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

analyze2.0ms (0%)

Memory

4.3MiB live, 4.3MiB 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)

sample765.0ms (11.3%)

Memory

-81.6MiB live, 747.8MiB allocated

Samples

573.0ms	8 256×	0	valid
0.0ms	3×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 184.0ms

ival-mult: 68.0ms (37% of total)

ival-sqrt: 57.0ms (31% of total)

ival-sub: 44.0ms (23.9% of total)

ival-true: 6.0ms (3.3% of total)

exact: 5.0ms (2.7% of total)

ival-assert: 3.0ms (1.6% of total)

Bogosity

preprocess911.0ms (13.4%)

Memory

33.3MiB live, 852.9MiB 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)

explain70.0ms (1%)

Memory

16.2MiB live, 135.2MiB 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

26.0ms

512×

valid

Compiler

Compiled 50 to 24 computations (52% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-mult: 8.0ms (52.9% of total)

ival-sqrt: 4.0ms (26.4% of total)

ival-sub: 2.0ms (13.2% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB 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)

simplify620.0ms (9.1%)

Memory

-18.5MiB live, 739.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

localize75.0ms (1.1%)

Memory

-26.1MiB live, 58.6MiB allocated

Localize:

Found 3 expressions of interest:

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

Samples

10.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-mult: 2.0ms (38.2% of total)

ival-sqrt: 2.0ms (38.2% of total)

ival-sub: 1.0ms (19.1% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

4.1MiB live, 4.0MiB allocated

Counts

3 → 36

Calls

Call 1

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

Outputs
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))>
#<alt (* x (sqrt -1))>
#<alt (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))>
#<alt (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))>
#<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))))))>
#<alt (* -1 (* x (sqrt -1)))>
#<alt (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))>
#<alt (* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))>
#<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)))))))>
#<alt 1>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

9 calls:

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

simplify223.0ms (3.3%)

Memory

-13.7MiB live, 374.1MiB 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	150	286
2	415	278
3	1271	264
4	3831	263
5	6202	263
0	8200	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)))
(* 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 (* 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
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(* -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))
(* -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)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 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 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/16 binary64)) #s(literal -1/8 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* x (sqrt -1))
(*.f64 x (sqrt.f64 #s(literal -1 binary64)))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(fma.f64 x (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(fma.f64 x (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* 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 x (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (.f64 x (.f64 x x))))))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (sqrt -1)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (.f64 x (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 x (-.f64 (/.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (.f64 x (.f64 x x))))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* -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 x (+.f64 (/.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (.f64 x (.f64 x x))))) (-.f64 (/.f64 #s(literal -1/16 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* -1 (pow x 2))
(*.f64 x (neg.f64 x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* -1 (pow x 2))
(*.f64 x (neg.f64 x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite312.0ms (4.6%)

Memory

-3.5MiB live, 635.4MiB allocated

Algorithm

1×	batch-egg-rewrite

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

eval54.0ms (0.8%)

Memory: 8.1MiB live, 124.2MiB allocated
Compiler: Compiled 16 505 to 1 243 computations (92.5% saved)

prune51.0ms (0.7%)

Memory

9.9MiB live, 88.6MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	388	3	391
Fresh	0	0	0
Picked	1	0	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 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
▶	99.6%	#s(approx (sqrt (- 1 (* x x))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
▶	99.2%	#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Status

Accuracy

Program

▶

100.0%

(sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))

▶

99.6%

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

▶

99.2%

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

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify1.2s (17.1%)

Memory

4.0MiB live, 692.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

Rules

37 974×	`lower-fma.f32`
37 970×	`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	13	49
0	20	49
1	33	49
2	41	49
3	52	49
4	65	49
5	85	49
6	145	49
7	349	49
8	625	49
9	1183	49
10	2195	49
11	3189	49
12	3933	49
13	4231	49
14	4541	49
15	4697	49
16	4774	49
17	4983	49
18	5746	49
19	5952	49
20	7633	49
0	8099	49

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

localize83.0ms (1.2%)

Memory

8.2MiB live, 46.0MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
✓	accuracy	100.0%	(neg.f64 x)
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
✓	accuracy	99.6%	#s(approx (sqrt (- 1 (* x x))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
✓	accuracy	99.2%	#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Samples

70.0ms

256×

valid

Compiler

Compiled 45 to 14 computations (68.9% saved)

Precisions

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

ival-mult: 5.0ms (37.1% of total)

ival-sqrt: 3.0ms (22.3% of total)

ival-add: 2.0ms (14.8% of total)

ival-sub: 1.0ms (7.4% of total)

ival-neg: 1.0ms (7.4% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

3.1MiB live, 3.1MiB allocated

Counts

7 → 84

Calls

Call 1

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

Outputs
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))>
#<alt (* x (sqrt -1))>
#<alt (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))>
#<alt (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))>
#<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))))))>
#<alt (* -1 (* x (sqrt -1)))>
#<alt (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))>
#<alt (* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))>
#<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)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))>
#<alt (* x (sqrt -1))>
#<alt (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))>
#<alt (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))>
#<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))))))>
#<alt (* -1 (* x (sqrt -1)))>
#<alt (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))>
#<alt (* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))>
#<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)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))>
#<alt (* x (sqrt -1))>
#<alt (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))>
#<alt (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))>
#<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))))))>
#<alt (* -1 (* x (sqrt -1)))>
#<alt (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))>
#<alt (* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))>
#<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)))))))>
#<alt 1>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>

Calls

21 calls:

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

simplify285.0ms (4.2%)

Memory

14.9MiB live, 518.6MiB allocated

Algorithm

1×	egg-herbie

Rules

9 464×	`lower-fma.f64`
9 464×	`lower-fma.f32`
3 072×	`lower-*.f64`
3 072×	`lower-*.f32`
1 530×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	785
1	156	776
2	425	752
3	1294	710
4	3978	707
5	6481	707
0	8169	665

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

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

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

rewrite295.0ms (4.3%)

Memory

-44.7MiB live, 487.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 298×	`lower-fma.f32`
4 294×	`lower-fma.f64`
2 736×	`lower-*.f32`
2 734×	`lower-*.f64`
1 752×	`lower-/.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	43
0	20	43
1	71	43
2	466	43
3	4263	38
0	8634	38

Stop Event

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

Counts

7 → 345

Calls

Call 1

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

Outputs
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))
#s(approx (sqrt (- 1 (* x x))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))
(+.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64)) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(-.f64 #s(literal 0 binary64) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64)) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64)) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/8 binary64))) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(fma.f64 x (neg.f64 (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))
(fma.f64 x (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 x (exp.f64 (log.f64 (*.f64 x #s(literal -1/2 binary64)))) #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 (.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))))
(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))
(fma.f64 (.f64 x x) (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #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 (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) (/.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))))
(fma.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (/.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/2 binary64)))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/2 binary64) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))))
(fma.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/4 binary64))) (/.f64 x (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (/.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))))
(fma.f64 (neg.f64 (*.f64 x #s(literal -1/2 binary64))) x #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) x #s(literal 1 binary64))
(fma.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64)) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))))
(fma.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64)) (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/8 binary64)) #s(literal -1 binary64))) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))))
(fma.f64 (exp.f64 (log.f64 (*.f64 x #s(literal -1/2 binary64)))) x #s(literal 1 binary64))
(fma.f64 (exp.f64 (log.f64 #s(literal -1/2 binary64))) (*.f64 x x) #s(literal 1 binary64))
(neg.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(neg.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (neg.f64 (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(neg.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (neg.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x x)))) #s(literal -1/512 binary64) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) #s(literal 1/64 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/8 binary64)) #s(literal 1 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) #s(literal 1/64 binary64) #s(literal -1 binary64)) (.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/8 binary64)) #s(literal -1 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) #s(literal 1/64 binary64) #s(literal -1 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) #s(literal 1/16 binary64) (fma.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64)))))
(/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/8 binary64)) #s(literal -1 binary64)) (neg.f64 (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) #s(literal 1/16 binary64) #s(literal -1 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64))))
(/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64)) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x x)))) #s(literal -1/512 binary64) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) #s(literal 1/64 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) #s(literal 1/64 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/8 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) #s(literal 1/64 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) #s(literal 1/16 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))
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(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)) (.f64 (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64)) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal -1 binary64)))) (fma.f64 x (fma.f64 x (*.f64 x x) x) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x (.f64 x (.f64 x x)) #s(literal 1 binary64))) #s(literal 1 binary64))) (fma.f64 (.f64 x (fma.f64 x (.f64 x x) x)) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 x (.f64 x (.f64 x x)) #s(literal 1 binary64)) #s(literal 1 binary64))) (fma.f64 x (fma.f64 x (*.f64 x x) x) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(.f64 (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 1 binary64)) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64)))
(.f64 (exp.f64 (log1p.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (exp.f64 (neg.f64 (log1p.f64 (.f64 x (fma.f64 x (.f64 x x) x))))))
(.f64 (exp.f64 (log.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1 binary64)))) (exp.f64 (neg.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64))))))
(.f64 (exp.f64 (.f64 #s(literal 2 binary64) (log1p.f64 (.f64 x x)))) (exp.f64 (neg.f64 (log1p.f64 (.f64 x x)))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
x
(+.f64 x #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) x)
(exp.f64 (log.f64 x))
(exp.f64 (-.f64 (.f64 (log.f64 (.f64 x x)) #s(literal 3/2 binary64)) (log.f64 (*.f64 x x))))
(exp.f64 (-.f64 (.f64 (log.f64 x) #s(literal 3 binary64)) (log.f64 (.f64 x x))))
(-.f64 #s(literal 0 binary64) x)
(-.f64 (/.f64 #s(literal 0 binary64) x) x)
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 x x)) x)
(fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))
(fma.f64 x #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 x #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) x #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) #s(literal 0 binary64))
(neg.f64 x)
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 x x) x)
(/.f64 (.f64 x (.f64 x x)) (*.f64 x x))
(/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) #s(literal 0 binary64))))
(pow.f64 x #s(literal 1 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/2 binary64))
(pow.f64 (/.f64 x (*.f64 x x)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) x)
(*.f64 x #s(literal 1 binary64))
(*.f64 x #s(literal -1 binary64))
(.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal -1 binary64) x)
(.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 x))

eval83.0ms (1.2%)

Memory: 14.0MiB live, 130.1MiB allocated
Compiler: Compiled 9 997 to 977 computations (90.2% saved)

prune47.0ms (0.7%)

Memory

9.3MiB live, 134.8MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	428	1	429
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	429	3	432

Accuracy

100.0%

Counts

432 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

100.0%

(sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))

▶

99.6%

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

✓

99.2%

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

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify676.0ms (10%)

Memory

7.3MiB live, 1 182.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New

Metric

Score

Program

✓

cost-diff

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

✓

cost-diff

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

✓

cost-diff

#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x #s(literal -1/2 binary64)) 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	9	25
0	12	25
1	23	25
2	32	25
3	40	25
4	55	25
5	75	25
6	118	25
7	317	25
8	600	25
9	1171	25
10	2197	25
11	3199	25
12	3942	25
13	4240	25
14	4550	25
15	4706	25
16	4783	25
17	4992	25
18	5755	25
19	5961	25
20	7642	25
0	8108	25

Stop Event

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

Calls

Call 1

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

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

localize29.0ms (0.4%)

Memory

-21.2MiB live, 34.5MiB allocated

Localize:

Found 3 expressions of interest:

New

Metric

Score

Program

✓

accuracy

100.0%

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

✓

accuracy

100.0%

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

✓

accuracy

99.6%

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

Samples

15.0ms

256×

valid

Compiler

Compiled 21 to 11 computations (47.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 5.0ms (52.5% of total)

ival-sqrt: 2.0ms (21% of total)

ival-sub: 1.0ms (10.5% of total)

ival-add: 1.0ms (10.5% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

2.1MiB live, 2.1MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs

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

#<alt (fma.f64 (*.f64 x #s(literal -1/2 binary64)) x #s(literal 1 binary64))>

#<alt (*.f64 x #s(literal -1/2 binary64))>

Outputs
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))>
#<alt (* x (sqrt -1))>
#<alt (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))>
#<alt (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))>
#<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))))))>
#<alt (* -1 (* x (sqrt -1)))>
#<alt (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))>
#<alt (* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))>
#<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)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>

Calls

9 calls:

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

simplify239.0ms (3.5%)

Memory

41.1MiB live, 394.2MiB 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	61	306
1	146	306
2	404	298
3	1255	284
4	3824	283
5	6220	283
0	8254	263

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

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

rewrite359.0ms (5.3%)

Memory

-33.1MiB live, 410.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 682×	`lower-fma.f32`
4 680×	`lower-fma.f64`
3 936×	`lower-/.f64`
3 936×	`lower-/.f32`
3 652×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
0	12	22
1	50	22
2	319	22
3	2584	22
0	9496	21

Stop Event

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

Counts

3 → 134

Calls

Call 1

Inputs

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

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

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

Outputs
#s(approx (sqrt (- 1 (* x x))) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))
(+.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) #s(literal -1 binary64)))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/64 binary64))) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/8 binary64) #s(literal -1 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/8 binary64) #s(literal -1 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/64 binary64))) (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/16 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64)))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/16 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64)))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/16 binary64)) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/8 binary64) #s(literal 1 binary64)) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/64 binary64))) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/8 binary64) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/8 binary64) #s(literal -1 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/64 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/16 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/16 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/16 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (.f64 (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 (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (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 (/.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/64 binary64))) (/.f64 #s(literal -1 binary64) (.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (.f64 (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)))))) (fma.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (fma.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))))))) (/.f64 (/.f64 #s(literal -1 binary64) (.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (.f64 (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))))) (fma.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (fma.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))))))))
(-.f64 (/.f64 (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))) (fma.f64 x (/.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))))) (/.f64 (.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64)))) (fma.f64 x (/.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))))))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(fma.f64 x (/.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
(fma.f64 x (pow.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 x (exp.f64 (log.f64 (*.f64 x #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 (.f64 x x) (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
(fma.f64 (*.f64 x x) (exp.f64 (log.f64 #s(literal -1/2 binary64))) #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (/.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/2 binary64)))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
(fma.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) (/.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
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(fma.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (/.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
(fma.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/4 binary64))) (/.f64 x (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
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(fma.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
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(fma.f64 (pow.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x #s(literal 1 binary64))
(fma.f64 (exp.f64 (log.f64 (*.f64 x #s(literal -1/2 binary64)))) x #s(literal 1 binary64))
(fma.f64 (exp.f64 (log.f64 #s(literal -1/2 binary64))) (*.f64 x x) #s(literal 1 binary64))
(neg.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/8 binary64) #s(literal 1 binary64)) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
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(neg.f64 (-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
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(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/4 binary64))))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
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(/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))
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(/.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) #s(literal -1/512 binary64) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/64 binary64) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1/8 binary64) #s(literal 1 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/64 binary64) #s(literal -1 binary64)) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/8 binary64) #s(literal -1 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/64 binary64) #s(literal -1 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/16 binary64) (fma.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))))
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(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/64 binary64))) (/.f64 #s(literal -1 binary64) (.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (.f64 (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 #s(literal -1 binary64) (.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (.f64 (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))))))) (neg.f64 (fma.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (fma.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))) (.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64)))))) (neg.f64 (fma.f64 x (/.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/8 binary64) #s(literal 1 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) #s(literal -1/512 binary64) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) (neg.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/64 binary64) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1/8 binary64) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/64 binary64) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))) (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/8 binary64) #s(literal -1 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/64 binary64) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))))) (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/16 binary64) (fma.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/16 binary64) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))))) (neg.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/8 binary64) #s(literal -1 binary64)))) (neg.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/4 binary64))))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64)))))
(.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (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 (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/8 binary64) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/8 binary64) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (fma.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1/8 binary64) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1/8 binary64) #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/8 binary64) #s(literal 1 binary64))) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))))) (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/8 binary64) #s(literal 1 binary64)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (.f64 (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 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/64 binary64))))) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/16 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/8 binary64) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (+.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (.f64 x (.f64 x #s(literal -1/2 binary64)))))) (+.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/8 binary64) #s(literal -1 binary64))) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) #s(literal -1/512 binary64) #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/64 binary64) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1/8 binary64) #s(literal 1 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/64 binary64) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/8 binary64) #s(literal -1 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/64 binary64) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/16 binary64) (fma.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/16 binary64) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64))))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)))
(*.f64 x #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) x)
(.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))

eval21.0ms (0.3%)

Memory: 2.1MiB live, 39.6MiB allocated
Compiler: Compiled 5 784 to 404 computations (93% saved)

prune18.0ms (0.3%)

Memory

11.8MiB live, 50.8MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	170	3	173

Accuracy

100.0%

Counts

173 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

100.0%

(sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))

✓

99.6%

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

✓

99.2%

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

Compiler

Compiled 47 to 24 computations (48.9% saved)

regimes8.0ms (0.1%)

Memory

19.7MiB live, 19.7MiB allocated

Counts

5 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))

Calls

4 calls:

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

regimes8.0ms (0.1%)

Memory

-20.8MiB live, 18.1MiB allocated

Counts

4 → 1

Calls

Call 1

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

3.0ms	(*.f64 x x)
2.0ms	x
2.0ms	(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)

regimes6.0ms (0.1%)

Memory

16.5MiB live, 16.5MiB 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 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))

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

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

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
99.6%	1	`x`
99.6%	1	`(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
99.6%	1	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
99.6%	1	`(*.f64 x x)`

Compiler

Compiled 19 to 12 computations (36.8% saved)

regimes7.0ms (0.1%)

Memory

-27.7MiB live, 12.7MiB 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:

4.0ms	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
99.2%	1	`x`
99.2%	1	`(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
99.2%	1	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
99.2%	1	`(*.f64 x x)`

Compiler

Compiled 19 to 12 computations (36.8% saved)

simplify7.0ms (0.1%)

Memory

16.2MiB live, 16.2MiB 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	15	33
1	25	33
2	31	33
3	34	33
4	35	33

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness332.0ms (4.9%)

Memory

-4.9MiB live, 226.1MiB allocated

Rules

8 366×	`lower-fma.f64`
8 366×	`lower-fma.f32`
4 716×	`lower-fma.f64`
4 716×	`lower-fma.f32`
4 136×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	295
1	150	286
2	415	278
3	1271	264
4	3831	263
5	6202	263
0	8200	252
0	5	14
0	8	14
1	32	14
2	187	14
3	1340	14
0	9365	12

Stop Event

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

Compiler

Compiled 44 to 25 computations (43.2% saved)

preprocess28.0ms (0.4%)

Memory: 34.6MiB live, 73.2MiB allocated
Remove: (abs x)
Compiler: Compiled 86 to 50 computations (41.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0%)

sample765.0ms (11.3%)

preprocess911.0ms (13.4%)

explain70.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify620.0ms (9.1%)

localize75.0ms (1.1%)

series2.0ms (0%)

simplify223.0ms (3.3%)

rewrite312.0ms (4.6%)

eval54.0ms (0.8%)

prune51.0ms (0.7%)

simplify1.2s (17.1%)

localize83.0ms (1.2%)

series2.0ms (0%)

simplify285.0ms (4.2%)

rewrite295.0ms (4.3%)

eval83.0ms (1.2%)

prune47.0ms (0.7%)

simplify676.0ms (10%)

localize29.0ms (0.4%)

series2.0ms (0%)

simplify239.0ms (3.5%)

rewrite359.0ms (5.3%)

eval21.0ms (0.3%)

prune18.0ms (0.3%)

regimes8.0ms (0.1%)

regimes8.0ms (0.1%)

regimes6.0ms (0.1%)

regimes7.0ms (0.1%)

simplify7.0ms (0.1%)

soundness332.0ms (4.9%)

preprocess28.0ms (0.4%)

end0.0ms (0%)

Profiling