Metrics for arccos

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze15.0ms (0.4%)

Memory

-29.9MiB live, 10.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.1s (27.6%)

Memory

-23.0MiB live, 1 318.7MiB allocated

Samples

572.0ms	8 256×	0	valid
1.0ms	22×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 411.0ms

ival-add: 84.0ms (20.4% of total)

ival-atan: 78.0ms (19% of total)

ival-sqrt: 74.0ms (18% of total)

ival-div: 56.0ms (13.6% of total)

ival-mult: 55.0ms (13.4% of total)

ival-sub: 49.0ms (11.9% of total)

exact: 7.0ms (1.7% of total)

ival-true: 6.0ms (1.5% of total)

ival-assert: 3.0ms (0.7% of total)

Bogosity

explain92.0ms (2.2%)

Memory

37.9MiB live, 196.0MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

37.0ms

512×

valid

Compiler

Compiled 103 to 31 computations (69.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-div: 5.0ms (21% of total)

ival-atan: 5.0ms (21% of total)

ival-mult: 4.0ms (16.8% of total)

ival-sqrt: 4.0ms (16.8% of total)

ival-add: 3.0ms (12.6% of total)

ival-sub: 3.0ms (12.6% of total)

exact: 1.0ms (4.2% of total)

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

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

preprocess34.0ms (0.8%)

Memory

-18.4MiB live, 55.4MiB allocated

Algorithm

1×	egg-herbie

Rules

208×	`lower-fma.f64`
208×	`lower-fma.f32`
132×	`lower-*.f32`
130×	`lower-*.f64`
84×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	31	22
2	59	22
3	108	22
4	180	22
5	350	22
6	620	22
7	647	22
0	9	11
0	15	11
1	24	11
2	30	11
3	41	11
4	64	11
5	98	11
6	135	11
7	208	11
8	330	11
9	498	11
10	529	11
0	529	11

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Compiler

Compiled 11 to 9 computations (18.2% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 11 to 9 computations (18.2% saved)

simplify13.0ms (0.3%)

Memory

24.7MiB live, 24.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

208×	`lower-fma.f64`
208×	`lower-fma.f32`
132×	`lower-*.f32`
130×	`lower-*.f64`
74×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	44
0	15	44
1	24	44
2	30	44
3	41	44
4	64	44
5	98	44
6	135	44
7	208	44
8	330	44
9	498	44
10	529	44
0	529	44

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize35.0ms (0.9%)

Memory

-23.2MiB live, 54.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
accuracy	0.0078125	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
accuracy	0.0078125	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
accuracy	0.01953125	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))

Samples

29.0ms

256×

valid

Compiler

Compiled 46 to 11 computations (76.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-sub: 7.0ms (45.1% of total)

ival-div: 2.0ms (12.9% of total)

ival-mult: 2.0ms (12.9% of total)

ival-atan: 2.0ms (12.9% of total)

ival-sqrt: 2.0ms (12.9% of total)

ival-add: 1.0ms (6.4% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

9.3MiB live, 9.3MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#s(alt (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())
#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())

Outputs
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* 1/2 x) 1))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 x)) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* 2 x) 2))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (+ 2 (* -2 x))) 2))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor inf x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor inf x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor inf x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor inf x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1))))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ 1 x)) 1) (taylor inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2)))) (taylor inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2)))) (taylor inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (patch (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ 1 x)) 1) (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1) (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1) (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify129.0ms (3.2%)

Memory

9.0MiB live, 159.8MiB allocated

Algorithm

1×	egg-herbie

Rules

10 954×	`lower-fma.f64`
10 954×	`lower-fma.f32`
2 906×	`lower-*.f64`
2 906×	`lower-*.f32`
1 802×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	541
1	276	480
2	764	466
3	2111	454
4	6112	448
0	8073	437

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
1
(+ 1 (* -2 x))
(+ 1 (* x (- (* 2 x) 2)))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
-1
(- (* 2 (/ 1 x)) 1)
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
-1
(- (* 2 (/ 1 x)) 1)
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)

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

rewrite103.0ms (2.5%)

Memory

8.5MiB live, 126.2MiB allocated

Rules

2 152×	`lower-fma.f64`
2 152×	`lower-fma.f32`
2 042×	`lower-*.f32`
2 040×	`lower-*.f64`
1 870×	`lower-/.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	35
0	15	36
1	52	36
2	339	36
3	4589	8
0	9824	8

Stop Event

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

Counts

4 → 7

Calls

Call 1

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

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

eval8.0ms (0.2%)

Memory: -24.1MiB live, 13.0MiB allocated
Compiler: Compiled 642 to 135 computations (79% saved)

prune6.0ms (0.2%)

Memory

16.9MiB live, 16.9MiB allocated

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	50	5	55
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	50	6	56

Accuracy

100.0%

Counts

56 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	96.8%	(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
✓	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
▶	98.9%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))))))
▶	99.0%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
▶	98.5%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
▶	97.9%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))

Compiler

Compiled 113 to 99 computations (12.4% saved)

simplify326.0ms (8%)

Memory

-11.2MiB live, 147.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Rules

6 240×	`lower-fma.f32`
6 224×	`lower-fma.f64`
1 596×	`lower-*.f32`
1 586×	`lower-*.f64`
968×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	314
0	63	314
1	92	314
2	130	314
3	281	314
4	542	314
5	861	314
6	1402	314
7	2343	314
8	2893	314
9	3457	314
10	4043	314
11	4537	314
12	4781	314
13	4834	314
14	4837	314
15	4837	314
16	4892	314
17	4894	314
18	4894	314
19	5002	314
20	5046	314
21	5046	314
0	5046	314

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize78.0ms (1.9%)

Memory

15.2MiB live, 127.2MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))))))
accuracy	0.0078125	(sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))))
accuracy	0.0078125	(atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64)))))
accuracy	0.7549595756848588	#s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64)))
accuracy	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
accuracy	0	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
accuracy	0.0078125	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
accuracy	0.9685507489038586	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
accuracy	0	(-.f64 #s(literal 1 binary64) x)
accuracy	0	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
accuracy	0.0078125	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
accuracy	1.3801210699656263	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
accuracy	0	(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
accuracy	0	(atan.f64 #s(literal 1 binary64))
accuracy	0	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
accuracy	0.006191259768442017	(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
accuracy	0.0078125	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
accuracy	0.6415350408272179	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))

Samples

51.0ms

256×

valid

Compiler

Compiled 218 to 33 computations (84.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-mult: 14.0ms (40.1% of total)

ival-add: 10.0ms (28.6% of total)

ival-sqrt: 4.0ms (11.5% of total)

ival-atan: 3.0ms (8.6% of total)

ival-div: 2.0ms (5.7% of total)

ival-sub: 2.0ms (5.7% of total)

exact: 1.0ms (2.9% of total)

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

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

series11.0ms (0.3%)

Memory

21.1MiB live, 21.1MiB allocated

Counts

19 → 204

Calls

Call 1

Inputs
#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64)) (patch (.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (atan.f64 #s(literal 1 binary64)) (patch (atan.f64 #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())
#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64)))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64)))))) #<representation binary64>) () ())
#s(alt (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))))) (patch (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64)))) (patch (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* 1/2 x) 1))) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* 1/2 x) 1))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* 1/2 x) 1))) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* 1/2 x) 1))) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64)))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64)))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64)))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))))) (patch (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))))) (patch (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))))) (patch (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))))) (patch (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64)))) (patch (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64)))) (patch (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64)))) (patch (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64)))) (patch (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor -inf x) (#s(alt #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ 1 x)) 1) (taylor -inf x) (#s(alt #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1) (taylor -inf x) (#s(alt #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1) (taylor -inf x) (#s(alt #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 1/2))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 1/2))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 1/2))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

-inf

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

1.0ms

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

simplify303.0ms (7.4%)

Memory

4.1MiB live, 215.7MiB allocated

Algorithm

1×	egg-herbie

Rules

12 140×	`lower-fma.f64`
12 140×	`lower-fma.f32`
3 838×	`lower-*.f64`
3 838×	`lower-*.f32`
2 538×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	149	2172
1	410	1920
2	1267	1884
3	4228	1840
0	8166	1772

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* 1/2 x) 1)))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
1
(+ 1 (* -2 x))
(+ 1 (* x (- (* 2 x) 2)))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
-1
(- (* 1/2 x) 1)
(- (* 1/2 x) 1)
(- (* 1/2 x) 1)
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
-1
(- (* 2 (/ 1 x)) 1)
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
(* 1/2 x)
(* x (- 1/2 (/ 1 x)))
(* x (- 1/2 (/ 1 x)))
(* x (- 1/2 (/ 1 x)))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(* -1/2 (pow x 3))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
-1
(- (* 2 (/ 1 x)) 1)
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)
(* 1/2 x)
(* -1 (* x (- (/ 1 x) 1/2)))
(* -1 (* x (- (/ 1 x) 1/2)))
(* -1 (* x (- (/ 1 x) 1/2)))

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

rewrite266.0ms (6.5%)

Memory

-0.3MiB live, 349.6MiB allocated

Rules

6 674×	`lower-fma.f32`
6 658×	`lower-fma.f64`
4 364×	`lower-/.f64`
4 364×	`lower-/.f32`
3 496×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	262
0	63	262
1	213	262
2	1464	262
0	8381	262

Stop Event

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

Counts

19 → 191

Calls

Call 1

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

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

eval64.0ms (1.6%)

Memory: -2.4MiB live, 80.1MiB allocated
Compiler: Compiled 7 301 to 1 172 computations (83.9% saved)

prune74.0ms (1.8%)

Memory

-11.3MiB live, 25.7MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	394	1	395
Fresh	0	0	0
Picked	0	5	5
Done	0	1	1
Total	394	7	401

Accuracy

100.0%

Counts

401 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	96.8%	(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
✓	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
✓	98.9%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))))))
✓	99.0%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
✓	98.5%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
✓	97.9%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
▶	4.3%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))))

Compiler

Compiled 72 to 63 computations (12.5% saved)

simplify206.0ms (5%)

Memory

-8.0MiB live, 28.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

664×	`lower-fma.f64`
664×	`lower-fma.f32`
316×	`lower-*.f32`
310×	`lower-*.f64`
176×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	102
0	23	102
1	39	102
2	52	102
3	79	102
4	138	102
5	228	102
6	383	102
7	594	102
8	768	102
9	861	102
10	890	102
11	899	102
12	900	102
0	900	94

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize61.0ms (1.5%)

Memory

21.8MiB live, 57.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(.f64 (.f64 x x) #s(literal 1/2 binary64))
accuracy	0.0078125	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
accuracy	0.9685507489038586	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
accuracy	61.242578946220114	#s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))

Samples

52.0ms

256×

valid

Compiler

Compiled 50 to 19 computations (62% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-mult: 33.0ms (74.9% of total)

ival-add: 4.0ms (9.1% of total)

ival-div: 2.0ms (4.5% of total)

ival-atan: 2.0ms (4.5% of total)

ival-sub: 2.0ms (4.5% of total)

ival-sqrt: 2.0ms (4.5% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

5.5MiB live, 5.5MiB allocated

Counts

5 → 60

Calls

Call 1

Inputs
#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())
#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor 0 x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* 1/2 x) 1))) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1))) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* 1/2 x) 1))) (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* 1/2 x) 1))) (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (- 1 x) (+ 1 x)))) (taylor inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (taylor inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1))))) (taylor inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))) (taylor inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor inf x) (#s(alt #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/2 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x))) (taylor inf x) (#s(alt #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x))) (taylor inf x) (#s(alt #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) (patch (.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (patch (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (patch #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/2 (/ 1 x))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x)))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x)))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

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

1.0ms

inf

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

1.0ms

-inf

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

simplify170.0ms (4.1%)

Memory

0.5MiB live, 157.1MiB allocated

Algorithm

1×	egg-herbie

Rules

9 934×	`lower-fma.f64`
9 934×	`lower-fma.f32`
2 720×	`lower-*.f64`
2 720×	`lower-*.f32`
1 652×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	90	591
1	230	530
2	678	524
3	1922	516
4	5748	504
0	8322	484

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

Inputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* 1/2 x) 1)))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))

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

rewrite195.0ms (4.8%)

Memory

-45.8MiB live, 211.4MiB allocated

Rules

6 160×	`lower-fma.f64`
6 160×	`lower-fma.f32`
4 336×	`lower-*.f32`
4 330×	`lower-*.f64`
3 762×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	96
0	23	96
1	88	96
2	611	96
3	7769	96
0	8633	88

Stop Event

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

Counts

5 → 11

Calls

Call 1

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

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

eval7.0ms (0.2%)

Memory: 12.5MiB live, 12.5MiB allocated
Compiler: Compiled 826 to 128 computations (84.5% saved)

prune6.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	71	7	78

Accuracy

100.0%

Counts

78 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	96.8%	(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
✓	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
✓	98.9%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))))))
✓	99.0%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
✓	98.5%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
✓	97.9%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
✓	4.3%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(approx (+ ( (+ (* 1/2 x) -1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64))))))

Compiler

Compiled 144 to 105 computations (27.1% saved)

regimes13.0ms (0.3%)

Memory

-13.5MiB live, 25.6MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

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

Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes10.0ms (0.2%)

Memory

26.4MiB live, 26.4MiB allocated

Counts

5 → 1

Calls

Call 1

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

Outputs

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
99.0%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
99.0%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
99.0%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes10.0ms (0.2%)

Memory

-15.3MiB live, 23.4MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
98.5%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
98.5%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
98.5%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
98.5%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`
98.5%	1	`x`

Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes11.0ms (0.3%)

Memory

-21.4MiB live, 20.7MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))

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

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

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

Calls

5 calls:

5.0ms	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
2.0ms	x
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
1.0ms	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
97.9%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
97.9%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
97.9%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
97.9%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`
97.9%	1	`x`

Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes5.0ms (0.1%)

Memory

12.4MiB live, 12.4MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))

Outputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
96.8%	1	`x`
96.8%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
96.8%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
96.8%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
96.8%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 36 to 28 computations (22.2% saved)

simplify96.0ms (2.3%)

Memory

8.1MiB live, 46.7MiB allocated

Algorithm

1×	egg-herbie

Rules

12×	`-commutative-binary64-.f64`
6×	`+-commutative-binary64-+.f64`
4×	`sub-neg-binary64-neg.f64-+.f64--.f64`
2×	`1-exp-binary32-exp.f32`
2×	`1-exp-binary64-exp.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	71
1	43	71
2	46	71
3	48	71
4	49	71

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness531.0ms (13%)

Memory

-14.2MiB live, 222.4MiB allocated

Rules

10 954×	`lower-fma.f64`
10 954×	`lower-fma.f32`
2 906×	`lower-*.f64`
2 906×	`lower-*.f32`
2 152×	`lower-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	35
0	15	36
1	52	36
2	339	36
3	4589	8
0	9824	8
0	107	541
1	276	480
2	764	466
3	2111	454
4	6112	448
0	8073	437

Stop Event

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

Compiler

Compiled 76 to 54 computations (28.9% saved)

preprocess75.0ms (1.8%)

Memory: 5.9MiB live, 86.4MiB allocated
Compiler: Compiled 116 to 74 computations (36.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	11	24
1	31	22
2	59	22
3	108	22
4	180	22
5	350	22
6	620	22
7	647	22
0	9	11
0	15	11
1	24	11
2	30	11
3	41	11
4	64	11
5	98	11
6	135	11
7	208	11
8	330	11
9	498	11
10	529	11
0	529	11

Iter	Nodes	Cost
0	9	44
0	15	44
1	24	44
2	30	44
3	41	44
4	64	44
5	98	44
6	135	44
7	208	44
8	330	44
9	498	44
10	529	44
0	529	44

Iter	Nodes	Cost
0	19	102
0	23	102
1	39	102
2	52	102
3	79	102
4	138	102
5	228	102
6	383	102
7	594	102
8	768	102
9	861	102
10	890	102
11	899	102
12	900	102
0	900	94

Iter	Nodes	Cost
0	11	24
1	31	22
2	59	22
3	108	22
4	180	22
5	350	22
6	620	22
7	647	22
0	9	11
0	15	11
1	24	11
2	30	11
3	41	11
4	64	11
5	98	11
6	135	11
7	208	11
8	330	11
9	498	11
10	529	11
0	529	11

Iter	Nodes	Cost
0	9	44
0	15	44
1	24	44
2	30	44
3	41	44
4	64	44
5	98	44
6	135	44
7	208	44
8	330	44
9	498	44
10	529	44
0	529	44

Iter	Nodes	Cost
0	19	102
0	23	102
1	39	102
2	52	102
3	79	102
4	138	102
5	228	102
6	383	102
7	594	102
8	768	102
9	861	102
10	890	102
11	899	102
12	900	102
0	900	94

start0.0ms (0%)

analyze15.0ms (0.4%)

sample1.1s (27.6%)

explain92.0ms (2.2%)

preprocess34.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify13.0ms (0.3%)

localize35.0ms (0.9%)

series4.0ms (0.1%)

simplify129.0ms (3.2%)

rewrite103.0ms (2.5%)

eval8.0ms (0.2%)

prune6.0ms (0.2%)

simplify326.0ms (8%)

localize78.0ms (1.9%)

series11.0ms (0.3%)

simplify303.0ms (7.4%)

rewrite266.0ms (6.5%)

eval64.0ms (1.6%)

prune74.0ms (1.8%)

simplify206.0ms (5%)

localize61.0ms (1.5%)

series4.0ms (0.1%)

simplify170.0ms (4.1%)

rewrite195.0ms (4.8%)

eval7.0ms (0.2%)

prune6.0ms (0.1%)

regimes13.0ms (0.3%)

regimes10.0ms (0.2%)

regimes10.0ms (0.2%)

regimes11.0ms (0.3%)

regimes5.0ms (0.1%)

simplify96.0ms (2.3%)

soundness531.0ms (13%)

preprocess75.0ms (1.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	11	24
1	31	22
2	59	22
3	108	22
4	180	22
5	350	22
6	620	22
7	647	22
0	9	11
0	15	11
1	24	11
2	30	11
3	41	11
4	64	11
5	98	11
6	135	11
7	208	11
8	330	11
9	498	11
10	529	11
0	529	11

Iter	Nodes	Cost
0	9	44
0	15	44
1	24	44
2	30	44
3	41	44
4	64	44
5	98	44
6	135	44
7	208	44
8	330	44
9	498	44
10	529	44
0	529	44

Iter	Nodes	Cost
0	19	102
0	23	102
1	39	102
2	52	102
3	79	102
4	138	102
5	228	102
6	383	102
7	594	102
8	768	102
9	861	102
10	890	102
11	899	102
12	900	102
0	900	94