Metrics for arccos

analyze5.0ms (0.1%)

Memory

8.8MiB live, 8.8MiB 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)

sample957.0ms (17.3%)

Memory

-1.3MiB live, 1 511.2MiB allocated

Samples

705.0ms	8 256×	0	valid
1.0ms	24×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 533.0ms

ival-sqrt: 143.0ms (26.8% of total)

ival-atan: 140.0ms (26.3% of total)

ival-div: 69.0ms (13% of total)

ival-mult: 63.0ms (11.8% of total)

ival-sub: 53.0ms (9.9% of total)

ival-add: 49.0ms (9.2% of total)

exact: 7.0ms (1.3% of total)

ival-true: 6.0ms (1.1% of total)

ival-assert: 4.0ms (0.8% of total)

Bogosity

preprocess34.0ms (0.6%)

Memory

18.2MiB live, 57.3MiB 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)))))

explain201.0ms (3.6%)

Memory

-0.7MiB live, 204.3MiB 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

126.0ms

512×

valid

Compiler

Compiled 116 to 40 computations (65.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 112.0ms

ival-add: 87.0ms (77.6% of total)

ival-mult: 9.0ms (8% of total)

ival-atan: 5.0ms (4.5% of total)

ival-sub: 4.0ms (3.6% of total)

ival-sqrt: 4.0ms (3.6% of total)

ival-div: 3.0ms (2.7% of total)

exact: 1.0ms (0.9% of total)

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

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

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB 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

-9.7MiB live, 28.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

localize32.0ms (0.6%)

Memory

-14.5MiB live, 66.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
✓	accuracy	100.0%	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
✓	accuracy	100.0%	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))

Samples

19.0ms

256×

valid

Compiler

Compiled 46 to 11 computations (76.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-sub: 3.0ms (24.3% of total)

ival-div: 2.0ms (16.2% of total)

ival-mult: 2.0ms (16.2% of total)

ival-atan: 2.0ms (16.2% of total)

ival-sqrt: 2.0ms (16.2% of total)

ival-add: 1.0ms (8.1% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

11.1MiB live, 11.1MiB 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)))))

simplify323.0ms (5.8%)

Memory

16.6MiB live, 452.7MiB 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))

rewrite173.0ms (3.1%)

Memory

2.2MiB live, 233.2MiB allocated

Algorithm

1×	batch-egg-rewrite

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)

eval5.0ms (0.1%)

Memory: 12.0MiB live, 12.0MiB allocated
Compiler: Compiled 650 to 103 computations (84.2% saved)

prune10.0ms (0.2%)

Memory

-18.3MiB live, 18.6MiB allocated

Pruning

6 alts after pruning (5 fresh and 1 done)

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

Accuracy

100.0%

Counts

56 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.9%	(*.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)))))
▶	99.5%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64))))))
▶	99.6%	(*.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)))))
▶	99.5%	(*.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)))))
▶	99.2%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))

Compiler

Compiled 118 to 89 computations (24.6% saved)

simplify206.0ms (3.7%)

Memory

-6.6MiB live, 233.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Rules

3 512×	`lower-fma.f32`
3 498×	`lower-fma.f64`
1 084×	`lower-*.f32`
1 074×	`lower-*.f64`
608×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	292
0	60	292
1	108	292
2	181	292
3	258	292
4	376	292
5	622	292
6	1171	292
7	2087	292
8	2557	292
9	2806	292
10	2998	292
11	3214	292
12	3307	292
13	3340	292
14	3381	292
15	3393	292
16	3393	292
17	3393	292
0	3393	292

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize106.0ms (1.9%)

Memory

12.2MiB live, 292.9MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64))))))
✓	accuracy	100.0%	(sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64))))
✓	accuracy	100.0%	(atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64)))))
✓	accuracy	99.4%	#s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64)))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))
✓	accuracy	100.0%	(*.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	100.0%	(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))))
✓	accuracy	99.5%	#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	100.0%	(-.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
✓	accuracy	100.0%	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
✓	accuracy	99.2%	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
✓	accuracy	100.0%	(atan.f64 #s(literal 1 binary64))
✓	accuracy	100.0%	(fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(*.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	100.0%	(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))))
✓	accuracy	99.7%	#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)))

Samples

63.0ms

256×

valid

Compiler

Compiled 205 to 31 computations (84.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.0ms

ival-add: 18.0ms (38.9% of total)

ival-mult: 18.0ms (38.9% of total)

ival-atan: 3.0ms (6.5% of total)

ival-sqrt: 3.0ms (6.5% of total)

ival-div: 2.0ms (4.3% of total)

ival-sub: 2.0ms (4.3% of total)

exact: 1.0ms (2.2% of total)

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

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

series15.0ms (0.3%)

Memory

-6.1MiB live, 32.2MiB allocated

Counts

20 → 216

Calls

Call 1

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

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

Calls

54 calls:

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

simplify509.0ms (9.2%)

Memory

31.6MiB live, 955.3MiB allocated

Algorithm

1×	egg-herbie

Rules

15 280×	`lower-fma.f64`
15 280×	`lower-fma.f32`
3 772×	`lower-*.f64`
3 772×	`lower-*.f32`
2 552×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	152	2208
1	418	1960
2	1292	1924
3	4335	1884
0	8205	1797

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

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 (* 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)))))
(* 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 (* -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)
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)))))
-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)))

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

rewrite504.0ms (9.1%)

Memory

-19.5MiB live, 529.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 786×	`lower-fma.f32`
6 772×	`lower-fma.f64`
4 188×	`lower-/.f64`
4 188×	`lower-/.f32`
3 424×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	254
0	60	254
1	216	254
2	1576	254
0	8444	254

Stop Event

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

Counts

20 → 256

Calls

Call 1

Inputs
(*.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))
(*.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 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64))))))
(atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64)))))
(sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64))))
#s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64)))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 x #s(literal 1/2 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 (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(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)))
(+.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(+.f64 (*.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 (.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (.f64 x x)) (-.f64 #s(literal 1 binary64) x))
(+.f64 (/.f64 (.f64 x (.f64 (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (*.f64 x (fma.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 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))) (neg.f64 (/.f64 #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 (+.f64 #s(literal 1 binary64) (.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (.f64 x x))) (neg.f64 x))
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(-.f64 (+.f64 #s(literal 1 binary64) (.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (.f64 x x))) x)
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eval80.0ms (1.4%)

Memory: 9.4MiB live, 123.1MiB allocated
Compiler: Compiled 9 964 to 1 289 computations (87.1% saved)

prune70.0ms (1.3%)

Memory

0.4MiB live, 129.9MiB allocated

Pruning

9 alts after pruning (3 fresh and 6 done)

	Pruned	Kept	Total
New	469	3	472
Fresh	0	0	0
Picked	0	5	5
Done	0	1	1
Total	469	9	478

Accuracy

100.0%

Counts

478 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	97.9%	(*.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)))))
✓	99.5%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64))))))
▶	99.6%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (.f64 x x) (-.f64 #s(literal 1 binary64) x)))))
▶	99.5%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x)))))
✓	99.6%	(*.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)))))
✓	99.5%	(*.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)))))
▶	99.2%	(*.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)))))
✓	99.2%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))

Compiler

Compiled 107 to 77 computations (28% saved)

simplify350.0ms (6.3%)

Memory

17.4MiB live, 481.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 x x) (-.f64 #s(literal 1 binary64) x))))
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (.f64 x x) (-.f64 #s(literal 1 binary64) x)))))
✓	cost-diff	128	(fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 x x) (-.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))))
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x)))))
✓	cost-diff	128	(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))
✓	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

13 122×	`lower-fma.f32`
13 114×	`lower-fma.f64`
2 440×	`lower-*.f32`
2 432×	`lower-*.f64`
2 004×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	236
0	44	246
1	74	246
2	109	246
3	246	246
4	531	246
5	1191	216
6	2912	216
7	5253	216
0	8444	208

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

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

localize123.0ms (2.2%)

Memory

-21.4MiB live, 185.0MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (.f64 x x) (-.f64 #s(literal 1 binary64) x)))))
✓	accuracy	100.0%	(fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 x x) (-.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 x x) (-.f64 #s(literal 1 binary64) x))))
✓	accuracy	99.7%	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x)))))
✓	accuracy	100.0%	(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x))))
✓	accuracy	99.5%	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x)))
✓	accuracy	100.0%	(*.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	100.0%	(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))
✓	accuracy	100.0%	(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))
✓	accuracy	99.2%	#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))

Samples

45.0ms	255×	0	valid
0.0ms	1×	1	valid

Compiler

Compiled 154 to 24 computations (84.4% saved)

Precisions

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

ival-add: 12.0ms (38.3% of total)

ival-mult: 8.0ms (25.5% of total)

ival-div: 3.0ms (9.6% of total)

ival-atan: 3.0ms (9.6% of total)

ival-sub: 3.0ms (9.6% of total)

ival-sqrt: 2.0ms (6.4% of total)

exact: 1.0ms (3.2% of total)

adjust: 0.0ms (0% of total)

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

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

series8.0ms (0.1%)

Memory

20.6MiB live, 20.6MiB allocated

Counts

12 → 144

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

Calls

36 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	(+ (* (+ (* x -1/2) 1/2) (* x x)) (- 1 x))
0.0ms	x	@	inf	(+ (* (* x x) 1/2) (- 1 x))

simplify443.0ms (8%)

Memory

24.3MiB live, 691.4MiB allocated

Algorithm

1×	egg-herbie

Rules

12 010×	`lower-fma.f64`
12 010×	`lower-fma.f32`
3 448×	`lower-*.f64`
3 448×	`lower-*.f32`
2 518×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	117	1579
1	320	1388
2	1059	1366
3	3568	1334
4	7452	1334
0	8288	1289

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

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

rewrite351.0ms (6.3%)

Memory

1.1MiB live, 662.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 976×	`lower-fma.f32`
5 968×	`lower-fma.f64`
4 684×	`lower-/.f32`
4 682×	`lower-/.f64`
3 752×	`lower-*.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	201
0	44	201
1	163	181
2	1228	181
0	8823	181

Stop Event

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

Counts

12 → 457

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

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

eval84.0ms (1.5%)

Memory: 24.3MiB live, 171.9MiB allocated
Compiler: Compiled 18 701 to 2 046 computations (89.1% saved)

prune118.0ms (2.1%)

Memory

-24.9MiB live, 169.3MiB allocated

Pruning

9 alts after pruning (0 fresh and 9 done)

	Pruned	Kept	Total
New	601	0	601
Fresh	0	0	0
Picked	0	3	3
Done	0	6	6
Total	601	9	610

Accuracy

100.0%

Counts

610 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	97.9%	(*.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)))))
✓	99.5%	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 #s(approx (/ (- 1 x) (+ 1 x)) (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) #s(literal 1 binary64))))))
✓	99.6%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (.f64 x x) (-.f64 #s(literal 1 binary64) x)))))
✓	99.5%	(.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) x)))))
✓	99.6%	(*.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)))))
✓	99.5%	(*.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)))))
✓	99.2%	(*.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)))))
✓	99.2%	(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))

Compiler

Compiled 206 to 120 computations (41.7% saved)

regimes14.0ms (0.2%)

Memory

30.6MiB live, 30.6MiB allocated

Counts

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

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	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))
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))))

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)

regimes14.0ms (0.3%)

Memory

-6.5MiB live, 30.0MiB allocated

Counts

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

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

Calls

5 calls:

4.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
3.0ms	x
2.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
2.0ms	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
2.0ms	(/.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)

regimes12.0ms (0.2%)

Memory

-9.6MiB live, 27.2MiB 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 (.f64 x x) #s(literal 1/2 binary64) (-.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))) (/.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	(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
2.0ms	x
2.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
2.0ms	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
2.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))

Results

Accuracy	Segments	Branch
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)

regimes9.0ms (0.2%)

Memory

22.8MiB live, 22.8MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

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

Compiler

Compiled 41 to 28 computations (31.7% saved)

regimes10.0ms (0.2%)

Memory

-13.7MiB live, 20.9MiB 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:

4.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
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	(/.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
99.5%	1	`x`
99.5%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
99.5%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
99.5%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
99.5%	1	`(/.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

19.7MiB live, 19.7MiB 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:

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

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))`
99.2%	1	`(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))`
99.2%	1	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))`
99.2%	1	`(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 41 to 28 computations (31.7% saved)

regimes32.0ms (0.6%)

Memory

-33.2MiB live, 14.1MiB 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:

27.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms	x
1.0ms	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) 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))

Results

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

Compiler

Compiled 41 to 28 computations (31.7% saved)

simplify7.0ms (0.1%)

Memory

11.4MiB live, 11.4MiB allocated

Algorithm

1×	egg-herbie

Rules

16×	`*-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	41	114
1	54	114
2	57	114
3	59	114
4	60	114

Stop Event

1×

saturated

Calls

Call 1

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

soundness625.0ms (11.3%)

Memory

32.3MiB live, 478.6MiB allocated

Rules

10 954×	`lower-fma.f64`
10 954×	`lower-fma.f32`
6 786×	`lower-fma.f32`
6 772×	`lower-fma.f64`
4 188×	`lower-/.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	254
0	60	254
1	216	254
2	1576	254
0	8444	254
0	9	35
0	15	36
1	52	36
2	339	36
3	4589	8
0	9824	8
0	107	541
1	276	480
2	764	466
3	2114	454
4	6114	448
0	8084	437

Stop Event

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

Compiler

Compiled 159 to 98 computations (38.4% saved)

preprocess80.0ms (1.4%)

Memory: 3.3MiB live, 118.1MiB allocated
Compiler: Compiled 174 to 82 computations (52.9% 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

analyze5.0ms (0.1%)

sample957.0ms (17.3%)

preprocess34.0ms (0.6%)

explain201.0ms (3.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify18.0ms (0.3%)

localize32.0ms (0.6%)

series5.0ms (0.1%)

simplify323.0ms (5.8%)

rewrite173.0ms (3.1%)

eval5.0ms (0.1%)

prune10.0ms (0.2%)

simplify206.0ms (3.7%)

localize106.0ms (1.9%)

series15.0ms (0.3%)

simplify509.0ms (9.2%)

rewrite504.0ms (9.1%)

eval80.0ms (1.4%)

prune70.0ms (1.3%)

simplify350.0ms (6.3%)

localize123.0ms (2.2%)

series8.0ms (0.1%)

simplify443.0ms (8%)

rewrite351.0ms (6.3%)

eval84.0ms (1.5%)

prune118.0ms (2.1%)

regimes14.0ms (0.2%)

regimes14.0ms (0.3%)

regimes12.0ms (0.2%)

regimes9.0ms (0.2%)

regimes10.0ms (0.2%)

regimes6.0ms (0.1%)

regimes32.0ms (0.6%)

simplify7.0ms (0.1%)

soundness625.0ms (11.3%)

preprocess80.0ms (1.4%)

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