Metrics for Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze3.0ms (0.1%)

Memory

-34.6MiB live, 4.6MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample811.0ms (22.1%)

Memory

57.3MiB live, 877.5MiB allocated

Samples

598.0ms	8 256×	0	valid
0.0ms	3×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 420.0ms

ival-sqrt: 242.0ms (57.6% of total)

ival-mult: 122.0ms (29% of total)

ival-sub: 42.0ms (10% of total)

ival-true: 6.0ms (1.4% of total)

exact: 5.0ms (1.2% of total)

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

Bogosity

explain74.0ms (2%)

Memory

-14.5MiB live, 118.5MiB allocated

FPErrors

Click to see full error table

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

24.0ms

512×

valid

Compiler

Compiled 43 to 19 computations (55.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 4.0ms (36.7% of total)

ival-sqrt: 4.0ms (36.7% of total)

ival-sub: 2.0ms (18.4% of total)

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

exact: 0.0ms (0% of total)

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

preprocess519.0ms (14.2%)

Memory

6.2MiB live, 281.6MiB allocated

Algorithm

1×	egg-herbie

Rules

30 426×	`lower-fma.f64`
30 426×	`lower-fma.f32`
3 778×	`lower-*.f32`
3 776×	`lower-*.f64`
2 412×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	25	13
2	45	13
3	87	13
4	116	13
5	167	13
6	280	13
7	507	13
8	900	13
9	1467	13
10	3839	13
11	5537	13
12	6300	13
13	6598	13
14	6654	13
15	6686	13
16	6948	13
17	7542	13
0	5	6
0	8	6
1	15	6
2	22	6
3	30	6
4	45	6
5	65	6
6	108	6
7	305	6
8	585	6
9	1159	6
10	2070	6
11	3779	6
12	4733	6
13	5051	6
14	5337	6
15	5506	6
16	5583	6
17	5850	6
18	6848	6
19	7904	6
0	8289	6

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

Outputs
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

Symmetry

(abs x)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify325.0ms (8.9%)

Memory

-9.6MiB live, 220.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

30 426×	`lower-fma.f64`
30 426×	`lower-fma.f32`
3 778×	`lower-*.f32`
3 776×	`lower-*.f64`
2 412×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	15	16
2	22	16
3	30	16
4	45	16
5	65	16
6	108	16
7	305	16
8	585	16
9	1159	16
10	2070	16
11	3779	16
12	4733	16
13	5051	16
14	5337	16
15	5506	16
16	5583	16
17	5850	16
18	6848	16
19	7904	16
0	8289	16

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)
x

Outputs
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)
x

localize105.0ms (2.9%)

Memory

-52.1MiB live, 111.3MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 #s(literal 1 binary64) (*.f64 x x))
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

Samples

101.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-mult: 17.0ms (83.2% of total)

ival-sqrt: 2.0ms (9.8% of total)

ival-sub: 1.0ms (4.9% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

10.0MiB live, 10.0MiB allocated

Counts

3 → 36

Calls

Call 1

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

Inputs

#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #<representation binary64>) () ())

#s(alt (-.f64 #s(literal 1 binary64) (*.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (*.f64 x x)) #<representation binary64>) () ())

#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())

Outputs
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt -1)) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())

Calls

3 calls:

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

simplify113.0ms (3.1%)

Memory

-0.4MiB live, 153.9MiB allocated

Algorithm

1×	egg-herbie

Rules

8 366×	`lower-fma.f64`
8 366×	`lower-fma.f32`
3 130×	`lower-*.f64`
3 130×	`lower-*.f32`
1 412×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	295
1	149	286
2	419	278
3	1279	264
4	3834	263
5	6189	263
0	8166	252

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(+ 1 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(+ 1 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* x (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(fma.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (sqrt.f64 #s(literal -1 binary64))))) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (sqrt.f64 #s(literal -1 binary64))))) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* -1 (* x (sqrt -1)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64))) x (/.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
(fma.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))) (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (sqrt.f64 #s(literal -1 binary64)))))) x (/.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite234.0ms (6.4%)

Memory

36.4MiB live, 337.0MiB allocated

Rules

4 716×	`lower-fma.f64`
4 716×	`lower-fma.f32`
4 136×	`lower-/.f64`
4 136×	`lower-/.f32`
3 492×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	32	14
2	187	14
3	1340	14
0	9365	12

Stop Event

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

Counts

3 → 355

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)

Outputs
(.f64 (sqrt.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)))))) (sqrt.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))))
(.f64 (sqrt.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (-.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x)) #s(literal 1 binary64)) #s(literal 1 binary64))))
(.f64 (sqrt.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)) (neg.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64))))) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
(.f64 (sqrt.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)) (neg.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
(.f64 (sqrt.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(.f64 (sqrt.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)) (neg.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)) (neg.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (neg.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))))
(.f64 (pow.f64 (pow.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (pow.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64))))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) #s(literal 1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (-.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x)) #s(literal 1 binary64)) #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(.f64 (sqrt.f64 (neg.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64)))))
(.f64 (sqrt.f64 (neg.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64)))) (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))))))
(.f64 (sqrt.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)))) #s(literal 1/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64))))
(.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))))
(*.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))
(.f64 (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log1p.f64 (*.f64 x x)))
(pow.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/2 binary64))
(pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64))))) (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))))) (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))))) (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))))) (sqrt.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 x x) x) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))))) (sqrt.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) (.f64 (.f64 (.f64 (.f64 x x) x) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) (.f64 (.f64 (.f64 x x) x) (/.f64 x (fma.f64 x x #s(literal 1 binary64))))))) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (.f64 (.f64 (*.f64 x x) x) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)))) (.f64 (/.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (/.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)))))) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (/.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64)))))) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 (.f64 (.f64 (.f64 x x) x) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) (.f64 (.f64 (.f64 x x) x) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (.f64 (.f64 (*.f64 x x) x) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)))) (pow.f64 (/.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (fma.f64 (/.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (/.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (/.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))))))))
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64))))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))))) (sqrt.f64 (neg.f64 (neg.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
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(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x 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) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 (.f64 (.f64 (.f64 x x) x) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) (.f64 (.f64 (.f64 x x) x) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (.f64 (.f64 (.f64 x x) x) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x 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) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 (.f64 (.f64 (.f64 x x) x) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) (.f64 (.f64 (.f64 x x) x) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (.f64 (.f64 (*.f64 x x) x) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))))))))
(-.f64 (/.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)))) (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (fma.f64 (/.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (/.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (/.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))))))) (/.f64 (pow.f64 (/.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 3 binary64)) (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (fma.f64 (/.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (/.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (/.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))))))))
(-.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 (.f64 (.f64 x x) x) x)) (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
(-.f64 (/.f64 (.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)))) (/.f64 (.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)))) (/.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 x x) x) #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)) #s(literal 1 binary64)))) (/.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (fma.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 x x) x) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (/.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)) #s(literal 1 binary64))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (/.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)) #s(literal 1 binary64))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) x) x) (-.f64 (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)))) (/.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x)) (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)))) (/.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (.f64 (.f64 (*.f64 x x) x) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (.f64 (.f64 (*.f64 x x) x) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (/.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (neg.f64 x) x) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(exp.f64 (.f64 (neg.f64 (log1p.f64 (.f64 x x))) #s(literal -1 binary64)))
(exp.f64 (log1p.f64 (*.f64 x x)))
(+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (neg.f64 (.f64 (.f64 (*.f64 x x) x) (/.f64 x (fma.f64 x x #s(literal 1 binary64))))))
(+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64))) (neg.f64 (/.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(+.f64 (*.f64 (neg.f64 x) x) #s(literal 1 binary64))
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 x)) x))
(+.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (neg.f64 x) x)))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(.f64 #s(literal 1 binary64) (.f64 x x))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval83.0ms (2.3%)

Memory: -44.3MiB live, 130.9MiB allocated
Compiler: Compiled 16 505 to 1 237 computations (92.5% saved)

prune67.0ms (1.8%)

Memory

-1.2MiB live, 121.4MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	389	2	391
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	389	3	392

Accuracy

100.0%

Counts

392 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
▶	99.5%	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
▶	98.8%	#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Status

Accuracy

Program

✓

100.0%

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

▶

99.5%

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

▶

98.8%

#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify350.0ms (9.6%)

Memory

2.7MiB live, 280.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

37 974×	`lower-fma.f32`
37 972×	`lower-fma.f64`
4 830×	`lower-*.f32`
4 828×	`lower-*.f64`
2 582×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	34
0	13	34
1	24	34
2	34	34
3	42	34
4	57	34
5	77	34
6	120	34
7	322	34
8	606	34
9	1204	34
10	2236	34
11	3244	34
12	3987	34
13	4283	34
14	4593	34
15	4749	34
16	4826	34
17	5035	34
18	5798	34
19	6004	34
20	7685	34
0	8151	34

Stop Event

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

Calls

Call 1

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

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

localize19.0ms (0.5%)

Memory

29.0MiB live, 29.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.32543699030728696	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
accuracy	0.755393819905255	#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Samples

14.0ms

256×

valid

Compiler

Compiled 28 to 10 computations (64.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-mult: 3.0ms (37.8% of total)

ival-sqrt: 2.0ms (25.2% of total)

ival-sub: 1.0ms (12.6% of total)

ival-add: 1.0ms (12.6% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

4.9MiB live, 4.9MiB allocated

Counts

4 → 48

Calls

Call 1

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

Outputs
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 (* x x))) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 ( x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 (* x x))) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 ( x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 (* x x))) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 ( x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 (* x x))) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 ( x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt -1)) (taylor inf x) (#s(alt #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (taylor inf x) (#s(alt #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))) (taylor inf x) (#s(alt #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))) (taylor inf x) (#s(alt #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt -1)) (taylor inf x) (#s(alt #s(approx (sqrt (- 1 (* x x))) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 ( x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (taylor inf x) (#s(alt #s(approx (sqrt (- 1 (* x x))) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 ( x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))) (taylor inf x) (#s(alt #s(approx (sqrt (- 1 (* x x))) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 ( x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))) (taylor inf x) (#s(alt #s(approx (sqrt (- 1 (* x x))) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 ( x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt -1))) (taylor -inf x) (#s(alt #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt -1))) (taylor -inf x) (#s(alt #s(approx (sqrt (- 1 (* x x))) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 ( x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (- 1 (* x x))) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 ( x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (- 1 (* x x))) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 ( x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (- 1 (* x x))) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 ( x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

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

0.0ms

-inf

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

0.0ms

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

simplify137.0ms (3.7%)

Memory

-4.3MiB live, 70.8MiB allocated

Algorithm

1×	egg-herbie

Rules

8 602×	`lower-fma.f64`
8 602×	`lower-fma.f32`
3 138×	`lower-*.f64`
3 138×	`lower-*.f32`
1 440×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	502
1	144	502
2	404	486
3	1258	458
4	3795	456
5	6250	456
0	8283	425

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* x (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(fma.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (sqrt.f64 #s(literal -1 binary64))))) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (sqrt.f64 #s(literal -1 binary64))))) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* x (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(fma.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (sqrt.f64 #s(literal -1 binary64))))) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (sqrt.f64 #s(literal -1 binary64))))) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* -1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* -1 (* x (sqrt -1)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64))) x (/.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
(fma.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))) (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (sqrt.f64 #s(literal -1 binary64)))))) x (/.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* -1 (* x (sqrt -1)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64))) x (/.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
(fma.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))) (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (sqrt.f64 #s(literal -1 binary64)))))) x (/.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* -1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite302.0ms (8.2%)

Memory

-6.1MiB live, 150.5MiB allocated

Rules

5 158×	`lower-fma.f32`
5 156×	`lower-fma.f64`
3 852×	`lower-*.f32`
3 850×	`lower-*.f64`
2 972×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
0	13	30
1	51	30
2	330	30
3	2676	30
0	8770	28

Stop Event

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

Counts

4 → 132

Calls

Call 1

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

Outputs
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))
#s(approx (sqrt (- 1 (* x x))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64)) (fma.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x)) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64)) (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) x)) x #s(literal 1 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x)) (.f64 (*.f64 x x) x) #s(literal 1 binary64)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x))) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x #s(literal -1 binary64)) (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1 binary64))) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x))))) (-.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x))))
(.f64 (/.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1 binary64)) (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64))) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))))) (fma.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x)) (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x)))))
(.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x #s(literal -1 binary64)) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x #s(literal -1 binary64))) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x)) (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x)) (.f64 (*.f64 x x) x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x)) (.f64 (*.f64 x x) x) #s(literal 1 binary64)))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) x)) x #s(literal -1 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) x)) x #s(literal -1 binary64)))
(.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) x)) x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))))) (neg.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))))) (neg.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) x)) x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) (neg.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) (neg.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x)) (.f64 (*.f64 x x) x) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 (.f64 x x) x) x) (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))))) (.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))))) (neg.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))) (/.f64 #s(literal -1 binary64) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64))) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))))) (/.f64 #s(literal -1 binary64) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64))) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))))) (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))) (.f64 (.f64 (.f64 (.f64 x x) x) x) (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))) (fma.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x #s(literal -1 binary64))))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x)) #s(literal -1 binary64)) #s(literal 1 binary64))) (neg.f64 (.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x #s(literal 1 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) #s(literal -1 binary64)) #s(literal 1 binary64))) (neg.f64 (.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x #s(literal 1 binary64))) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) #s(literal -1 binary64)) #s(literal 1 binary64))) (neg.f64 (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1 binary64)) (fma.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
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(/.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x #s(literal -1 binary64))) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))
(/.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x #s(literal -1 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64)))
(/.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1 binary64)) (fma.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) x)) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x #s(literal -1 binary64))) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64))))
(neg.f64 (/.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1 binary64)) (fma.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(neg.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))))
(neg.f64 (/.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1 binary64)) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(fma.f64 (exp.f64 (log.f64 #s(literal -1/2 binary64))) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (exp.f64 (log.f64 (*.f64 #s(literal -1/2 binary64) x))) x #s(literal 1 binary64))
(fma.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64))
(fma.f64 (/.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x) (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1 binary64))) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))))
(fma.f64 (/.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x #s(literal -1 binary64))) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))))
(fma.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) x) x) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))))
(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) x) (/.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))))
(fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 (.f64 x x) x) x) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(fma.f64 (.f64 (.f64 (.f64 x x) x) x) (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))))
(fma.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) x) x) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) (exp.f64 (log.f64 #s(literal -1/2 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 x (exp.f64 (log.f64 (*.f64 #s(literal -1/2 binary64) x))) #s(literal 1 binary64))
(fma.f64 x (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 x (/.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) x) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))))
(fma.f64 x (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) (/.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) x) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))))
(-.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)))) #s(literal -1 binary64)))
(+.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(.f64 #s(literal 1 binary64) (.f64 x x))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval65.0ms (1.8%)

Memory: -12.9MiB live, 24.2MiB allocated
Compiler: Compiled 5 182 to 390 computations (92.5% saved)

prune16.0ms (0.4%)

Memory

25.4MiB live, 25.4MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	180	3	183

Accuracy

100.0%

Counts

183 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

100.0%

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

✓

99.5%

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

✓

98.8%

#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Compiler

Compiled 34 to 19 computations (44.1% saved)

regimes6.0ms (0.2%)

Memory

8.1MiB live, 8.1MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

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

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

Outputs
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

Calls

4 calls:

2.0ms	x
1.0ms	(*.f64 x x)
1.0ms	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
1.0ms	(-.f64 #s(literal 1 binary64) (*.f64 x x))

Results

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

Compiler

Compiled 19 to 12 computations (36.8% saved)

regimes44.0ms (1.2%)

Memory

-42.2MiB live, 9.3MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

4 calls:

40.0ms	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
2.0ms	x
1.0ms	(*.f64 x x)
1.0ms	(-.f64 #s(literal 1 binary64) (*.f64 x x))

Results

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

Compiler

Compiled 19 to 12 computations (36.8% saved)

regimes4.0ms (0.1%)

Memory

9.4MiB live, 9.4MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Outputs
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Calls

4 calls:

1.0ms	x
1.0ms	(*.f64 x x)
1.0ms	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
1.0ms	(-.f64 #s(literal 1 binary64) (*.f64 x x))

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
98.8%	1	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
98.8%	1	`(*.f64 x x)`

Compiler

Compiled 19 to 12 computations (36.8% saved)

simplify7.0ms (0.2%)

Memory

11.5MiB live, 11.5MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`*-commutative_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	27
1	20	27
2	27	27
3	31	27
4	33	27

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

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

#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Outputs

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

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

#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

soundness263.0ms (7.2%)

Memory

-12.3MiB live, 97.5MiB allocated

Rules

8 366×	`lower-fma.f64`
8 366×	`lower-fma.f32`
3 130×	`lower-*.f64`
3 130×	`lower-*.f32`
1 412×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	295
1	149	286
2	419	278
3	1279	264
4	3834	263
5	6189	263
0	8166	252

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 25 to 14 computations (44% saved)

preprocess112.0ms (3.1%)

Memory: 26.9MiB live, 70.8MiB allocated
Remove: (abs x)
Compiler: Compiled 74 to 44 computations (40.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze3.0ms (0.1%)

sample811.0ms (22.1%)

explain74.0ms (2%)

preprocess519.0ms (14.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify325.0ms (8.9%)

localize105.0ms (2.9%)

series3.0ms (0.1%)

simplify113.0ms (3.1%)

rewrite234.0ms (6.4%)

eval83.0ms (2.3%)

prune67.0ms (1.8%)

simplify350.0ms (9.6%)

localize19.0ms (0.5%)

series3.0ms (0.1%)

simplify137.0ms (3.7%)

rewrite302.0ms (8.2%)

eval65.0ms (1.8%)

prune16.0ms (0.4%)

regimes6.0ms (0.2%)

regimes44.0ms (1.2%)

regimes4.0ms (0.1%)

simplify7.0ms (0.2%)

soundness263.0ms (7.2%)

preprocess112.0ms (3.1%)

end0.0ms (0%)

Profiling