	1	`(-.f64 #s(literal 1 binary64) x)`
3.9%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))`
3.9%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))`
3.9%	1	`(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))`
3.9%	1	`(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))`
3.9%	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))))))`
3.9%	1	`x`

Compiler

Compiled 44 to 41 computations (6.8% saved)

regimes6.0ms (0.1%)

Memory

16.4MiB live, 16.4MiB allocated; 0ms collecting garbage

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:

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	(*.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	(/.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	`(-.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)))))`
0.0%	1	`x`

Compiler

Compiled 44 to 41 computations (6.8% saved)

simplify12.0ms (0.1%)

Memory

25.6MiB live, 25.6MiB allocated; 0ms collecting garbage

Stop Event

1×	iter limit
1×	unsound

Calls

Call 1

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

derivations1.6s (13.7%)

Memory

-26.5MiB live, 691.7MiB allocated; 104ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	50	333
0	87	312
1	304	304
2	2275	304
0	9609	302
0	11	39
0	19	35
1	81	35
2	513	23
3	6339	23
0	8483	23
0	151	782
1	431	721
2	1513	705
3	5998	696
0	8585	660
0	125	612
1	366	572
2	1334	550
3	5565	547
0	8150	523

Stop Event

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

Compiler

Compiled 139 to 55 computations (60.4% saved)

preprocess50.0ms (0.4%)

Memory: 12.5MiB live, 58.3MiB allocated; 5ms collecting garbage
Compiler: Compiled 308 to 136 computations (55.8% saved)

end0.0ms (0%)

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

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%)

sample4.6s (40.4%)

explain330.0ms (2.9%)

preprocess79.0ms (0.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify5.0ms (0%)

localize128.0ms (1.1%)

series5.0ms (0%)

simplify251.0ms (2.2%)

rewrite372.0ms (3.3%)

eval193.0ms (1.7%)

prune125.0ms (1.1%)

simplify7.0ms (0.1%)

localize87.0ms (0.8%)

series7.0ms (0.1%)

simplify220.0ms (1.9%)

rewrite15.0ms (0.1%)

eval16.0ms (0.1%)

prune18.0ms (0.2%)

simplify197.0ms (1.7%)

localize452.0ms (4%)

series6.0ms (0.1%)

simplify232.0ms (2%)

rewrite356.0ms (3.1%)

eval217.0ms (1.9%)

prune54.0ms (0.5%)

simplify234.0ms (2.1%)

localize514.0ms (4.5%)

series20.0ms (0.2%)

simplify211.0ms (1.9%)

rewrite301.0ms (2.6%)

eval187.0ms (1.6%)

prune74.0ms (0.6%)

regimes87.0ms (0.8%)

regimes46.0ms (0.4%)

regimes42.0ms (0.4%)

regimes9.0ms (0.1%)

regimes51.0ms (0.4%)

regimes6.0ms (0.1%)

simplify12.0ms (0.1%)

derivations1.6s (13.7%)

preprocess50.0ms (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