Metrics for arccos

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze5.0ms (0.1%)

Memory

8.2MiB live, 8.2MiB 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)

sample1.8s (34.7%)

Memory

84.0MiB live, 1 478.9MiB allocated

Samples

1.6s	8 256×	0	valid
1.0ms	21×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.0s

ival-add: 656.0ms (63.8% of total)

ival-sqrt: 103.0ms (10% of total)

ival-atan: 79.0ms (7.7% of total)

ival-mult: 68.0ms (6.6% of total)

ival-div: 56.0ms (5.4% of total)

ival-sub: 54.0ms (5.2% of total)

exact: 7.0ms (0.7% of total)

ival-true: 5.0ms (0.5% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

explain121.0ms (2.3%)

Memory

-35.2MiB live, 225.6MiB 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 104 to 31 computations (70.2% saved)

Precisions

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

ival-sqrt: 6.0ms (25.3% of total)

ival-atan: 5.0ms (21.1% of total)

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

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

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

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

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

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

exact: 0.0ms (0% of total)

preprocess34.0ms (0.6%)

Memory

12.9MiB live, 51.4MiB 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)))))

Compiler

Compiled 12 to 9 computations (25% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.7MiB live, 1.7MiB 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 12 to 9 computations (25% saved)

simplify18.0ms (0.3%)

Memory

-6.7MiB live, 32.1MiB 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)))))
#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)

localize30.0ms (0.6%)

Memory

21.1MiB live, 59.5MiB 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	0.00390625	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
accuracy	0.01171875	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
accuracy	0.0234375	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))

Samples

20.0ms

256×

valid

Compiler

Compiled 46 to 11 computations (76.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-atan: 5.0ms (37.9% of total)

ival-div: 2.0ms (15.2% of total)

ival-mult: 2.0ms (15.2% of total)

ival-sub: 2.0ms (15.2% of total)

ival-sqrt: 2.0ms (15.2% of total)

ival-add: 1.0ms (7.6% of total)

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

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

exact: 0.0ms (0% of total)

series10.0ms (0.2%)

Memory

-31.3MiB live, 11.9MiB 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 (* 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 (* 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 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 (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 (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 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 (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 (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 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 -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 -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

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(sqrt (/ (- 1 x) (+ 1 x)))
1.0ms	x	@	-inf	(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
0.0ms	x	@	-inf	(sqrt (/ (- 1 x) (+ 1 x)))
0.0ms	x	@	inf	(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
0.0ms	x	@	0	(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))

simplify181.0ms (3.4%)

Memory

-4.1MiB live, 317.9MiB 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	2114	454
4	6114	448
0	8084	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)))))
(* 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)))))
(* 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 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))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan (sqrt (/ (- 1 x) (+ 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)))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(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))))))
(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
(+ 1 (* -2 x))
(+ 1 (* x (- (* 2 x) 2)))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
-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 (/ 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 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #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 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 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))))))
(+.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x (sqrt.f64 #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 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 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 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) (.f64 x x))))
1
#s(literal 1 binary64)
(+ 1 (* -2 x))
(fma.f64 x #s(literal -2 binary64) #s(literal 1 binary64))
(+ 1 (* x (- (* 2 x) 2)))
(fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -2 binary64) #s(literal 2 binary64)) #s(literal -2 binary64)) #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(- (* 2 (/ 1 x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) x))
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(-.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) 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 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) x)) x))
-1
#s(literal -1 binary64)
(- (* 2 (/ 1 x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) x))
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) x))
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x)) x)) x))

rewrite147.0ms (2.8%)

Memory

38.3MiB live, 231.0MiB 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 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(atan.f64 #s(literal 1 binary64))
(neg.f64 (atan.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))
(neg.f64 (atan.f64 (/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
#s(literal 1 binary64)
#s(literal 1 binary64)

eval84.0ms (1.6%)

Memory: -28.1MiB live, 11.0MiB allocated
Compiler: Compiled 650 to 103 computations (84.2% saved)

prune6.0ms (0.1%)

Memory

14.2MiB live, 14.2MiB allocated

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	51	4	55
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	51	5	56

Accuracy

100.0%

Counts

56 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.6%	(*.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)))))
▶	99.7%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))))
▶	99.7%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))))
▶	99.6%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))

Compiler

Compiled 52 to 40 computations (23.1% saved)

simplify144.0ms (2.7%)

Memory

10.3MiB live, 93.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

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

Rules

2 920×	`lower-fma.f32`
2 910×	`lower-fma.f64`
856×	`lower-*.f32`
848×	`lower-*.f64`
496×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	210
0	46	210
1	83	210
2	140	210
3	211	210
4	329	210
5	575	210
6	1124	210
7	2029	210
8	2468	210
9	2631	210
10	2705	210
11	2808	210
12	2867	210
13	2867	210
0	2867	210

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

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

localize74.0ms (1.4%)

Memory

7.9MiB live, 163.7MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
accuracy	0	(atan.f64 #s(literal 1 binary64))
accuracy	0	(fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))
accuracy	0	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))))
accuracy	0.00390625	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
accuracy	0.16468386137993823	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
accuracy	0	(fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))
accuracy	0	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))))
accuracy	0.00390625	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
accuracy	0.1755654272943064	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #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	0.00390625	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
accuracy	0.23895789167842696	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))

Samples

45.0ms

256×

valid

Compiler

Compiled 152 to 26 computations (82.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-mult: 10.0ms (32.6% of total)

ival-add: 7.0ms (22.8% of total)

ival-atan: 5.0ms (16.3% of total)

ival-sub: 5.0ms (16.3% of total)

ival-div: 2.0ms (6.5% of total)

ival-sqrt: 2.0ms (6.5% of total)

exact: 1.0ms (3.3% of total)

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

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

series12.0ms (0.2%)

Memory

-12.9MiB live, 24.7MiB allocated

Counts

16 → 168

Calls

Call 1

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

Calls

42 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(+ (* x (+ (* x (+ (* x -1/2) 1/2)) -1)) 1)
0.0ms	x	@	inf	(+ (* x (+ (* x 1/2) -1)) 1)
0.0ms	x	@	-inf	(+ (* x (+ (* x (+ (* x -1/2) 1/2)) -1)) 1)
0.0ms	x	@	0	(+ (* x (+ (* x 1/2) -1)) 1)
0.0ms	x	@	inf	(- 1 x)

simplify317.0ms (6%)

Memory

4.5MiB live, 359.6MiB allocated

Algorithm

1×	egg-herbie

Rules

15 796×	`lower-fma.f64`
15 796×	`lower-fma.f32`
3 362×	`lower-*.f64`
3 362×	`lower-*.f32`
2 564×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	124	1667
1	338	1480
2	1115	1458
3	3731	1430
4	7775	1430
0	8148	1357

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

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

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

rewrite367.0ms (6.9%)

Memory

-0.9MiB live, 401.9MiB allocated

Rules

7 586×	`lower-fma.f32`
7 576×	`lower-fma.f64`
3 682×	`lower-/.f64`
3 682×	`lower-/.f32`
3 600×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	187
0	46	187
1	166	187
2	1226	187
0	8437	187

Stop Event

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

Counts

16 → 323

Calls

Call 1

Inputs
(*.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 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #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))
(fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))
(fma.f64 x #s(literal -1/2 binary64) #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))))
(*.f64 (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) (neg.f64 x))
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (neg.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) x))))
(+.f64 (neg.f64 x) #s(literal 1 binary64))
(+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (neg.f64 (/.f64 (.f64 x (.f64 x x)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))))
(+.f64 (.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)) (.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (-.f64 (*.f64 x x) x)))
(+.f64 (.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (-.f64 (.f64 x x) x)) (.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (.f64 (-.f64 (.f64 x x) x) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))))
(+.f64 (.f64 (-.f64 (.f64 x x) x) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) x)
(-.f64 #s(literal 0 binary64) (+.f64 x #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (/.f64 (.f64 x (.f64 x x)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (neg.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) x))))
(fma.f64 #s(literal 1 binary64) (neg.f64 x) #s(literal 1 binary64))
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(.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) (.f64 x #s(literal 1/2 binary64))))))
(.f64 (neg.f64 (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64))) (/.f64 #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 -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x #s(literal -1/2 binary64)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/2 binary64)))
(+.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(+.f64 (/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/2 binary64)))) (/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/2 binary64)))))
(fma.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (neg.f64 x) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64) #s(literal 1/2 binary64))
(fma.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64)))))
(fma.f64 (neg.f64 x) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(neg.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/8 binary64)) (neg.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64) (*.f64 x #s(literal 1/4 binary64))))))
(neg.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/4 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64) (*.f64 x #s(literal 1/4 binary64)))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/4 binary64))) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (-.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal -1/4 binary64)))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (*.f64 x x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/8 binary64)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64) (*.f64 x #s(literal 1/4 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 x (-.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal -1/4 binary64)))))
(/.f64 (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/4 binary64)) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64) (*.f64 x #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (-.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal -1/4 binary64))))))
(/.f64 (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/4 binary64))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (.f64 x x))) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64) (*.f64 x #s(literal 1/4 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/4 binary64)))) (neg.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (.f64 x x)))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (.f64 (/.f64 (.f64 x (*.f64 x #s(literal 1/4 binary64))) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64)))) (.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64))))) (+.f64 (/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64) (.f64 x #s(literal 1/4 binary64)))))
(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 x (-.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/4 binary64))))))
(.f64 (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) #s(literal -1/2 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64) (.f64 x #s(literal 1/4 binary64))))))
(.f64 (neg.f64 (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/2 binary64)))))

eval73.0ms (1.4%)

Memory: 7.8MiB live, 120.4MiB allocated
Compiler: Compiled 10 920 to 1 508 computations (86.2% saved)

prune54.0ms (1%)

Memory

2.8MiB live, 119.8MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	490	1	491
Fresh	0	0	0
Picked	0	4	4
Done	0	1	1
Total	490	6	496

Accuracy

100.0%

Counts

496 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.6%	(*.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)))))
✓	99.7%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))))
✓	99.7%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))))
▶	99.6%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))))
✓	99.6%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify289.0ms (5.4%)

Memory

4.0MiB live, 312.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))
cost-diff	0	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))
cost-diff	0	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))))
cost-diff	1088	(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))

Rules

17 570×	`lower-fma.f32`
17 568×	`lower-fma.f64`
2 396×	`lower-*.f32`
2 394×	`lower-*.f64`
1 960×	`lower-+.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	14	73
0	20	73
1	34	73
2	45	73
3	79	73
4	138	73
5	311	53
6	1117	53
7	3763	53
8	5426	53
9	6668	53
10	7377	53
11	7937	53
0	8007	53

Stop Event

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

Calls

Call 1

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

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

localize59.0ms (1.1%)

Memory

25.8MiB live, 61.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))))
accuracy	0.00390625	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))
accuracy	0.015625	(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))
accuracy	0.23895789167842696	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))

Samples

47.0ms

256×

valid

Compiler

Compiled 50 to 16 computations (68% saved)

Precisions

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

ival-div: 3.0ms (18.2% of total)

ival-mult: 3.0ms (18.2% of total)

ival-atan: 3.0ms (18.2% of total)

ival-sub: 3.0ms (18.2% of total)

ival-add: 2.0ms (12.1% of total)

ival-sqrt: 2.0ms (12.1% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

7.0MiB live, 7.0MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(/ (+ (* x x) -1) (- -1 x))
0.0ms	x	@	0	(/ (+ (* x x) -1) (- -1 x))
0.0ms	x	@	-inf	(/ (+ (* x x) -1) (- -1 x))
0.0ms	x	@	0	(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
0.0ms	x	@	inf	(sqrt (/ (- 1 x) (+ 1 x)))

simplify271.0ms (5.1%)

Memory

-51.6MiB live, 343.2MiB allocated

Algorithm

1×	egg-herbie

Rules

11 462×	`lower-fma.f64`
11 462×	`lower-fma.f32`
3 104×	`lower-*.f64`
3 104×	`lower-*.f32`
1 454×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	477
1	208	416
2	618	410
3	1614	402
4	5501	392
0	8188	388

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

rewrite434.0ms (8.2%)

Memory

-10.4MiB live, 390.3MiB allocated

Rules

7 108×	`lower-fma.f32`
7 106×	`lower-fma.f64`
4 160×	`lower-*.f32`
4 158×	`lower-*.f64`
4 022×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	63
0	20	63
1	88	43
2	669	43
0	8523	43

Stop Event

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

Counts

4 → 351

Calls

Call 1

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

Outputs
(+.f64 #s(literal 1 binary64) (neg.f64 x))
(+.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 x (-.f64 #s(literal -1 binary64) x))))
(+.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal -1 binary64) x)) (+.f64 x #s(literal 1 binary64))))
(+.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x)) (neg.f64 (*.f64 x (/.f64 x (+.f64 x #s(literal 1 binary64))))))
(+.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x)) (.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (.f64 x x)))
(+.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x)) (.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64)))))
(+.f64 (neg.f64 x) #s(literal 1 binary64))
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64)))) (neg.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 x (fma.f64 x x #s(literal 1 binary64))))))
(+.f64 (.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (.f64 x x)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x)))
(+.f64 (.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))) (-.f64 (*.f64 x x) x)))
(+.f64 (.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))) (-.f64 (.f64 x x) x)) (.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x)))) #s(literal 1 binary64)))
(+.f64 (.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x x #s(literal 1 binary64))) (.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))) (neg.f64 x)))
(+.f64 (.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64)))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x)))
(+.f64 (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))) (.f64 (-.f64 (.f64 x x) x) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x))))))
(+.f64 (.f64 (-.f64 (.f64 x x) x) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x))))))
(+.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))) (.f64 (neg.f64 x) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) x)
(-.f64 #s(literal 0 binary64) (+.f64 x #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x)) (*.f64 x (/.f64 x (+.f64 x #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64)))) (/.f64 (.f64 x (.f64 x x)) (+.f64 x (fma.f64 x x #s(literal 1 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 x (.f64 x (*.f64 x x))) (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal -1 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal -1 binary64) x)))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (-.f64 #s(literal -1 binary64) x) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal -1 binary64) x) (fma.f64 x x #s(literal 1 binary64)))))
(fma.f64 x #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (neg.f64 (*.f64 x (/.f64 x (+.f64 x #s(literal 1 binary64))))))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (.f64 x x)))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64)))))
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (fma.f64 x (neg.f64 x) #s(literal 1 binary64))) (neg.f64 (*.f64 x (/.f64 x (+.f64 x #s(literal 1 binary64))))))
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (fma.f64 x (neg.f64 x) #s(literal 1 binary64))) (.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (.f64 x x)))
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (fma.f64 x (neg.f64 x) #s(literal 1 binary64))) (.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64)))))
(fma.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (*.f64 x (/.f64 x (+.f64 x #s(literal 1 binary64))))))
(fma.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64))) (.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (.f64 x x)))
(fma.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64))) (.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64)))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x)) (neg.f64 (*.f64 x (/.f64 x (+.f64 x #s(literal 1 binary64))))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x)) (.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (.f64 x x)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x)) (.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64)))))
(fma.f64 #s(literal 1 binary64) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64)))) (neg.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 x (fma.f64 x x #s(literal 1 binary64))))))
(fma.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))) (.f64 (-.f64 (.f64 x x) x) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))))
(fma.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (*.f64 x (/.f64 x (+.f64 x #s(literal 1 binary64))))))
(fma.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))) (.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (.f64 x x)))
(fma.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))) (.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64)))))
(fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))) (fma.f64 x (neg.f64 x) #s(literal 1 binary64))) (neg.f64 (*.f64 x (/.f64 x (+.f64 x #s(literal 1 binary64))))))
(fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))) (fma.f64 x (neg.f64 x) #s(literal 1 binary64))) (.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (.f64 x x)))
(fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))) (fma.f64 x (neg.f64 x) #s(literal 1 binary64))) (.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64)))))
(fma.f64 (*.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x)))
(fma.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (*.f64 x (/.f64 x (+.f64 x #s(literal 1 binary64))))))
(fma.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (.f64 x x)))
(fma.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64)))))
(fma.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) x)) (neg.f64 (*.f64 x (/.f64 x (+.f64 x #s(literal 1 binary64))))))
(fma.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (.f64 x x)))
(fma.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64)))))
(fma.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x)) #s(literal 1 binary64) (neg.f64 (*.f64 x (/.f64 x (+.f64 x #s(literal 1 binary64))))))
(fma.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x)) #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (.f64 x x)))
(fma.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x)) #s(literal 1 binary64) (.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64)))))
(fma.f64 (-.f64 (.f64 x x) x) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))))
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(.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64)))))
(.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64)))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64)))
(.f64 (/.f64 #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 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x)))
(.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal -1 binary64) x)))
(.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal -1 binary64) x) (fma.f64 x x #s(literal 1 binary64)))))
(.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64)))))
(.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))))
(.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 (-.f64 #s(literal -1 binary64) x) (fma.f64 x x #s(literal 1 binary64)))))
(*.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))
(*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(.f64 (fma.f64 x (.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 x (fma.f64 x x #s(literal 1 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))))
(.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (*.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))) (.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x)))) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))
(.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))) (.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (.f64 x x) #s(literal -1 binary64))) (*.f64 (+.f64 x (fma.f64 x x #s(literal 1 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (/.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))
(.f64 (pow.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (+.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) x))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x)))
(.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x)))) (/.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))
(.f64 (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x)))) (+.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64)) x))
(*.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64))))
(.f64 (/.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (fma.f64 x (neg.f64 x) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))))
(.f64 (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))
(.f64 (/.f64 #s(literal -1 binary64) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (.f64 x x) #s(literal -1 binary64)))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 x (fma.f64 x x #s(literal 1 binary64)))))
(.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (/.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))
(.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (.f64 x x) #s(literal -1 binary64)))) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x (fma.f64 x x #s(literal 1 binary64)))))
(.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))
(.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (.f64 x x) #s(literal -1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x (fma.f64 x x #s(literal 1 binary64)))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (fma.f64 (fma.f64 x x x) (.f64 (fma.f64 x x x) (fma.f64 x x x)) #s(literal 1 binary64))) (fma.f64 (fma.f64 x x x) (-.f64 (fma.f64 x x x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x x) (fma.f64 x x x)))) (-.f64 #s(literal 1 binary64) (fma.f64 x x x)))
(.f64 (/.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))) (fma.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x (.f64 x (*.f64 x x)))))))
(.f64 (/.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 x x #s(literal 1 binary64))))) (-.f64 (.f64 x (.f64 x (*.f64 x x))) (fma.f64 x x #s(literal 1 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64))) (fma.f64 x (-.f64 (.f64 x (.f64 x x)) 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(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))

eval99.0ms (1.9%)

Memory: -3.6MiB live, 116.3MiB allocated
Compiler: Compiled 10 167 to 1 420 computations (86% saved)

prune49.0ms (0.9%)

Memory

28.2MiB live, 144.5MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	399	0	399
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	399	6	405

Accuracy

100.0%

Counts

405 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.6%	(*.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)))))
✓	99.7%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))))
✓	99.7%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))))
✓	99.6%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))))
✓	99.6%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))

Compiler

Compiled 125 to 78 computations (37.6% saved)

regimes12.0ms (0.2%)

Memory

-8.9MiB live, 28.1MiB allocated

Counts

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
100.0%	1	`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 41 to 28 computations (31.7% saved)

regimes12.0ms (0.2%)

Memory

-12.0MiB live, 24.8MiB 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))) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))))

Outputs

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

Calls

5 calls:

4.0ms	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
99.7%	1	`x`
99.7%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
99.7%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
99.7%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
99.7%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 41 to 28 computations (31.7% saved)

regimes8.0ms (0.1%)

Memory

19.7MiB live, 19.7MiB 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))) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))))

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

Calls

5 calls:

2.0ms	x
1.0ms	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms	(/.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
99.7%	1	`x`
99.7%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
99.7%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
99.7%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
99.7%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 41 to 28 computations (31.7% saved)

regimes8.0ms (0.2%)

Memory

-19.4MiB live, 17.7MiB allocated

Counts

2 → 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))))

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

Calls

5 calls:

3.0ms	x
1.0ms	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
1.0ms	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
99.6%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
99.6%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
99.6%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 41 to 28 computations (31.7% saved)

regimes6.0ms (0.1%)

Memory

15.4MiB live, 15.4MiB 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	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
1.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))

Results

Accuracy	Segments	Branch
98.6%	1	`x`
98.6%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
98.6%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
98.6%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
98.6%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 41 to 28 computations (31.7% saved)

simplify6.0ms (0.1%)

Memory

15.2MiB live, 15.2MiB allocated

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

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

soundness475.0ms (9%)

Memory

-3.4MiB live, 295.4MiB 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	107	541
1	276	480
2	764	466
3	2114	454
4	6114	448
0	8084	437
0	9	35
0	15	36
1	52	36
2	339	36
3	4589	8
0	9824	8

Stop Event

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

Compiler

Compiled 80 to 51 computations (36.3% saved)

preprocess51.0ms (1%)

Memory: 5.5MiB live, 119.8MiB allocated
Compiler: Compiled 120 to 68 computations (43.3% 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	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

start0.0ms (0%)

analyze5.0ms (0.1%)

sample1.8s (34.7%)

explain121.0ms (2.3%)

preprocess34.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify18.0ms (0.3%)

localize30.0ms (0.6%)

series10.0ms (0.2%)

simplify181.0ms (3.4%)

rewrite147.0ms (2.8%)

eval84.0ms (1.6%)

prune6.0ms (0.1%)

simplify144.0ms (2.7%)

localize74.0ms (1.4%)

series12.0ms (0.2%)

simplify317.0ms (6%)

rewrite367.0ms (6.9%)

eval73.0ms (1.4%)

prune54.0ms (1%)

simplify289.0ms (5.4%)

localize59.0ms (1.1%)

series3.0ms (0.1%)

simplify271.0ms (5.1%)

rewrite434.0ms (8.2%)

eval99.0ms (1.9%)

prune49.0ms (0.9%)

regimes12.0ms (0.2%)

regimes12.0ms (0.2%)

regimes8.0ms (0.1%)

regimes8.0ms (0.2%)

regimes6.0ms (0.1%)

simplify6.0ms (0.1%)

soundness475.0ms (9%)

preprocess51.0ms (1%)

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