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

analyze2.0ms (0%)

Memory

3.2MiB live, 3.2MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	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)

sample498.0ms (6.8%)

Memory

29.3MiB live, 727.7MiB allocated

Samples

346.0ms	8 256×	0	valid
0.0ms	4×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 180.0ms

ival-mult: 66.0ms (36.6% of total)

ival-sqrt: 58.0ms (32.2% of total)

ival-sub: 42.0ms (23.3% of total)

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

exact: 5.0ms (2.8% of total)

ival-assert: 3.0ms (1.7% of total)

Bogosity

preprocess892.0ms (12.2%)

Memory

18.3MiB live, 1 051.0MiB allocated

Algorithm

2×	egg-herbie

Rules

30 426×	`accelerator-lowering-fma.f32`
30 426×	`accelerator-lowering-fma.f64`
3 778×	`-lowering-.f32`
3 778×	`-lowering-.f64`
2 412×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	28	19
2	48	19
3	90	19
4	119	19
5	170	19
6	283	19
7	498	19
8	892	19
9	1458	19
10	3820	19
11	5529	19
12	6297	19
13	6595	19
14	6651	19
15	6683	19
16	6948	19
17	7542	19
0	5	6
1	12	6
2	19	6
3	27	6
4	42	6
5	62	6
6	105	6
7	299	6
8	580	6
9	1120	6
10	2014	6
11	3727	6
12	4682	6
13	5002	6
14	5288	6
15	5457	6
16	5534	6
17	5801	6
18	6799	6
19	7855	6
0	8240	6

Stop Event

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

Calls

Call 1

Inputs
(sqrt (- 1 (* x x)))

Outputs
(sqrt (- 1 (* x x)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))

Call 2

Inputs
(sqrt (- 1 (* x x)))
(sqrt (- 1 (* (neg x) (neg x))))
(neg (sqrt (- 1 (* (neg x) (neg x)))))

Outputs
(sqrt (- 1 (* x x)))
(sqrt (- 1 (* (neg x) (neg x))))
(sqrt (- 1 (* x x)))
(neg (sqrt (- 1 (* (neg x) (neg x)))))
(neg (sqrt (- 1 (* x x))))

Symmetry

(abs x)

explain73.0ms (1%)

Memory

-61.4MiB live, 151.2MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

37.0ms

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 (37.3% of total)

ival-sqrt: 4.0ms (37.3% of total)

ival-sub: 2.0ms (18.6% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify759.0ms (10.4%)

Memory

-8.3MiB live, 859.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	-64	(*.f64 x x)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (*.f64 x x))
✓	cost-diff	0	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

Rules

30 426×	`accelerator-lowering-fma.f32`
30 426×	`accelerator-lowering-fma.f64`
3 778×	`-lowering-.f32`
3 778×	`-lowering-.f64`
2 412×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
1	12	16
2	19	16
3	27	16
4	42	16
5	62	16
6	105	16
7	299	16
8	580	16
9	1120	16
10	2014	16
11	3727	16
12	4682	16
13	5002	16
14	5288	16
15	5457	16
16	5534	16
17	5801	16
18	6799	16
19	7855	16
0	8240	16

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(sqrt (- 1 (* x x)))
(- 1 (* x x))
1
(* x x)
x

Outputs
(sqrt (- 1 (* x x)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(- 1 (* x x))
(-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64)))
1
#s(literal 1 binary64)
(* x x)
(fma.f64 x x #s(literal 0 binary64))
x

localize18.0ms (0.2%)

Memory

5.6MiB live, 44.0MiB 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

11.0ms

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 (37.7% of total)

ival-sqrt: 2.0ms (37.7% of total)

ival-sub: 1.0ms (18.9% 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

6.9MiB live, 6.9MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (sqrt (- 1 (* x x)))>
#<alt (- 1 (* x x))>
#<alt (* 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	@	0	(* x x)
0.0ms	x	@	-inf	(sqrt (- 1 (* x x)))

rewrite463.0ms (6.3%)

Memory

25.0MiB live, 653.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 716×	`accelerator-lowering-fma.f32`
4 716×	`accelerator-lowering-fma.f64`
4 136×	`/-lowering-/.f32`
4 136×	`/-lowering-/.f64`
3 492×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
1	29	14
2	184	14
3	1337	14
0	9359	12

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 355

Calls

Call 1

Inputs
(sqrt (- 1 (* x x)))
(- 1 (* x x))
(* x x)

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

simplify293.0ms (4%)

Memory

-27.4MiB live, 464.2MiB allocated

Algorithm

1×	egg-herbie

Rules

8 366×	`accelerator-lowering-fma.f32`
8 366×	`accelerator-lowering-fma.f64`
3 130×	`-lowering-.f32`
3 130×	`-lowering-.f64`
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) (fma.f64 x x #s(literal 0 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 x x #s(literal 0 binary64)) (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 (fma.f64 x x #s(literal 0 binary64)) (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))
(fma.f64 x (sqrt.f64 #s(literal -1 binary64)) #s(literal 0 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) (fma.f64 x (sqrt.f64 #s(literal -1 binary64)) #s(literal 0 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) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (.f64 x (fma.f64 x x #s(literal 0 binary64)))) #s(literal 0 binary64)))) (/.f64 #s(literal 1/2 binary64) (fma.f64 x (sqrt.f64 #s(literal -1 binary64)) #s(literal 0 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 (fma.f64 x x #s(literal 0 binary64)) (.f64 x (.f64 x (fma.f64 x x #s(literal 0 binary64))))) (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) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (.f64 x (fma.f64 x x #s(literal 0 binary64)))) #s(literal 0 binary64))))) (/.f64 #s(literal 1/2 binary64) (fma.f64 x (sqrt.f64 #s(literal -1 binary64)) #s(literal 0 binary64))))
(* -1 (* x (sqrt -1)))
(-.f64 #s(literal 0 binary64) (fma.f64 x (sqrt.f64 #s(literal -1 binary64)) #s(literal 0 binary64)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (fma.f64 x (sqrt.f64 #s(literal -1 binary64)) #s(literal 0 binary64))) (fma.f64 x (sqrt.f64 #s(literal -1 binary64)) #s(literal 0 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) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (.f64 x (fma.f64 x x #s(literal 0 binary64)))) #s(literal 0 binary64))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/2 binary64) (fma.f64 x (sqrt.f64 #s(literal -1 binary64)) #s(literal 0 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) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (.f64 x (fma.f64 x x #s(literal 0 binary64)))) #s(literal 0 binary64))) (-.f64 (/.f64 #s(literal -1/16 binary64) (.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 x (.f64 x (fma.f64 x x #s(literal 0 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/2 binary64) (fma.f64 x (sqrt.f64 #s(literal -1 binary64)) #s(literal 0 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64)))
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64)))
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64)))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))

eval75.0ms (1%)

Memory: -9.5MiB live, 107.6MiB allocated
Compiler: Compiled 16 686 to 1 252 computations (92.5% saved)

prune57.0ms (0.8%)

Memory

10.8MiB live, 89.1MiB 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
▶	99.7%	(fma.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal 0 binary64)) #s(literal 1 binary64))
▶	100.0%	(sqrt.f64 (/.f64 (-.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 1 binary64)))))
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
▶	99.5%	#s(literal 1 binary64)

Compiler

Compiled 37 to 25 computations (32.4% saved)

simplify460.0ms (6.3%)

Memory

-0.3MiB live, 414.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 x x #s(literal 0 binary64))
✓	cost-diff	0	(fma.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal 0 binary64)) #s(literal 1 binary64))
✓	cost-diff	0	(-.f64 #s(literal 0 binary64) (*.f64 x x))
✓	cost-diff	0	(sqrt.f64 (/.f64 (-.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 1 binary64)))))
✓	cost-diff	384	(-.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (*.f64 x x))))
✓	cost-diff	1856	(/.f64 (-.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 1 binary64))))

Rules

11 732×	`accelerator-lowering-fma.f32`
11 732×	`accelerator-lowering-fma.f64`
2 258×	`-lowering-.f32`
2 258×	`-lowering-.f64`
1 452×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	90
1	48	84
2	123	76
3	324	68
4	985	56
5	1944	56
6	3200	56
7	6231	56
0	8181	54

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
1
(sqrt (/ (- -1 (* (* x x) (- 0 (* x x)))) (- 0 (+ (* x x) 1))))
(/ (- -1 (* (* x x) (- 0 (* x x)))) (- 0 (+ (* x x) 1)))
(- -1 (* (* x x) (- 0 (* x x))))
-1
(* (* x x) (- 0 (* x x)))
(* x x)
x
(- 0 (* x x))
0
(- 0 (+ (* x x) 1))
(+ (* x x) 1)
1
(+ (* -1/2 (+ (* x x) 0)) 1)
-1/2
(+ (* x x) 0)
x
0
1

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

localize56.0ms (0.8%)

Memory

11.5MiB live, 50.3MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x x #s(literal 0 binary64))
✓	accuracy	100.0%	(fma.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal 0 binary64)) #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(sqrt.f64 (/.f64 (-.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 1 binary64)))))
✓	accuracy	100.0%	(/.f64 (-.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 1 binary64))))
✓	accuracy	99.8%	(.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (*.f64 x x)))

Samples

37.0ms

256×

valid

Compiler

Compiled 97 to 18 computations (81.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-div: 13.0ms (48.6% of total)

ival-mult: 5.0ms (18.7% of total)

ival-sub: 3.0ms (11.2% of total)

ival-add: 3.0ms (11.2% of total)

ival-sqrt: 2.0ms (7.5% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

5.6MiB live, 5.6MiB allocated

Counts

8 → 96

Calls

Call 1

Inputs
#<alt (/ (- -1 (* (* x x) (- 0 (* x x)))) (- 0 (+ (* x x) 1)))>
#<alt (- -1 (* (* x x) (- 0 (* x x))))>
#<alt (sqrt (/ (- -1 (* (* x x) (- 0 (* x x)))) (- 0 (+ (* x x) 1))))>
#<alt (- 0 (* x x))>
#<alt (+ (* -1/2 (+ (* x x) 0)) 1)>
#<alt (+ (* x x) 0)>
#<alt (* (* x x) (- 0 (* x x)))>
#<alt (* x x)>

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

24 calls:

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

rewrite729.0ms (9.9%)

Memory

-17.5MiB live, 422.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 956×	`accelerator-lowering-fma.f32`
4 956×	`accelerator-lowering-fma.f64`
3 092×	`/-lowering-/.f32`
3 092×	`/-lowering-/.f64`
2 396×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	70
1	124	39
2	1267	37
0	8878	36

Stop Event

1×	iter limit
1×	node limit

Counts

8 → 516

Calls

Call 1

Inputs
(/ (- -1 (* (* x x) (- 0 (* x x)))) (- 0 (+ (* x x) 1)))
(- -1 (* (* x x) (- 0 (* x x))))
(sqrt (/ (- -1 (* (* x x) (- 0 (* x x)))) (- 0 (+ (* x x) 1))))
(- 0 (* x x))
(+ (* -1/2 (+ (* x x) 0)) 1)
(+ (* x x) 0)
(* (* x x) (- 0 (* x x)))
(* x x)

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

simplify679.0ms (9.3%)

Memory

0.9MiB live, 709.1MiB allocated

Algorithm

1×	egg-herbie

Rules

13 736×	`accelerator-lowering-fma.f32`
13 736×	`accelerator-lowering-fma.f64`
3 548×	`-lowering-.f32`
3 548×	`-lowering-.f64`
1 300×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	541
1	140	532
2	395	532
3	1143	512
4	2817	497
5	5627	496
0	8091	477

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

Inputs
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
-1
(- (pow x 4) 1)
(- (pow x 4) 1)
(- (pow x 4) 1)
(pow x 4)
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(pow x 4)
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
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 (/ (sqrt -1) (pow x 2)))))
(* x (+ (sqrt -1) (+ (* -1/2 (/ (sqrt -1) (pow x 2))) (* -1/8 (/ (sqrt -1) (pow x 4))))))
(* x (+ (sqrt -1) (+ (* -1/2 (/ (sqrt -1) (pow x 2))) (+ (* -1/8 (/ (sqrt -1) (pow x 4))) (* -1/16 (/ (sqrt -1) (pow x 6)))))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* -1/2 (/ (sqrt -1) (pow x 2))))))
(* -1 (* x (+ (sqrt -1) (+ (* -1/2 (/ (sqrt -1) (pow x 2))) (* -1/8 (/ (sqrt -1) (pow x 4)))))))
(* -1 (* x (+ (sqrt -1) (+ (* -1/2 (/ (sqrt -1) (pow x 2))) (+ (* -1/8 (/ (sqrt -1) (pow x 4))) (* -1/16 (/ (sqrt -1) (pow x 6))))))))
(* -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 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(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 (pow x 2)))
(-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64)))
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64)))
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64)))
-1
#s(literal -1 binary64)
(- (pow x 4) 1)
(fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal -1 binary64))
(- (pow x 4) 1)
(fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal -1 binary64))
(- (pow x 4) 1)
(fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal -1 binary64))
(pow x 4)
(fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal -1 binary64))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal -1 binary64))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal -1 binary64))
(pow x 4)
(fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal -1 binary64))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal -1 binary64))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #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) (- (* -1/8 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) #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 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x (*.f64 x (fma.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal -1/16 binary64) #s(literal -1/8 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* x (sqrt -1))
(fma.f64 x (sqrt.f64 #s(literal -1 binary64)) #s(literal 0 binary64))
(* x (+ (sqrt -1) (* -1/2 (/ (sqrt -1) (pow x 2)))))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 x (/.f64 #s(literal -1/2 binary64) x)) #s(literal 0 binary64))
(* x (+ (sqrt -1) (+ (* -1/2 (/ (sqrt -1) (pow x 2))) (* -1/8 (/ (sqrt -1) (pow x 4))))))
(fma.f64 x (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) x) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (fma.f64 x x #s(literal 0 binary64)))) #s(literal 0 binary64)))
(* x (+ (sqrt -1) (+ (* -1/2 (/ (sqrt -1) (pow x 2))) (+ (* -1/8 (/ (sqrt -1) (pow x 4))) (* -1/16 (/ (sqrt -1) (pow x 6)))))))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 x (/.f64 #s(literal -1/16 binary64) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))) x) (fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) x) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (fma.f64 x x #s(literal 0 binary64)))) #s(literal 0 binary64)))
(* -1 (* x (sqrt -1)))
(fma.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 0 binary64))
(* -1 (* x (+ (sqrt -1) (* -1/2 (/ (sqrt -1) (pow x 2))))))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) x) x) #s(literal 0 binary64))
(* -1 (* x (+ (sqrt -1) (+ (* -1/2 (/ (sqrt -1) (pow x 2))) (* -1/8 (/ (sqrt -1) (pow x 4)))))))
(-.f64 #s(literal 0 binary64) (fma.f64 x (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) x) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (fma.f64 x x #s(literal 0 binary64)))) #s(literal 0 binary64))))
(* -1 (* x (+ (sqrt -1) (+ (* -1/2 (/ (sqrt -1) (pow x 2))) (+ (* -1/8 (/ (sqrt -1) (pow x 4))) (* -1/16 (/ (sqrt -1) (pow x 6))))))))
(fma.f64 x (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/16 binary64) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64))))) #s(literal 0 binary64)) (fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) x) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (fma.f64 x x #s(literal 0 binary64)))) #s(literal 0 binary64)))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64)))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 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)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(* -1 (pow x 4))
(-.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))
(* -1 (pow x 4))
(-.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))
(* -1 (pow x 4))
(-.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))
(* -1 (pow x 4))
(-.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))
(* -1 (pow x 4))
(-.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))
(* -1 (pow x 4))
(-.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))
(* -1 (pow x 4))
(-.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))
(* -1 (pow x 4))
(-.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))
(* -1 (pow x 4))
(-.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))
(* -1 (pow x 4))
(-.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))
(* -1 (pow x 4))
(-.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))
(* -1 (pow x 4))
(-.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))

eval87.0ms (1.2%)

Memory: 36.5MiB live, 227.4MiB allocated
Compiler: Compiled 22 438 to 2 095 computations (90.7% saved)

prune73.0ms (1%)

Memory

-31.6MiB live, 207.2MiB allocated

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	679	2	681
Fresh	0	0	0
Picked	2	1	3
Done	0	1	1
Total	681	4	685

Accuracy

100.0%

Counts

685 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(fma.f64 (*.f64 #s(literal -1/2 binary64) 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)))
✓	99.5%	#s(literal 1 binary64)

Compiler

Compiled 26 to 19 computations (26.9% saved)

simplify609.0ms (8.3%)

Memory

23.7MiB live, 1 102.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	-64	(*.f64 #s(literal -1/2 binary64) x)
✓	cost-diff	0	(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
✓	cost-diff	0	(fma.f64 x x #s(literal -1 binary64))
✓	cost-diff	0	(/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64)))
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64)))))

Rules

22 902×	`accelerator-lowering-fma.f32`
22 902×	`accelerator-lowering-fma.f64`
3 560×	`-lowering-.f32`
3 560×	`-lowering-.f64`
2 732×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	22	46
2	29	46
3	46	46
4	75	46
5	141	46
6	309	46
7	593	46
8	2129	46
9	3317	46
10	4789	46
11	5521	46
12	5836	46
13	6015	46
14	6091	46
15	6391	46
16	7344	46
17	7628	46
18	7854	46
0	8027	41

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize35.0ms (0.5%)

Memory

-0.2MiB live, 117.7MiB allocated

Localize:

Found 6 expressions of interest:

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

Samples

22.0ms

256×

valid

Compiler

Compiled 43 to 14 computations (67.4% saved)

Precisions

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

ival-mult: 5.0ms (37.6% of total)

ival-div: 3.0ms (22.6% of total)

ival-add: 2.0ms (15% of total)

ival-sqrt: 2.0ms (15% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

9.9MiB live, 9.9MiB allocated

Counts

6 → 72

Calls

Call 1

Inputs
#<alt (/ 1 (sqrt (/ -1 (+ (* x x) -1))))>
#<alt (sqrt (/ -1 (+ (* x x) -1)))>
#<alt (/ -1 (+ (* x x) -1))>
#<alt (+ (* x x) -1)>
#<alt (+ (* (* -1/2 x) x) 1)>
#<alt (* -1/2 x)>

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))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>

Calls

18 calls:

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

rewrite359.0ms (4.9%)

Memory

-11.5MiB live, 611.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 600×	`accelerator-lowering-fma.f32`
4 600×	`accelerator-lowering-fma.f64`
3 150×	`-lowering-.f32`
3 150×	`-lowering-.f64`
2 274×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	68	39
2	435	35
3	3846	35
0	8703	30

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 579

Calls

Call 1

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

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

simplify525.0ms (7.2%)

Memory

37.2MiB live, 913.7MiB allocated

Algorithm

1×	egg-herbie

Rules

18 550×	`accelerator-lowering-fma.f32`
18 550×	`accelerator-lowering-fma.f64`
5 672×	`-lowering-.f32`
5 672×	`-lowering-.f64`
3 510×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	129	822
1	353	699
2	1153	693
3	3892	661
0	8457	617

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

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

Outputs
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (/ (pow x 2) (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 x (.f64 x (fma.f64 x (*.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) #s(literal 1/16 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)))) (-.f64 #s(literal 0 binary64) 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 (+.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))) (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 (sqrt -1)))
(/.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (- (/ 1 (sqrt -1)) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(-.f64 #s(literal 0 binary64) (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 (-.f64 #s(literal 0 binary64) (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))))))
(-.f64 #s(literal 0 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))) (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))))))
(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 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal -1 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))
(-.f64 #s(literal 0 binary64) (/.f64 (sqrt.f64 #s(literal -1 binary64)) x))
(* -1 (/ (+ (sqrt -1) (* 1/2 (/ (sqrt -1) (pow x 2)))) x))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) (-.f64 #s(literal 0 binary64) 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))) (-.f64 #s(literal 0 binary64) 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 (-.f64 (.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) #s(literal -5/16 binary64)) (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
#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 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)) #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 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x)))))) (.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 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x)))))) (.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))
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))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))

eval73.0ms (1%)

Memory: -23.5MiB live, 166.2MiB allocated
Compiler: Compiled 16 415 to 2 052 computations (87.5% saved)

prune70.0ms (1%)

Memory

31.5MiB live, 192.0MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	651	0	651
Fresh	0	0	0
Picked	0	2	2
Done	0	2	2
Total	651	4	655

Accuracy

100.0%

Counts

655 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(fma.f64 (*.f64 #s(literal -1/2 binary64) 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)))
✓	99.5%	#s(literal 1 binary64)

Compiler

Compiled 75 to 42 computations (44% saved)

regimes35.0ms (0.5%)

Memory

-25.0MiB live, 14.1MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal 0 binary64)) #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)))))
(sqrt.f64 (/.f64 (-.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 1 binary64)))))

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

Calls

4 calls:

28.0ms	(-.f64 #s(literal 1 binary64) (*.f64 x x))
2.0ms	x
2.0ms	(*.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)

regimes6.0ms (0.1%)

Memory

11.1MiB live, 11.1MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal 0 binary64)) #s(literal 1 binary64))

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
99.7%	1	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
99.7%	1	`(*.f64 x x)`

Compiler

Compiled 19 to 12 computations (36.8% saved)

regimes4.0ms (0.1%)

Memory

9.3MiB live, 9.3MiB 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	(-.f64 #s(literal 1 binary64) (*.f64 x x))
1.0ms	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

Results

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

Compiler

Compiled 19 to 12 computations (36.8% saved)

simplify8.0ms (0.1%)

Memory

10.7MiB live, 10.7MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	24	13
3	28	13
4	30	13

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness357.0ms (4.9%)

Memory

-68.9MiB live, 204.6MiB allocated

Rules

8 366×	`accelerator-lowering-fma.f32`
8 366×	`accelerator-lowering-fma.f64`
4 956×	`accelerator-lowering-fma.f32`
4 956×	`accelerator-lowering-fma.f64`
3 130×	`-lowering-.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	16	70
1	124	39
2	1267	37
0	8878	36

Stop Event

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

Compiler

Compiled 31 to 21 computations (32.3% saved)

preprocess26.0ms (0.4%)

Memory: 35.5MiB live, 74.6MiB allocated
Remove: (abs x)
Compiler: Compiled 84 to 56 computations (33.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0%)

sample498.0ms (6.8%)

preprocess892.0ms (12.2%)

explain73.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify759.0ms (10.4%)

localize18.0ms (0.2%)

series2.0ms (0%)

rewrite463.0ms (6.3%)

simplify293.0ms (4%)

eval75.0ms (1%)

prune57.0ms (0.8%)

simplify460.0ms (6.3%)

localize56.0ms (0.8%)

series4.0ms (0.1%)

rewrite729.0ms (9.9%)

simplify679.0ms (9.3%)

eval87.0ms (1.2%)

prune73.0ms (1%)

simplify609.0ms (8.3%)

localize35.0ms (0.5%)

series5.0ms (0.1%)

rewrite359.0ms (4.9%)

simplify525.0ms (7.2%)

eval73.0ms (1%)

prune70.0ms (1%)

regimes35.0ms (0.5%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

simplify8.0ms (0.1%)

soundness357.0ms (4.9%)

preprocess26.0ms (0.4%)

end0.0ms (0%)

Profiling