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

analyze2.0ms (0%)

Memory

4.7MiB live, 4.7MiB 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)

sample723.0ms (8.1%)

Memory

-7.5MiB live, 1 092.9MiB allocated

Samples

519.0ms	8 256×	0	valid
0.0ms	5×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 200.0ms

ival-mult: 88.0ms (43.9% of total)

ival-sqrt: 59.0ms (29.4% of total)

ival-sub: 41.0ms (20.5% of total)

ival-true: 5.0ms (2.5% of total)

exact: 4.0ms (2% of total)

ival-assert: 3.0ms (1.5% of total)

Bogosity

preprocess724.0ms (8.1%)

Memory

-3.6MiB live, 852.2MiB 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)

explain67.0ms (0.7%)

Memory

-6.5MiB live, 109.0MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

24.0ms

512×

valid

Compiler

Compiled 50 to 24 computations (52% saved)

Precisions

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

ival-mult: 4.0ms (38% of total)

ival-sqrt: 4.0ms (38% of total)

ival-sub: 2.0ms (19% 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: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify1.0s (11.1%)

Memory

14.8MiB live, 703.8MiB 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

localize41.0ms (0.5%)

Memory

-2.3MiB live, 39.1MiB allocated

Localize:

Found 3 expressions of interest:

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

Samples

34.0ms

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 (39% of total)

ival-sqrt: 2.0ms (39% of total)

ival-sub: 1.0ms (19.5% 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

5.9MiB live, 5.9MiB 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)

rewrite340.0ms (3.8%)

Memory

5.0MiB live, 658.7MiB 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)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64))) (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (-.f64 (.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))) (.f64 (fma.f64 x (.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)) (.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 x (.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x (.f64 x (.f64 x x)))))) (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 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 binary64))) (sqrt.f64 (.f64 (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)) (fma.f64 x (*.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)))))
(/.f64 (sqrt.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)))))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 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 (sqrt.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)))))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (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 (sqrt.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))) (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (sqrt.f64 (neg.f64 (neg.f64 (fma.f64 x (.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x)))))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (/.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 x (.f64 x (fma.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))))) (pow.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (fma.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))) (fma.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (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 x (.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (*.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))))))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))))) (/.f64 (.f64 (.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 x x #s(literal 1 binary64)) (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))))))) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 x x #s(literal 1 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (.f64 x (.f64 x (*.f64 x x))) (fma.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 (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))

simplify256.0ms (2.9%)

Memory

16.8MiB live, 508.9MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	295
1	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)

eval57.0ms (0.6%)

Memory: -19.7MiB live, 133.7MiB allocated
Compiler: Compiled 16 469 to 1 243 computations (92.5% saved)

prune44.0ms (0.5%)

Memory

-0.0MiB live, 121.7MiB allocated

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	388	3	391
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	388	4	392

Accuracy

100.0%

Counts

392 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
▶	100.0%	(/.f64 (sqrt.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (sqrt.f64 (neg.f64 (neg.f64 (fma.f64 x (.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))))))
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
▶	99.6%	#s(literal 1 binary64)

Compiler

Compiled 45 to 29 computations (35.6% saved)

simplify563.0ms (6.3%)

Memory

-5.2MiB live, 670.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
✓	cost-diff	0	(sqrt.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))))
✓	cost-diff	0	(/.f64 (sqrt.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (sqrt.f64 (neg.f64 (neg.f64 (fma.f64 x (.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))))))
✓	cost-diff	128	(+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))
✓	cost-diff	256	(neg.f64 (neg.f64 (fma.f64 x (*.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))))

Rules

19 872×	`lower-fma.f32`
19 866×	`lower-fma.f64`
3 550×	`lower-*.f32`
3 540×	`lower-*.f64`
2 268×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	164
0	36	134
1	76	103
2	165	103
3	404	103
4	687	103
5	1156	103
6	1760	103
7	2671	103
8	3728	103
9	5001	103
10	5960	103
11	6468	103
12	6876	103
13	6926	103
14	6943	103
15	7293	103
16	7646	103
0	8040	102

Stop Event

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

Calls

Call 1

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

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

localize63.0ms (0.7%)

Memory

34.3MiB live, 108.9MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(sqrt.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)))))
✓	accuracy	99.9%	(.f64 x (.f64 x (*.f64 x x)))
✓	accuracy	99.9%	(.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))))
✓	accuracy	99.9%	(.f64 x (.f64 x x))

Samples

37.0ms

256×

valid

Compiler

Compiled 179 to 23 computations (87.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-mult: 10.0ms (43.7% of total)

ival-add: 4.0ms (17.5% of total)

ival-sqrt: 3.0ms (13.1% of total)

ival-neg: 3.0ms (13.1% of total)

ival-div: 2.0ms (8.7% of total)

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

exact: 0.0ms (0% of total)

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

series18.0ms (0.2%)

Memory

-51.1MiB live, 16.5MiB allocated

Counts

10 → 120

Calls

Call 1

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

Outputs
#<alt 1>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (* (pow x 2) (+ 1 (pow x 2))))>
#<alt (+ 1 (* (pow x 2) (+ 1 (pow x 2))))>
#<alt (pow x 4)>
#<alt (* (pow x 4) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 4) (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))))>
#<alt (pow x 4)>
#<alt (* (pow x 4) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 4) (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))))>
#<alt -1>
#<alt (- (pow x 6) 1)>
#<alt (- (pow x 6) 1)>
#<alt (- (pow x 6) 1)>
#<alt (pow x 6)>
#<alt (* (pow x 6) (- 1 (/ 1 (pow x 6))))>
#<alt (* (pow x 6) (- 1 (/ 1 (pow x 6))))>
#<alt (* (pow x 6) (- 1 (/ 1 (pow x 6))))>
#<alt (pow x 6)>
#<alt (* (pow x 6) (- 1 (/ 1 (pow x 6))))>
#<alt (* (pow x 6) (- 1 (/ 1 (pow x 6))))>
#<alt (* (pow x 6) (- 1 (/ 1 (pow x 6))))>
#<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 6)))>
#<alt (+ 1 (* (pow x 6) (- (* -1/8 (pow x 6)) 1/2)))>
#<alt (+ 1 (* (pow x 6) (- (* (pow x 6) (- (* -1/16 (pow x 6)) 1/8)) 1/2)))>
#<alt (* (pow x 3) (sqrt -1))>
#<alt (* (pow x 3) (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 6) (sqrt -1))))))>
#<alt (* (pow x 3) (- (+ (sqrt -1) (/ 1/2 (* (pow x 6) (sqrt -1)))) (/ 1/8 (* (pow x 12) (pow (sqrt -1) 3)))))>
#<alt (* (pow x 3) (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 6) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 18) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 12) (pow (sqrt -1) 3))))))>
#<alt (* -1 (* (pow x 3) (sqrt -1)))>
#<alt (* -1 (* (pow x 3) (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 6) (sqrt -1)))))))>
#<alt (* -1 (* (pow x 3) (- (+ (sqrt -1) (/ 1/2 (* (pow x 6) (sqrt -1)))) (/ 1/8 (* (pow x 12) (pow (sqrt -1) 3))))))>
#<alt (* -1 (* (pow x 3) (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 6) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 18) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 12) (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 (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 6)>
#<alt (pow x 6)>
#<alt (pow x 6)>
#<alt (pow x 6)>
#<alt (pow x 6)>
#<alt (pow x 6)>
#<alt (pow x 6)>
#<alt (pow x 6)>
#<alt (pow x 6)>
#<alt (pow x 6)>
#<alt (pow x 6)>
#<alt (pow x 6)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt 1>
#<alt (+ 1 (* 1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (+ 1/2 (* 3/8 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 3/8 (* -3/16 (pow x 2)))))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (+ (/ 3/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* (pow x 2) (- (+ 1 (+ (/ 3/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2))))) (* 3/16 (/ 1 (pow x 6)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (+ (/ 3/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* (pow x 2) (- (+ 1 (+ (/ 3/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2))))) (* 3/16 (/ 1 (pow x 6)))))>

Calls

30 calls:

Time	Variable		Point	Expression
11.0ms	x	@	0	(sqrt (neg (+ -1 (* (* x x) (* x (* x (* x x)))))))
1.0ms	x	@	inf	(sqrt (neg (+ -1 (* (* x x) (* x (* x (* x x)))))))
0.0ms	x	@	0	(+ (* -1/2 (* x x)) 1)
0.0ms	x	@	inf	(+ -1 (* (* x x) (* x (* x (* x x)))))
0.0ms	x	@	0	(neg (neg (+ (* x (* x (+ (* x x) 1))) 1)))

rewrite380.0ms (4.2%)

Memory

28.7MiB live, 567.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

10 794×	`lower-fma.f32`
10 788×	`lower-fma.f64`
5 368×	`lower-*.f32`
5 358×	`lower-*.f64`
3 426×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	111
0	36	84
1	137	52
2	887	52
0	8704	52

Stop Event

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

Counts

10 → 446

Calls

Call 1

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

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

simplify543.0ms (6%)

Memory

17.0MiB live, 853.3MiB allocated

Algorithm

1×	egg-herbie

Rules

21 214×	`lower-fma.f64`
21 214×	`lower-fma.f32`
4 236×	`lower-*.f64`
4 236×	`lower-*.f32`
3 362×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	140	926
1	377	914
2	1091	866
3	3923	844
4	7852	844
0	8026	796

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
1
(+ 1 (pow x 2))
(+ 1 (* (pow x 2) (+ 1 (pow x 2))))
(+ 1 (* (pow x 2) (+ 1 (pow x 2))))
(pow x 4)
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(* (pow x 4) (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))))
(* (pow x 4) (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))))
(pow x 4)
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(* (pow x 4) (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))))
(* (pow x 4) (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))))
-1
(- (pow x 6) 1)
(- (pow x 6) 1)
(- (pow x 6) 1)
(pow x 6)
(* (pow x 6) (- 1 (/ 1 (pow x 6))))
(* (pow x 6) (- 1 (/ 1 (pow x 6))))
(* (pow x 6) (- 1 (/ 1 (pow x 6))))
(pow x 6)
(* (pow x 6) (- 1 (/ 1 (pow x 6))))
(* (pow x 6) (- 1 (/ 1 (pow x 6))))
(* (pow x 6) (- 1 (/ 1 (pow x 6))))
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 6)))
(+ 1 (* (pow x 6) (- (* -1/8 (pow x 6)) 1/2)))
(+ 1 (* (pow x 6) (- (* (pow x 6) (- (* -1/16 (pow x 6)) 1/8)) 1/2)))
(* (pow x 3) (sqrt -1))
(* (pow x 3) (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 6) (sqrt -1))))))
(* (pow x 3) (- (+ (sqrt -1) (/ 1/2 (* (pow x 6) (sqrt -1)))) (/ 1/8 (* (pow x 12) (pow (sqrt -1) 3)))))
(* (pow x 3) (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 6) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 18) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 12) (pow (sqrt -1) 3))))))
(* -1 (* (pow x 3) (sqrt -1)))
(* -1 (* (pow x 3) (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 6) (sqrt -1)))))))
(* -1 (* (pow x 3) (- (+ (sqrt -1) (/ 1/2 (* (pow x 6) (sqrt -1)))) (/ 1/8 (* (pow x 12) (pow (sqrt -1) 3))))))
(* -1 (* (pow x 3) (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 6) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 18) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 12) (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)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 6)
(pow x 6)
(pow x 6)
(pow x 6)
(pow x 6)
(pow x 6)
(pow x 6)
(pow x 6)
(pow x 6)
(pow x 6)
(pow x 6)
(pow x 6)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* 3/8 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 3/8 (* -3/16 (pow x 2)))))))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1 (+ (/ 3/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2))))))
(* (pow x 2) (- (+ 1 (+ (/ 3/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2))))) (* 3/16 (/ 1 (pow x 6)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1 (+ (/ 3/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2))))))
(* (pow x 2) (- (+ 1 (+ (/ 3/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2))))) (* 3/16 (/ 1 (pow x 6)))))

Outputs
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1 (pow x 2))))
(fma.f64 x (fma.f64 x (*.f64 x x) x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1 (pow x 2))))
(fma.f64 x (fma.f64 x (*.f64 x x) x) #s(literal 1 binary64))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x x) x))
(* (pow x 4) (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))))
(fma.f64 x (fma.f64 x (*.f64 x x) x) #s(literal 1 binary64))
(* (pow x 4) (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))))
(fma.f64 x (fma.f64 x (*.f64 x x) x) #s(literal 1 binary64))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x x) x))
(* (pow x 4) (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))))
(fma.f64 x (fma.f64 x (*.f64 x x) x) #s(literal 1 binary64))
(* (pow x 4) (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))))
(fma.f64 x (fma.f64 x (*.f64 x x) x) #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(- (pow x 6) 1)
(+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))
(- (pow x 6) 1)
(+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))
(- (pow x 6) 1)
(+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))
(pow x 6)
(pow.f64 x #s(literal 6 binary64))
(* (pow x 6) (- 1 (/ 1 (pow x 6))))
(+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- 1 (/ 1 (pow x 6))))
(+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- 1 (/ 1 (pow x 6))))
(+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))
(pow x 6)
(pow.f64 x #s(literal 6 binary64))
(* (pow x 6) (- 1 (/ 1 (pow x 6))))
(+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- 1 (/ 1 (pow x 6))))
(+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- 1 (/ 1 (pow x 6))))
(+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #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 (.f64 x x) (.f64 (.f64 x 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))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 x (sqrt.f64 #s(literal -1 binary64)) (fma.f64 x (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 (.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)))
(*.f64 x (neg.f64 (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 (.f64 x x) (.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))))) (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 (neg.f64 x) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))) (fma.f64 x (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (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 6)))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 6) (- (* -1/8 (pow x 6)) 1/2)))
(fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 12 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(+ 1 (* (pow x 6) (- (* (pow x 6) (- (* -1/16 (pow x 6)) 1/8)) 1/2)))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/2 binary64) (fma.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/16 binary64) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)))
(* (pow x 3) (sqrt -1))
(.f64 (.f64 x x) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))
(* (pow x 3) (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 6) (sqrt -1))))))
(.f64 (.f64 x (.f64 x x)) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 #s(literal -1 binary64))))))
(* (pow x 3) (- (+ (sqrt -1) (/ 1/2 (* (pow x 6) (sqrt -1)))) (/ 1/8 (* (pow x 12) (pow (sqrt -1) 3)))))
(.f64 x (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 12 binary64))))))))
(* (pow x 3) (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 6) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 18) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 12) (pow (sqrt -1) 3))))))
(.f64 (.f64 x (.f64 x x)) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 x #s(literal 18 binary64))))) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 12 binary64)))))))
(* -1 (* (pow x 3) (sqrt -1)))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 6) (sqrt -1)))))))
(.f64 (.f64 x (.f64 x x)) (-.f64 (/.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* (pow x 3) (- (+ (sqrt -1) (/ 1/2 (* (pow x 6) (sqrt -1)))) (/ 1/8 (* (pow x 12) (pow (sqrt -1) 3))))))
(.f64 (.f64 x (.f64 x x)) (-.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 12 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 #s(literal -1 binary64))))))
(* -1 (* (pow x 3) (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 6) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 18) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 12) (pow (sqrt -1) 3)))))))
(.f64 (.f64 x (.f64 x x)) (-.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 12 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 x #s(literal 18 binary64)))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(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 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 6)
(pow.f64 x #s(literal 6 binary64))
(pow x 6)
(pow.f64 x #s(literal 6 binary64))
(pow x 6)
(pow.f64 x #s(literal 6 binary64))
(pow x 6)
(pow.f64 x #s(literal 6 binary64))
(pow x 6)
(pow.f64 x #s(literal 6 binary64))
(pow x 6)
(pow.f64 x #s(literal 6 binary64))
(pow x 6)
(pow.f64 x #s(literal 6 binary64))
(pow x 6)
(pow.f64 x #s(literal 6 binary64))
(pow x 6)
(pow.f64 x #s(literal 6 binary64))
(pow x 6)
(pow.f64 x #s(literal 6 binary64))
(pow x 6)
(pow.f64 x #s(literal 6 binary64))
(pow x 6)
(pow.f64 x #s(literal 6 binary64))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* 3/8 (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 3/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 3/8 (* -3/16 (pow x 2)))))))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -3/16 binary64) #s(literal 3/8 binary64)) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal 1/2 binary64))
(* (pow x 2) (+ 1 (+ (/ 3/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1/2 binary64) (fma.f64 x x (/.f64 #s(literal 3/8 binary64) (*.f64 x x))))
(* (pow x 2) (- (+ 1 (+ (/ 3/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2))))) (* 3/16 (/ 1 (pow x 6)))))
(fma.f64 x (+.f64 x (.f64 (/.f64 #s(literal -3/16 binary64) (pow.f64 x #s(literal 6 binary64))) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) (.f64 x x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal 1/2 binary64))
(* (pow x 2) (+ 1 (+ (/ 3/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1/2 binary64) (fma.f64 x x (/.f64 #s(literal 3/8 binary64) (*.f64 x x))))
(* (pow x 2) (- (+ 1 (+ (/ 3/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2))))) (* 3/16 (/ 1 (pow x 6)))))
(fma.f64 x (+.f64 x (.f64 (/.f64 #s(literal -3/16 binary64) (pow.f64 x #s(literal 6 binary64))) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) (.f64 x x))))

eval163.0ms (1.8%)

Memory: 17.5MiB live, 165.7MiB allocated
Compiler: Compiled 20 982 to 1 996 computations (90.5% saved)

prune64.0ms (0.7%)

Memory

-5.4MiB live, 145.6MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	605	1	606
Fresh	0	0	0
Picked	1	2	3
Done	0	1	1
Total	606	4	610

Accuracy

100.0%

Counts

610 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
▶	100.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	99.6%	#s(literal 1 binary64)

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify965.0ms (10.7%)

Memory

-115.7MiB live, 1 160.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

37 598×	`lower-fma.f64`
37 598×	`lower-fma.f32`
4 686×	`lower-*.f32`
4 684×	`lower-*.f64`
2 534×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	35
0	12	35
1	19	35
2	26	35
3	34	35
4	49	35
5	71	35
6	125	35
7	339	35
8	642	35
9	1221	35
10	2230	35
11	3126	35
12	3822	35
13	4125	35
14	4426	35
15	4586	35
16	4660	35
17	4871	35
18	5638	35
19	5836	35
20	7508	35
0	8031	32

Stop Event

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

Calls

Call 1

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

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

localize25.0ms (0.3%)

Memory

-15.2MiB live, 63.0MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

15.0ms

256×

valid

Compiler

Compiled 37 to 9 computations (75.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-div: 3.0ms (33.6% of total)

ival-mult: 3.0ms (33.6% of total)

ival-sqrt: 2.0ms (22.4% of total)

ival-sub: 1.0ms (11.2% 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

6.2MiB live, 6.2MiB allocated

Counts

5 → 60

Calls

Call 1

Inputs
#<alt (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x)))>
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.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 (pow x 2))>
#<alt (+ 1 (* (pow x 2) (+ 1 (pow x 2))))>
#<alt (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1 (pow x 2))))))>
#<alt (/ -1 (pow x 2))>
#<alt (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 2)))>
#<alt (/ (- (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 2))) 1) (pow x 2))>
#<alt (/ (- (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 4))) (+ 1 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 2)))>
#<alt (/ (- (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 2))) 1) (pow x 2))>
#<alt (/ (- (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 4))) (+ 1 (/ 1 (pow x 2)))) (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 (* 1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (+ 1/2 (* 3/8 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 3/8 (* 5/16 (pow x 2)))))))>
#<alt (/ (sqrt -1) x)>
#<alt (/ (- (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))) x)>
#<alt (/ (- (+ (sqrt -1) (* -1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (* (pow x 4) (sqrt -1))))) (/ 1/2 (* (pow x 2) (sqrt -1)))) x)>
#<alt (/ (- (+ (sqrt -1) (+ (* -1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (* (pow x 4) (sqrt -1)))) (* -1/2 (/ (+ 1 (* 1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* (pow x 6) (sqrt -1)))))) (/ 1/2 (* (pow x 2) (sqrt -1)))) x)>
#<alt (* -1 (/ (sqrt -1) x))>
#<alt (* -1 (/ (- (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))) x))>
#<alt (* -1 (/ (- (+ (sqrt -1) (* -1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (* (pow x 4) (sqrt -1))))) (/ 1/2 (* (pow x 2) (sqrt -1)))) x))>
#<alt (* -1 (/ (- (+ (sqrt -1) (+ (* -1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (* (pow x 4) (sqrt -1)))) (* -1/2 (/ (+ 1 (* 1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* (pow x 6) (sqrt -1)))))) (/ 1/2 (* (pow x 2) (sqrt -1)))) x))>
#<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

15 calls:

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

rewrite130.0ms (1.4%)

Memory

1.9MiB live, 196.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

1 014×	`lower-*.f32`
1 012×	`lower-*.f64`
888×	`lower-fma.f64`
888×	`lower-fma.f32`
848×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	33
0	12	33
1	53	28
2	294	28
0	2112	27

Stop Event

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

Counts

5 → 308

Calls

Call 1

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

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

simplify360.0ms (4%)

Memory

16.7MiB live, 644.5MiB allocated

Algorithm

1×	egg-herbie

Rules

13 322×	`lower-fma.f64`
13 322×	`lower-fma.f32`
3 792×	`lower-*.f64`
3 792×	`lower-*.f32`
2 240×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	119	699
1	329	614
2	965	598
3	2883	573
0	8132	551

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

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

eval54.0ms (0.6%)

Memory: 4.2MiB live, 128.2MiB allocated
Compiler: Compiled 8 447 to 1 280 computations (84.8% saved)

prune43.0ms (0.5%)

Memory

22.5MiB live, 103.4MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	367	1	368
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	368	4	372

Accuracy

100.0%

Counts

372 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
▶	100.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64)))))
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	99.6%	#s(literal 1 binary64)

Compiler

Compiled 26 to 19 computations (26.9% saved)

simplify684.0ms (7.6%)

Memory

4.6MiB live, 955.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

29 686×	`lower-fma.f32`
29 684×	`lower-fma.f64`
4 178×	`lower-*.f64`
4 178×	`lower-*.f32`
2 800×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	29
0	12	29
1	18	29
2	24	29
3	41	29
4	72	29
5	138	29
6	298	29
7	581	29
8	2055	29
9	3167	29
10	4457	29
11	5139	29
12	5432	29
13	5619	29
14	5701	29
15	6015	29
16	6561	29
17	7672	29
0	8092	29

Stop Event

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

Calls

Call 1

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

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

localize58.0ms (0.6%)

Memory

-3.8MiB live, 34.2MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

15.0ms

256×

valid

Compiler

Compiled 35 to 10 computations (71.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-div: 3.0ms (35% of total)

ival-mult: 2.0ms (23.4% of total)

ival-sqrt: 2.0ms (23.4% of total)

ival-add: 1.0ms (11.7% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0%)

Memory

4.9MiB live, 4.9MiB allocated

Counts

4 → 48

Calls

Call 1

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

Outputs
#<alt 1>
#<alt (+ 1 (* 1/2 (/ (pow x 2) (pow (sqrt -1) 2))))>
#<alt (+ 1 (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 4))) (* 1/2 (/ 1 (pow (sqrt -1) 2))))))>
#<alt (+ 1 (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 6))) (* 1/8 (/ 1 (pow (sqrt -1) 4))))) (* 1/2 (/ 1 (pow (sqrt -1) 2))))))>
#<alt (/ x (sqrt -1))>
#<alt (* x (- (/ 1 (sqrt -1)) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))>
#<alt (* x (+ (* -1 (/ (+ (* 1/2 (/ 1 (sqrt -1))) (* 1/8 (/ 1 (* (pow x 2) (sqrt -1))))) (pow x 2))) (/ 1 (sqrt -1))))>
#<alt (* x (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (sqrt -1))) (* 1/16 (/ 1 (* (pow x 2) (sqrt -1))))) (pow x 4))) (/ 1 (sqrt -1))) (/ 1/2 (* (pow x 2) (sqrt -1)))))>
#<alt (* -1 (/ x (sqrt -1)))>
#<alt (* -1 (* x (- (/ 1 (sqrt -1)) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ (* 1/2 (/ 1 (sqrt -1))) (* 1/8 (/ 1 (* (pow x 2) (sqrt -1))))) (pow x 2))) (/ 1 (sqrt -1)))))>
#<alt (* -1 (* x (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (sqrt -1))) (* 1/16 (/ 1 (* (pow x 2) (sqrt -1))))) (pow x 4))) (/ 1 (sqrt -1))) (/ 1/2 (* (pow x 2) (sqrt -1))))))>
#<alt (pow (sqrt -1) 2)>
#<alt (+ (* -1/2 (pow x 2)) (pow (sqrt -1) 2))>
#<alt (+ (* (pow x 2) (- (* -1/2 (* (pow x 2) (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))))) 1/2)) (pow (sqrt -1) 2))>
#<alt (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/2 (* (pow x 2) (+ 1 (* 1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))))) (* -1/2 (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2))))))) 1/2)) (pow (sqrt -1) 2))>
#<alt (/ (sqrt -1) x)>
#<alt (/ (+ (sqrt -1) (* 1/2 (/ (sqrt -1) (pow x 2)))) x)>
#<alt (/ (+ (sqrt -1) (+ (* 3/8 (/ (sqrt -1) (pow x 4))) (* 1/2 (/ (sqrt -1) (pow x 2))))) x)>
#<alt (/ (+ (sqrt -1) (+ (* 5/16 (/ (sqrt -1) (pow x 6))) (+ (* 3/8 (/ (sqrt -1) (pow x 4))) (* 1/2 (/ (sqrt -1) (pow x 2)))))) x)>
#<alt (* -1 (/ (sqrt -1) x))>
#<alt (* -1 (/ (+ (sqrt -1) (* 1/2 (/ (sqrt -1) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (sqrt -1) (+ (* 3/8 (/ (sqrt -1) (pow x 4))) (* 1/2 (/ (sqrt -1) (pow x 2))))) x))>
#<alt (* -1 (/ (+ (sqrt -1) (+ (* 5/16 (/ (sqrt -1) (pow x 6))) (+ (* 3/8 (/ (sqrt -1) (pow x 4))) (* 1/2 (/ (sqrt -1) (pow x 2)))))) x))>
#<alt 1>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (* (pow x 2) (+ 1 (pow x 2))))>
#<alt (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1 (pow x 2))))))>
#<alt (/ -1 (pow x 2))>
#<alt (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 2)))>
#<alt (/ (- (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 2))) 1) (pow x 2))>
#<alt (/ (- (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 4))) (+ 1 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ -1 (pow x 2))>
#<alt (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 2)))>
#<alt (/ (- (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 2))) 1) (pow x 2))>
#<alt (/ (- (* -1 (/ (+ 1 (/ 1 (pow x 2))) (pow x 4))) (+ 1 (/ 1 (pow x 2)))) (pow x 2))>
#<alt -1>
#<alt (- (pow x 2) 1)>
#<alt (- (pow x 2) 1)>
#<alt (- (pow x 2) 1)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>

Calls

12 calls:

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

rewrite243.0ms (2.7%)

Memory

-32.7MiB live, 454.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 982×	`lower-/.f32`
2 978×	`lower-/.f64`
2 520×	`lower-fma.f32`
2 518×	`lower-fma.f64`
1 780×	`lower-*.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	7	26
0	12	26
1	52	25
2	300	23
3	2479	21
0	9207	21

Stop Event

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

Counts

4 → 755

Calls

Call 1

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

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

simplify434.0ms (4.8%)

Memory

74.9MiB live, 861.3MiB allocated

Algorithm

1×	egg-herbie

Rules

18 370×	`lower-fma.f64`
18 370×	`lower-fma.f32`
5 624×	`lower-*.f64`
5 624×	`lower-*.f32`
3 488×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	125	667
1	345	589
2	1136	583
3	3876	551
0	8509	516

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval115.0ms (1.3%)

Memory: -7.5MiB live, 326.0MiB allocated
Compiler: Compiled 24 409 to 3 151 computations (87.1% saved)

prune123.0ms (1.4%)

Memory

-28.4MiB live, 291.7MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	803	0	803
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	803	4	807

Accuracy

100.0%

Counts

807 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
✓	100.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64)))))
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	99.6%	#s(literal 1 binary64)

Compiler

Compiled 87 to 47 computations (46% saved)

regimes8.0ms (0.1%)

Memory

23.3MiB live, 23.3MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

regimes25.0ms (0.3%)

Memory

-23.1MiB live, 16.5MiB allocated

Counts

3 → 1

Calls

Call 1

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

20.0ms	x
1.0ms	(*.f64 x x)
1.0ms	(-.f64 #s(literal 1 binary64) (*.f64 x x))
1.0ms	(sqrt.f64 (-.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)

regimes5.0ms (0.1%)

Memory

15.5MiB live, 15.5MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
99.8%	1	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
99.8%	1	`(*.f64 x x)`

Compiler

Compiled 19 to 12 computations (36.8% saved)

regimes4.0ms (0%)

Memory

16.5MiB live, 16.5MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)

Outputs
#s(literal 1 binary64)

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
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)

simplify12.0ms (0.1%)

Memory

-45.1MiB live, 20.1MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	20	22
2	26	22
3	30	22
4	32	22

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness611.0ms (6.8%)

Memory

13.4MiB live, 520.1MiB allocated

Rules

10 794×	`lower-fma.f32`
10 788×	`lower-fma.f64`
8 366×	`lower-fma.f64`
8 366×	`lower-fma.f32`
5 368×	`lower-*.f32`

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	19	111
0	36	84
1	137	52
2	887	52
0	8704	52
0	7	33
0	12	33
1	53	28
2	294	28
0	2112	27
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×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit

Compiler

Compiled 42 to 26 computations (38.1% saved)

preprocess29.0ms (0.3%)

Memory: 19.1MiB live, 57.3MiB allocated
Remove: (abs x)
Compiler: Compiled 100 to 62 computations (38% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0%)

sample723.0ms (8.1%)

preprocess724.0ms (8.1%)

explain67.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify1.0s (11.1%)

localize41.0ms (0.5%)

series2.0ms (0%)

rewrite340.0ms (3.8%)

simplify256.0ms (2.9%)

eval57.0ms (0.6%)

prune44.0ms (0.5%)

simplify563.0ms (6.3%)

localize63.0ms (0.7%)

series18.0ms (0.2%)

rewrite380.0ms (4.2%)

simplify543.0ms (6%)

eval163.0ms (1.8%)

prune64.0ms (0.7%)

simplify965.0ms (10.7%)

localize25.0ms (0.3%)

series2.0ms (0%)

rewrite130.0ms (1.4%)

simplify360.0ms (4%)

eval54.0ms (0.6%)

prune43.0ms (0.5%)

simplify684.0ms (7.6%)

localize58.0ms (0.6%)

series3.0ms (0%)

rewrite243.0ms (2.7%)

simplify434.0ms (4.8%)

eval115.0ms (1.3%)

prune123.0ms (1.4%)

regimes8.0ms (0.1%)

regimes25.0ms (0.3%)

regimes5.0ms (0.1%)

regimes4.0ms (0%)

simplify12.0ms (0.1%)

soundness611.0ms (6.8%)

preprocess29.0ms (0.3%)

end0.0ms (0%)

Profiling