Metrics for bug366, discussion (missed optimization)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze30.0ms (0.4%)

Memory

7.0MiB live, 45.7MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
30.8%	25%	56.2%	0.1%	0%	18.7%	0%	5
32%	25%	53.1%	0.1%	0%	21.9%	0%	6
55.8%	37.5%	29.7%	0.1%	0%	32.8%	0%	7
57.8%	37.5%	27.3%	0.1%	0%	35.1%	0%	8
74.2%	43.7%	15.2%	0.1%	0%	41%	0%	9
75.9%	43.7%	13.9%	0.1%	0%	42.3%	0%	10
85.9%	46.8%	7.7%	0.1%	0%	45.4%	0%	11
87%	46.8%	7%	0.1%	0%	46.1%	0%	12

Compiler

Compiled 10 to 8 computations (20% saved)

sample809.0ms (11%)

Memory

24.6MiB live, 1 078.7MiB allocated

Samples

521.0ms	8 256×	0	valid
46.0ms	634×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 341.0ms

ival-mult: 192.0ms (56.3% of total)

ival-sqrt: 102.0ms (29.9% of total)

ival-sub: 38.0ms (11.1% of total)

ival-true: 6.0ms (1.8% of total)

ival-assert: 3.0ms (0.9% of total)

Bogosity

explain113.0ms (1.5%)

Memory

-24.5MiB live, 115.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
120	-	-	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
7	-	-	`(-.f64 (.f64 a a) (.f64 b b))`
0	-	-	`(*.f64 a a)`
0	-	-	`a`
0	-	-	`b`
0	-	-	`(*.f64 b b)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`	oflow-rescue	112	0
↳	`(*.f64 b b)`	overflow	7
↳	`(-.f64 (.f64 a a) (.f64 b b))`	overflow	112
↳	`(*.f64 a a)`	overflow	112
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`	uflow-rescue	8	0
↳	`(*.f64 b b)`	underflow	103
↳	`(-.f64 (.f64 a a) (.f64 b b))`	underflow	8
↳	`(*.f64 a a)`	underflow	8
`-.f64`	`(-.f64 (.f64 a a) (.f64 b b))`	nan-rescue	7	0
↳	`(*.f64 a a)`	overflow	112
↳	`(*.f64 b b)`	overflow	7

Confusion

	Predicted +	Predicted -
+	120	0
-	0	136

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	120	0	0
-	0	0	136

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	136
1	113
2	7

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

44.0ms

512×

valid

Compiler

Compiled 60 to 22 computations (63.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-mult: 7.0ms (51.7% of total)

ival-sqrt: 4.0ms (29.5% of total)

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

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

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

preprocess783.0ms (10.6%)

Memory

20.6MiB live, 404.4MiB allocated

Algorithm

1×	egg-herbie

Rules

24 584×	`lower-fma.f64`
24 584×	`lower-fma.f32`
5 200×	`lower-+.f64`
5 200×	`lower-+.f32`
3 968×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	42
1	54	42
2	128	42
3	331	42
4	827	42
5	1200	42
6	1876	42
7	2756	42
8	3566	42
9	4032	42
10	4138	42
11	4184	42
12	4202	42
13	6464	42
14	7171	42
15	7815	42
0	6	8
0	10	8
1	18	8
2	29	8
3	55	8
4	115	8
5	318	8
6	587	8
7	1257	8
8	2531	8
9	4197	8
10	5056	8
11	5425	8
12	5655	8
13	5769	8
14	5769	8
15	6729	8
16	6889	8
17	7209	8
18	7209	8
19	7609	8
20	7769	8
21	7849	8
22	7849	8
23	7849	8
0	10335	8

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Outputs
(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
(sqrt.f64 (*.f64 (+.f64 a b) (-.f64 a b)))

Symmetry

(abs b)

(abs a)

Compiler

Compiled 10 to 6 computations (40% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.1%	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Compiler

Compiled 10 to 6 computations (40% saved)

simplify580.0ms (7.9%)

Memory

-28.6MiB live, 375.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 b b)
cost-diff	0	(*.f64 a a)
cost-diff	0	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
cost-diff	128	(-.f64 (.f64 a a) (.f64 b b))

Rules

24 584×	`lower-fma.f64`
24 584×	`lower-fma.f32`
5 200×	`lower-+.f64`
5 200×	`lower-+.f32`
3 968×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	23
0	10	23
1	18	23
2	29	23
3	55	23
4	115	23
5	318	23
6	587	23
7	1257	23
8	2531	23
9	4197	23
10	5056	23
11	5425	23
12	5655	23
13	5769	23
14	5769	23
15	6729	23
16	6889	23
17	7209	23
18	7209	23
19	7609	23
20	7769	23
21	7849	23
22	7849	23
23	7849	23
0	10335	23

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
(-.f64 (.f64 a a) (.f64 b b))
(*.f64 a a)
a
(*.f64 b b)
b

Outputs
(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
(sqrt.f64 (*.f64 (+.f64 a b) (-.f64 a b)))
(-.f64 (.f64 a a) (.f64 b b))
(*.f64 (+.f64 a b) (-.f64 a b))
(*.f64 a a)
a
(*.f64 b b)
b

localize36.0ms (0.5%)

Memory

4.5MiB live, 41.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 b b)
accuracy	0	(*.f64 a a)
accuracy	1.3945312500000002	(-.f64 (.f64 a a) (.f64 b b))
accuracy	27.958279443076552	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Samples

12.0ms

256×

valid

Compiler

Compiled 25 to 8 computations (68% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-mult: 3.0ms (47.7% of total)

ival-sqrt: 2.0ms (31.8% of total)

ival-sub: 1.0ms (15.9% of total)

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

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

series6.0ms (0.1%)

Memory

13.1MiB live, 13.1MiB allocated

Counts

4 → 72

Calls

Call 1

Inputs
#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())
#s(alt (.f64 a a) (patch (.f64 a a) #<representation binary64>) () ())
#s(alt (.f64 b b) (patch (.f64 b b) #<representation binary64>) () ())

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

Calls

18 calls:

Time	Variable		Point	Expression
1.0ms	a	@	inf	(sqrt (- (* a a) (* b b)))
0.0ms	a	@	0	(sqrt (- (* a a) (* b b)))
0.0ms	b	@	inf	(sqrt (- (* a a) (* b b)))
0.0ms	a	@	0	(- (* a a) (* b b))
0.0ms	b	@	0	(sqrt (- (* a a) (* b b)))

simplify415.0ms (5.6%)

Memory

-9.4MiB live, 602.6MiB allocated

Algorithm

1×	egg-herbie

Rules

21 296×	`lower-fma.f64`
21 296×	`lower-fma.f32`
5 606×	`lower-*.f64`
5 606×	`lower-*.f32`
3 296×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	119	753
1	332	753
2	1125	740
3	4532	722
0	8248	682

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 70

Calls

Call 1

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

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

rewrite373.0ms (5.1%)

Memory

8.7MiB live, 489.0MiB allocated

Rules

6 736×	`lower-fma.f64`
6 736×	`lower-fma.f32`
3 576×	`lower-/.f64`
3 576×	`lower-/.f32`
3 476×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	36	21
2	239	21
3	2135	21
0	9378	21

Stop Event

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

Counts

4 → 326

Calls

Call 1

Inputs
(-.f64 (.f64 a a) (.f64 b b))
(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
(*.f64 a a)
(*.f64 b b)

Outputs
(+.f64 (.f64 a a) (neg.f64 (.f64 b b)))
(+.f64 (neg.f64 (.f64 b b)) (.f64 a a))
(+.f64 (/.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (fma.f64 a (.f64 a (.f64 a a)) (.f64 b (.f64 b (fma.f64 a a (.f64 b b)))))) (neg.f64 (/.f64 (.f64 (.f64 b (.f64 b b)) (.f64 b (.f64 b b))) (fma.f64 a (.f64 a (.f64 a a)) (.f64 b (.f64 b (fma.f64 a a (.f64 b b))))))))
(+.f64 (/.f64 (.f64 a (.f64 a (.f64 a a))) (fma.f64 a a (.f64 b b))) (neg.f64 (/.f64 (.f64 b (.f64 b (.f64 b b))) (fma.f64 a a (.f64 b b)))))
(+.f64 (.f64 (+.f64 a b) a) (.f64 (+.f64 a b) (neg.f64 b)))
(+.f64 (.f64 (-.f64 a b) a) (.f64 (-.f64 a b) b))
(+.f64 (.f64 (-.f64 a b) b) (.f64 (-.f64 a b) a))
(+.f64 (.f64 a (+.f64 a b)) (.f64 (neg.f64 b) (+.f64 a b)))
(+.f64 (.f64 a (-.f64 a b)) (.f64 b (-.f64 a b)))
(+.f64 (.f64 b (-.f64 a b)) (.f64 a (-.f64 a b)))
(exp.f64 (log.f64 (*.f64 (+.f64 a b) (-.f64 a b))))
(exp.f64 (.f64 (neg.f64 (log.f64 (.f64 (+.f64 a b) (-.f64 a b)))) #s(literal -1 binary64)))
(-.f64 (.f64 a a) (.f64 b b))
(-.f64 (/.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (fma.f64 a (.f64 a (.f64 a a)) (.f64 b (.f64 b (fma.f64 a a (.f64 b b)))))) (/.f64 (.f64 (.f64 b (.f64 b b)) (.f64 b (.f64 b b))) (fma.f64 a (.f64 a (.f64 a a)) (.f64 b (.f64 b (fma.f64 a a (.f64 b b)))))))
(-.f64 (/.f64 (.f64 a (.f64 a (.f64 a a))) (fma.f64 a a (.f64 b b))) (/.f64 (.f64 b (.f64 b (.f64 b b))) (fma.f64 a a (.f64 b b))))
(-.f64 #s(literal 0 binary64) (-.f64 (.f64 b b) (.f64 a a)))
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eval90.0ms (1.2%)

Memory: -19.0MiB live, 94.8MiB allocated
Compiler: Compiled 19 277 to 1 264 computations (93.4% saved)

prune64.0ms (0.9%)

Memory

35.5MiB live, 144.6MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	391	5	396
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	392	5	397

Accuracy

100.0%

Counts

397 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 a b)))
▶	56.3%	(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 a b)))
▶	56.2%	(sqrt.f64 #s(approx (- (* a a) (* b b)) (*.f64 a a)))
▶	99.9%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a))
▶	1.0%	#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))

Compiler

Compiled 88 to 52 computations (40.9% saved)

simplify203.0ms (2.8%)

Memory

18.3MiB live, 332.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

13 330×	`lower-fma.f32`
13 328×	`lower-fma.f64`
3 318×	`lower--.f32`
3 316×	`lower--.f64`
2 170×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	125
0	37	125
1	64	125
2	104	125
3	171	125
4	288	125
5	615	125
6	1567	125
7	3328	125
8	6528	125
0	8151	125

Stop Event

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

Calls

Call 1

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

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

localize92.0ms (1.3%)

Memory

-10.5MiB live, 157.9MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 a b)
accuracy	0	(sqrt.f64 (+.f64 a b))
accuracy	0.00390625	(sqrt.f64 (-.f64 a b))
accuracy	0.5	(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 a b)))
accuracy	0	(-.f64 a b)
accuracy	0	(+.f64 a b)
accuracy	0	(*.f64 (-.f64 a b) (+.f64 a b))
accuracy	27.958279443076552	(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 a b)))
accuracy	0	(*.f64 a a)
accuracy	0.10305629256899049	#s(approx (- (* a a) (* b b)) (*.f64 a a))
accuracy	27.958279443076552	(sqrt.f64 #s(approx (- (* a a) (* b b)) (*.f64 a a)))
accuracy	0	(neg.f64 a)
accuracy	63.33774071749769	#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
accuracy	0	(fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)
accuracy	0	(/.f64 b a)
accuracy	0.00390625	(*.f64 (/.f64 b a) #s(literal -1/2 binary64))
accuracy	0.05643971892594768	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a))

Samples

64.0ms

256×

valid

Compiler

Compiled 108 to 21 computations (80.6% saved)

Precisions

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

ival-sqrt: 11.0ms (35.4% of total)

ival-mult: 9.0ms (28.9% of total)

ival-neg: 4.0ms (12.9% of total)

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

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

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

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

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

exact: 0.0ms (0% of total)

series35.0ms (0.5%)

Memory

-10.3MiB live, 77.1MiB allocated

Counts

16 → 360

Calls

Call 1

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

Outputs
#s(alt (* b (sqrt -1)) (taylor 0 a) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1))) (taylor 0 a) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt (+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1))))))) (taylor 0 a) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt (+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1))))))) (taylor 0 a) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt a (taylor inf a) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))) (taylor inf a) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))) (taylor inf a) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))) (taylor inf a) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt (* -1 a) (taylor -inf a) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))) (taylor -inf a) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))) (taylor -inf a) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))) (taylor -inf a) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt a (taylor 0 b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt (+ a (* -1/2 (/ (pow b 2) a))) (taylor 0 b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt (+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a))))) (taylor 0 b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt (+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a))))) (taylor 0 b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt (* b (sqrt -1)) (taylor inf b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))) (taylor inf b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))) (taylor inf b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))) (taylor inf b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (sqrt -1))) (taylor -inf b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))) (taylor -inf b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))) (taylor -inf b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))) (taylor -inf b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)) #<representation binary64>) () ())) ())
#s(alt a (taylor 0 b) (#s(alt (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a) (patch (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a) #<representation binary64>) () ())) ())
#s(alt (+ a (* -1/2 (/ (pow b 2) a))) (taylor 0 b) (#s(alt (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a) (patch (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a) #<representation binary64>) () ())) ())
#s(alt (+ a (* -1/2 (/ (pow b 2) a))) (taylor 0 b) (#s(alt (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a) (patch (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a) #<representation binary64>) () ())) ())
#s(alt (+ a (* -1/2 (/ (pow b 2) a))) (taylor 0 b) (#s(alt (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a) (patch (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (/ (pow b 2) a)) (taylor inf b) (#s(alt (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a) (patch (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a) #<representation binary64>) () ())) ())
#s(alt (* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a)))) (taylor inf b) (#s(alt (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a) (patch (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a) #<representation binary64>) () ())) ())
#s(alt (* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a)))) (taylor inf b) (#s(alt (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a) (patch (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a) #<representation binary64>) () ())) ())
#s(alt (* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a)))) (taylor inf b) (#s(alt (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a) (patch (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (/ (pow b 2) a)) (taylor -inf b) (#s(alt (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a) (patch (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a) #<representation binary64>) () ())) ())
#s(alt (* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a)))) (taylor -inf b) (#s(alt (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a) (patch (fma.f64 b (.f64 (/.f64 b a) #s(literal -1/2 binary64)) a) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))) (taylor -inf b) (#s(alt (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 a b))) (patch (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 a b))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b))))) (taylor -inf b) (#s(alt (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 a b))) (patch (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 a b))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b))))) (taylor -inf b) (#s(alt (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 a b))) (patch (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 a b))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt b) (sqrt -1)) (taylor 0 a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1))) (taylor 0 a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1))) (taylor 0 a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1))) (taylor 0 a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (sqrt a) (taylor inf a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* a (+ (sqrt (/ 1 a)) (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)))) (taylor inf a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2)))))) (taylor inf a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* -1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3))))))) (taylor inf a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt a) (pow (sqrt -1) 2))) (taylor -inf a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))) (taylor -inf a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))) (taylor -inf a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (* (pow b 3) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))) (taylor -inf a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (sqrt a) (taylor 0 b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt a) (* -1/2 (* (sqrt (/ 1 a)) b))) (taylor 0 b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* -1/8 (* (sqrt (/ 1 (pow a 3))) b))))) (taylor 0 b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* -1/16 (* (sqrt (/ 1 (pow a 5))) b))))))) (taylor 0 b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt b) (sqrt -1)) (taylor inf b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* b (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))) (taylor inf b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))) (taylor inf b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))) (taylor inf b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt b) (sqrt -1))) (taylor -inf b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))) (taylor -inf b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))) (taylor -inf b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))) (taylor -inf b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (sqrt b) (taylor 0 a) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt b) (* 1/2 (* a (sqrt (/ 1 b))))) (taylor 0 a) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt b) (* a (+ (* -1/8 (* a (sqrt (/ 1 (pow b 3))))) (* 1/2 (sqrt (/ 1 b)))))) (taylor 0 a) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt b) (* a (+ (* 1/2 (sqrt (/ 1 b))) (* a (+ (* -1/8 (sqrt (/ 1 (pow b 3)))) (* 1/16 (* a (sqrt (/ 1 (pow b 5)))))))))) (taylor 0 a) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (sqrt a) (taylor inf a) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* a (+ (sqrt (/ 1 a)) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)))) (taylor inf a) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))) (taylor inf a) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)))))) (taylor inf a) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt a) (pow (sqrt -1) 2))) (taylor -inf a) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))) (taylor -inf a) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))) (taylor -inf a) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))) (taylor -inf a) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (sqrt a) (taylor 0 b) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt a) (* 1/2 (* (sqrt (/ 1 a)) b))) (taylor 0 b) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt a) (* b (+ (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)) (* 1/2 (sqrt (/ 1 a)))))) (taylor 0 b) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt a) (* b (+ (* 1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* 1/16 (* (sqrt (/ 1 (pow a 5))) b))))))) (taylor 0 b) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (sqrt b) (taylor inf b) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* b (+ (sqrt (/ 1 b)) (* 1/2 (* a (sqrt (/ 1 (pow b 3))))))) (taylor inf b) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))) (taylor inf b) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (pow a 3) (sqrt (/ 1 (pow b 7))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3))))))))) (taylor inf b) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt b) (pow (sqrt -1) 2))) (taylor -inf b) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2))))) (taylor -inf b) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))) (taylor -inf b) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2))))))) (taylor -inf b) (#s(alt (sqrt.f64 (+.f64 a b)) (patch (sqrt.f64 (+.f64 a b)) #<representation binary64>) () ())) ())

Calls

90 calls:

Time	Variable		Point	Expression
3.0ms	b	@	inf	(+ (* b (* (/ b a) -1/2)) a)
2.0ms	b	@	0	(sqrt (+ a b))
2.0ms	a	@	inf	(sqrt (+ a b))
1.0ms	a	@	-inf	(sqrt (+ a b))
1.0ms	b	@	-inf	(/ b a)

simplify342.0ms (4.6%)

Memory

6.9MiB live, 315.0MiB allocated

Algorithm

1×	egg-herbie

Rules

11 938×	`lower-fma.f64`
11 938×	`lower-fma.f32`
4 572×	`lower-*.f64`
4 572×	`lower-*.f32`
2 664×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	575	5151
1	1871	4359
2	7607	4351
0	8057	4106

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 338

Calls

Call 1

Inputs
(* b (sqrt -1))
(+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
a
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))
(* -1 a)
(* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))))
a
(+ a (* -1/2 (/ (pow b 2) a)))
(+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))
(+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a)))))
(* b (sqrt -1))
(* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))
(* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
(* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
(* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
(* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
a
(+ a (* -1/2 (/ (pow b 2) a)))
(+ a (* -1/2 (/ (pow b 2) a)))
(+ a (* -1/2 (/ (pow b 2) a)))
(* -1/2 (/ (pow b 2) a))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(* -1/2 (/ (pow b 2) a))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(* -1/2 (/ (pow b 2) a))
(/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)
(/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)
(/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)
a
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
a
(* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))
(* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))
(* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(* b (sqrt -1))
(+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
a
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))
(* -1 a)
(* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))))
a
(+ a (* -1/2 (/ (pow b 2) a)))
(+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))
(+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a)))))
(* b (sqrt -1))
(* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))
(* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
(* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
(* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
(* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
(* -1 a)
(* -1 a)
(* -1 a)
(* -1 a)
(* -1 a)
(* -1 a)
(* -1 a)
(* -1 a)
(* -1 a)
(* -1 a)
(* -1 a)
(* -1 a)
(* b (sqrt -1))
(+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
a
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))
(* -1 a)
(* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))))
a
(+ a (* -1/2 (/ (pow b 2) a)))
(+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))
(+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a)))))
(* b (sqrt -1))
(* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))
(* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
(* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
(* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
(* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(- (pow a 2) (pow b 2))
(- (pow a 2) (pow b 2))
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(pow a 2)
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(* -1 (pow b 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* -1 (pow b 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(* b (sqrt -1))
(+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))
a
(* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))
(* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))
(* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))
(* -1 (* a (pow (sqrt -1) 2)))
(* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
a
(+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))
(+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))
(+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))
(* b (sqrt -1))
(* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))
(* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))
(* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* -1 (pow b 2))
(+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(pow a 2)
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
(pow a 2)
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(pow a 2)
(+ (* b (+ a (* -1 a))) (pow a 2))
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(* -1 (pow b 2))
(* (pow b 2) (- (+ (* -1 (/ a b)) (/ a b)) 1))
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(* -1 (pow b 2))
(* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
(* -1 b)
(- a b)
(- a b)
(- a b)
a
(* a (+ 1 (* -1 (/ b a))))
(* a (+ 1 (* -1 (/ b a))))
(* a (+ 1 (* -1 (/ b a))))
a
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (- (/ b a) 1)))
a
(+ a (* -1 b))
(+ a (* -1 b))
(+ a (* -1 b))
(* -1 b)
(* b (- (/ a b) 1))
(* b (- (/ a b) 1))
(* b (- (/ a b) 1))
(* -1 b)
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
b
(+ a b)
(+ a b)
(+ a b)
a
(* a (+ 1 (/ b a)))
(* a (+ 1 (/ b a)))
(* a (+ 1 (/ b a)))
a
(* -1 (* a (- (* -1 (/ b a)) 1)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
a
(+ a b)
(+ a b)
(+ a b)
b
(* b (+ 1 (/ a b)))
(* b (+ 1 (/ a b)))
(* b (+ 1 (/ a b)))
b
(* -1 (* b (- (* -1 (/ a b)) 1)))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(* b (sqrt -1))
(+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))
a
(* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))
(* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))
(* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))
(* -1 (* a (pow (sqrt -1) 2)))
(* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
a
(+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))
(+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))
(+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))
(* b (sqrt -1))
(* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))
(* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))
(* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* (sqrt b) (sqrt -1))
(+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1)))
(+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1)))
(+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1)))
(sqrt a)
(* a (+ (sqrt (/ 1 a)) (* -1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* -1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3)))))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (* (pow b 3) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(sqrt a)
(+ (sqrt a) (* -1/2 (* (sqrt (/ 1 a)) b)))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)))))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* -1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(* (sqrt b) (sqrt -1))
(* b (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(* -1 (* (sqrt b) (sqrt -1)))
(* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
(sqrt b)
(+ (sqrt b) (* 1/2 (* a (sqrt (/ 1 b)))))
(+ (sqrt b) (* a (+ (* -1/8 (* a (sqrt (/ 1 (pow b 3))))) (* 1/2 (sqrt (/ 1 b))))))
(+ (sqrt b) (* a (+ (* 1/2 (sqrt (/ 1 b))) (* a (+ (* -1/8 (sqrt (/ 1 (pow b 3)))) (* 1/16 (* a (sqrt (/ 1 (pow b 5))))))))))
(sqrt a)
(* a (+ (sqrt (/ 1 a)) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(sqrt a)
(+ (sqrt a) (* 1/2 (* (sqrt (/ 1 a)) b)))
(+ (sqrt a) (* b (+ (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)) (* 1/2 (sqrt (/ 1 a))))))
(+ (sqrt a) (* b (+ (* 1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* 1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(sqrt b)
(* b (+ (sqrt (/ 1 b)) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))
(* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3))))))))
(* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (pow a 3) (sqrt (/ 1 (pow b 7))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))))
(* -1 (* (sqrt b) (pow (sqrt -1) 2)))
(* -1 (* b (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2))))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))

Outputs
(* b (sqrt -1))
(*.f64 b (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))
(fma.f64 b (sqrt.f64 #s(literal -1 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 a a)) (*.f64 b (sqrt.f64 #s(literal -1 binary64)))))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
(fma.f64 (.f64 a a) (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 a a) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 b (.f64 b (neg.f64 b))))) (/.f64 #s(literal 1/2 binary64) (.f64 b (sqrt.f64 #s(literal -1 binary64))))) (*.f64 b (sqrt.f64 #s(literal -1 binary64))))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
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a
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(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))
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a
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(+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))
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(* b (sqrt -1))
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(* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
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(* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
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(* -1 (* b (sqrt -1)))
(neg.f64 (*.f64 b (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
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(* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
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(* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
(.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 a #s(literal 6 binary64)) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 b #s(literal 6 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 a a) (.f64 b (.f64 b (sqrt.f64 #s(literal -1 binary64))))) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 a #s(literal 4 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 #s(literal -1 binary64) (pow.f64 b #s(literal 4 binary64)))))))) (neg.f64 b))
a
(+ a (* -1/2 (/ (pow b 2) a)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 b b) a) a)
(+ a (* -1/2 (/ (pow b 2) a)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 b b) a) a)
(+ a (* -1/2 (/ (pow b 2) a)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 b b) a) a)
(* -1/2 (/ (pow b 2) a))
(.f64 #s(literal -1/2 binary64) (/.f64 (.f64 b b) a))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(.f64 (.f64 b b) (+.f64 (/.f64 a (*.f64 b b)) (/.f64 #s(literal -1/2 binary64) a)))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(.f64 (.f64 b b) (+.f64 (/.f64 a (*.f64 b b)) (/.f64 #s(literal -1/2 binary64) a)))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(.f64 (.f64 b b) (+.f64 (/.f64 a (*.f64 b b)) (/.f64 #s(literal -1/2 binary64) a)))
(* -1/2 (/ (pow b 2) a))
(.f64 #s(literal -1/2 binary64) (/.f64 (.f64 b b) a))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(.f64 (.f64 b b) (+.f64 (/.f64 a (*.f64 b b)) (/.f64 #s(literal -1/2 binary64) a)))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(.f64 (.f64 b b) (+.f64 (/.f64 a (*.f64 b b)) (/.f64 #s(literal -1/2 binary64) a)))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(.f64 (.f64 b b) (+.f64 (/.f64 a (*.f64 b b)) (/.f64 #s(literal -1/2 binary64) a)))
(* -1/2 (/ (pow b 2) a))
(.f64 #s(literal -1/2 binary64) (/.f64 (.f64 b b) a))
(/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)
(/.f64 (fma.f64 b (.f64 b #s(literal -1/2 binary64)) (.f64 a a)) a)
(/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)
(/.f64 (fma.f64 b (.f64 b #s(literal -1/2 binary64)) (.f64 a a)) a)
(/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)
(/.f64 (fma.f64 b (.f64 b #s(literal -1/2 binary64)) (.f64 a a)) a)
a
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(fma.f64 a (/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) (*.f64 a a)) a)
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(fma.f64 a (/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) (*.f64 a a)) a)
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(fma.f64 a (/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) (*.f64 a a)) a)
a
(* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))
(fma.f64 (neg.f64 a) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 b b)) (*.f64 a a)) a)
(* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))
(fma.f64 (neg.f64 a) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 b b)) (*.f64 a a)) a)
(* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))
(fma.f64 (neg.f64 a) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 b b)) (*.f64 a a)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
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(* -1/2 (/ b a))
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(* -1/2 (/ b a))
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(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
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(* -1/2 (/ b a))
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(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
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(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(* -1/2 (/ b a))
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(* -1/2 (/ b a))
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(* -1/2 (/ b a))
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(* -1/2 (/ b a))
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(* -1/2 (/ b a))
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(* -1/2 (/ b a))
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(* -1/2 (/ b a))
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(* -1/2 (/ b a))
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(* -1/2 (/ b a))
(/.f64 (*.f64 b #s(literal -1/2 binary64)) a)
(/ b a)
(/.f64 b a)
(/ b a)
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(/ b a)
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(/ b a)
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(/ b a)
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(/ b a)
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(/ b a)
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(/ b a)
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(/ b a)
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(/ b a)
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(/ b a)
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(/ b a)
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(/ b a)
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(/ b a)
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(/ b a)
(/.f64 b a)
(/ b a)
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(* b (sqrt -1))
(*.f64 b (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))
(fma.f64 b (sqrt.f64 #s(literal -1 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 a a)) (*.f64 b (sqrt.f64 #s(literal -1 binary64)))))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
(fma.f64 (.f64 a a) (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 a a) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 b (.f64 b (neg.f64 b))))) (/.f64 #s(literal 1/2 binary64) (.f64 b (sqrt.f64 #s(literal -1 binary64))))) (*.f64 b (sqrt.f64 #s(literal -1 binary64))))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
(fma.f64 (.f64 a a) (fma.f64 a (.f64 a (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 a a) (.f64 (pow.f64 b #s(literal 5 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 b (.f64 b (neg.f64 b))))))) (/.f64 #s(literal 1/2 binary64) (.f64 b (sqrt.f64 #s(literal -1 binary64))))) (*.f64 b (sqrt.f64 #s(literal -1 binary64))))
a
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(fma.f64 a (/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) (*.f64 a a)) a)
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))
(fma.f64 a (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))) (/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) (*.f64 a a))) a)
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))
(fma.f64 a (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))) (fma.f64 (.f64 b b) (/.f64 #s(literal -1/2 binary64) (.f64 a a)) (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 b #s(literal 6 binary64))) (pow.f64 a #s(literal 6 binary64))))) a)
(* -1 a)
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(.f64 (fma.f64 (.f64 b b) (/.f64 #s(literal -1/2 binary64) (*.f64 a a)) #s(literal 1 binary64)) (neg.f64 a))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))
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(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))))
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a
(+ a (* -1/2 (/ (pow b 2) a)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 b b) a) a)
(+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))
(fma.f64 (.f64 b b) (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 b b) (.f64 a (.f64 a a))) (/.f64 #s(literal -1/2 binary64) a)) a)
(+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a)))))
(fma.f64 (.f64 b b) (fma.f64 (.f64 b b) (fma.f64 #s(literal -1/16 binary64) (/.f64 (.f64 b b) (pow.f64 a #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 a (*.f64 a a)))) (/.f64 #s(literal -1/2 binary64) a)) a)
(* b (sqrt -1))
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(* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))
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(* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
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(* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
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(* -1 (* b (sqrt -1)))
(neg.f64 (*.f64 b (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 a a) (.f64 b (.f64 b (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 b))
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a
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a
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a
(* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))
a
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a
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a
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a
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a
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a
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a
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a
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a
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(.f64 (neg.f64 b) (fma.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) a)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(.f64 (neg.f64 b) (fma.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) a)) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (.f64 (.f64 (.f64 a a) #s(literal -1/8 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))))))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
(.f64 (neg.f64 b) (fma.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (.f64 a (.f64 a a)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 7 binary64)))))) (fma.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) a)) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (.f64 (.f64 (.f64 a a) #s(literal -1/8 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64))))))))))
(sqrt b)
(sqrt.f64 b)
(+ (sqrt b) (* 1/2 (* a (sqrt (/ 1 b)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (*.f64 #s(literal 1/2 binary64) a) (sqrt.f64 b))
(+ (sqrt b) (* a (+ (* -1/8 (* a (sqrt (/ 1 (pow b 3))))) (* 1/2 (sqrt (/ 1 b))))))
(fma.f64 a (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 a #s(literal -1/8 binary64)))) (sqrt.f64 b))
(+ (sqrt b) (* a (+ (* 1/2 (sqrt (/ 1 b))) (* a (+ (* -1/8 (sqrt (/ 1 (pow b 3)))) (* 1/16 (* a (sqrt (/ 1 (pow b 5))))))))))
(fma.f64 a (fma.f64 a (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 a #s(literal 1/16 binary64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)))) (sqrt.f64 b))
(sqrt a)
(sqrt.f64 a)
(* a (+ (sqrt (/ 1 a)) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal 1/2 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 #s(literal -1/8 binary64) (.f64 b b)) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))
(.f64 a (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal 1/2 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) (.f64 (.f64 b (.f64 b b)) #s(literal 1/16 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 #s(literal -1/8 binary64) (.f64 b b)))))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(neg.f64 (neg.f64 (sqrt.f64 a)))
(* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(neg.f64 (.f64 a (fma.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (*.f64 b #s(literal 1/2 binary64))))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(.f64 (neg.f64 a) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 (/.f64 (.f64 b b) #s(literal -1 binary64)) #s(literal -1/8 binary64)) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (*.f64 b #s(literal 1/2 binary64))))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(neg.f64 (.f64 a (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (.f64 b b) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64))))) #s(literal -1 binary64)) (fma.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) (/.f64 (.f64 b (.f64 b b)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal 1/2 binary64))))))))
(sqrt a)
(sqrt.f64 a)
(+ (sqrt a) (* 1/2 (* (sqrt (/ 1 a)) b)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 b #s(literal 1/2 binary64)) (sqrt.f64 a))
(+ (sqrt a) (* b (+ (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)) (* 1/2 (sqrt (/ 1 a))))))
(fma.f64 b (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 #s(literal -1/8 binary64) b))) (sqrt.f64 a))
(+ (sqrt a) (* b (+ (* 1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* 1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(fma.f64 b (fma.f64 b (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 b #s(literal 1/16 binary64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))) (sqrt.f64 a))
(sqrt b)
(sqrt.f64 b)
(* b (+ (sqrt (/ 1 b)) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))
(.f64 b (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 #s(literal 1/2 binary64) a) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))))
(* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3))))))))
(.f64 b (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 #s(literal 1/2 binary64) a) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 (.f64 a a) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)))))
(* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (pow a 3) (sqrt (/ 1 (pow b 7))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))))
(.f64 b (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (fma.f64 #s(literal 1/2 binary64) (.f64 a (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 (.f64 a a) #s(literal -1/8 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 7 binary64)))) (.f64 #s(literal 1/16 binary64) (.f64 a (.f64 a a))))))))
(* -1 (* (sqrt b) (pow (sqrt -1) 2)))
(neg.f64 (neg.f64 (sqrt.f64 b)))
(* -1 (* b (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))
(.f64 (neg.f64 b) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (*.f64 #s(literal 1/2 binary64) a))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2))))))
(.f64 (neg.f64 b) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (fma.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (/.f64 (.f64 a a) #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (*.f64 #s(literal 1/2 binary64) a)))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))
(.f64 (neg.f64 b) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 7 binary64)))) (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 a (.f64 a a))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (fma.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (/.f64 (.f64 a a) #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 #s(literal 1/2 binary64) a))))))

rewrite332.0ms (4.5%)

Memory

-0.6MiB live, 390.7MiB allocated

Rules

8 510×	`lower-fma.f32`
8 508×	`lower-fma.f64`
6 222×	`lower-*.f32`
6 214×	`lower-*.f64`
4 500×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	110
0	37	109
1	115	109
2	765	109
0	9124	109

Stop Event

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

Counts

16 → 940

Calls

Call 1

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

Outputs
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (/.f64 (*.f64 b #s(literal -1/2 binary64)) a) a))
(+.f64 a (/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a))
(+.f64 (/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a) a)
(+.f64 (/.f64 (.f64 (/.f64 b a) (.f64 b (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 b b) a)))) (fma.f64 b (/.f64 (.f64 b #s(literal -1/2 binary64)) a) (neg.f64 a))) (neg.f64 (/.f64 (.f64 a a) (fma.f64 b (/.f64 (*.f64 b #s(literal -1/2 binary64)) a) (neg.f64 a)))))
(-.f64 (/.f64 (.f64 (/.f64 b a) (.f64 b (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 b b) a)))) (fma.f64 b (/.f64 (.f64 b #s(literal -1/2 binary64)) a) (neg.f64 a))) (/.f64 (.f64 a a) (fma.f64 b (/.f64 (*.f64 b #s(literal -1/2 binary64)) a) (neg.f64 a))))
(-.f64 (/.f64 (.f64 a a) (+.f64 a (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a)))) (/.f64 (.f64 (/.f64 b a) (.f64 b (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 b b) a)))) (+.f64 a (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 b b) a)))))
(fma.f64 a #s(literal 1 binary64) (/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a))
(fma.f64 b (/.f64 (*.f64 b #s(literal -1/2 binary64)) a) a)
(fma.f64 (*.f64 b b) (/.f64 #s(literal -1/2 binary64) a) a)
(fma.f64 (/.f64 b a) (*.f64 b #s(literal -1/2 binary64)) a)
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 b b) a) a)
(fma.f64 (/.f64 (*.f64 b #s(literal -1/2 binary64)) a) b a)
(fma.f64 (neg.f64 a) #s(literal -1 binary64) (/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a))
(fma.f64 (neg.f64 b) (.f64 (/.f64 #s(literal -1 binary64) a) (.f64 b #s(literal -1/2 binary64))) a)
(fma.f64 (.f64 (/.f64 b a) (.f64 b (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 b b) a)))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a) a)) (neg.f64 (/.f64 (.f64 a a) (fma.f64 b (/.f64 (*.f64 b #s(literal -1/2 binary64)) a) (neg.f64 a)))))
(fma.f64 #s(literal 1 binary64) a (/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a) a)
(fma.f64 (/.f64 #s(literal 1 binary64) a) (.f64 b (.f64 b #s(literal -1/2 binary64))) a)
(fma.f64 #s(literal -1 binary64) (neg.f64 a) (/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a))
(fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a)
(fma.f64 (*.f64 b #s(literal -1/2 binary64)) (/.f64 b a) a)
(fma.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) a) a)
(fma.f64 (pow.f64 a #s(literal 1/2 binary64)) (pow.f64 a #s(literal 1/2 binary64)) (/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a))
(fma.f64 (.f64 (.f64 b #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 b a) a)
(fma.f64 (.f64 (.f64 b #s(literal -1/2 binary64)) (neg.f64 b)) (/.f64 #s(literal -1 binary64) a) a)
(neg.f64 (/.f64 (fma.f64 (/.f64 (.f64 (.f64 b (.f64 b b)) (.f64 b (.f64 b b))) (.f64 a (.f64 a a))) #s(literal -1/8 binary64) (.f64 a (.f64 a a))) (neg.f64 (fma.f64 a (+.f64 a (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a))) (.f64 (/.f64 b a) (.f64 b (.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 b b) a))))))))
(neg.f64 (/.f64 (-.f64 (.f64 (/.f64 b a) (.f64 b (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 b b) a)))) (.f64 a a)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a) a)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (/.f64 (.f64 (.f64 b (.f64 b b)) (.f64 b (.f64 b b))) (.f64 a (.f64 a a))) #s(literal -1/8 binary64) (.f64 a (.f64 a a)))) (fma.f64 a (+.f64 a (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a))) (.f64 (/.f64 b a) (.f64 b (.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 b b) a)))))))
(neg.f64 (/.f64 (.f64 (fma.f64 b (/.f64 (.f64 b #s(literal -1/2 binary64)) a) a) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a) a)) (fma.f64 b (/.f64 (.f64 b #s(literal -1/2 binary64)) a) (neg.f64 a))))
(/.f64 (fma.f64 (/.f64 (.f64 (.f64 b (.f64 b b)) (.f64 b (.f64 b b))) (.f64 a (.f64 a a))) #s(literal -1/8 binary64) (.f64 a (.f64 a a))) (fma.f64 a (+.f64 a (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a))) (.f64 (/.f64 b a) (.f64 b (.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 b b) a))))))
(/.f64 (fma.f64 (/.f64 (.f64 (.f64 b (.f64 b b)) (.f64 b (.f64 b b))) (.f64 a (.f64 a a))) #s(literal -1/8 binary64) (.f64 a (.f64 a a))) (fma.f64 a a (.f64 (/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a) (fma.f64 b (/.f64 (*.f64 b #s(literal -1/2 binary64)) a) (neg.f64 a)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 b (/.f64 (*.f64 b #s(literal -1/2 binary64)) a) a)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 a a (.f64 (/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a) (fma.f64 b (/.f64 (.f64 b #s(literal -1/2 binary64)) a) (neg.f64 a)))) (fma.f64 (/.f64 (.f64 (.f64 b (.f64 b b)) (.f64 b (.f64 b b))) (.f64 a (.f64 a a))) #s(literal -1/8 binary64) (.f64 a (*.f64 a a)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 b (/.f64 (*.f64 b #s(literal -1/2 binary64)) a) a)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 a (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a))) (-.f64 (.f64 a a) (.f64 (/.f64 b a) (.f64 b (.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 b b) a)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 b (/.f64 (*.f64 b #s(literal -1/2 binary64)) a) a))))
(/.f64 (-.f64 (.f64 (/.f64 b a) (.f64 b (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 b b) a)))) (.f64 a a)) (fma.f64 b (/.f64 (.f64 b #s(literal -1/2 binary64)) a) (neg.f64 a)))
(/.f64 (neg.f64 (fma.f64 (/.f64 (.f64 (.f64 b (.f64 b b)) (.f64 b (.f64 b b))) (.f64 a (.f64 a a))) #s(literal -1/8 binary64) (.f64 a (.f64 a a)))) (neg.f64 (fma.f64 a (+.f64 a (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a))) (.f64 (/.f64 b a) (.f64 b (.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 b b) a)))))))
(/.f64 (neg.f64 (fma.f64 (/.f64 (.f64 (.f64 b (.f64 b b)) (.f64 b (.f64 b b))) (.f64 a (.f64 a a))) #s(literal -1/8 binary64) (.f64 a (.f64 a a)))) (neg.f64 (fma.f64 a a (.f64 (/.f64 (.f64 b (.f64 b #s(literal -1/2 binary64))) a) (fma.f64 b (/.f64 (*.f64 b #s(literal -1/2 binary64)) a) (neg.f64 a))))))
(/.f64 (.f64 (fma.f64 b (/.f64 (.f64 b #s(literal -1/2 binary64)) a) a) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a) a)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b b) a) a))
(/.f64 (-.f64 (.f64 a a) (.f64 (/.f64 b a) (.f64 b (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 b b) a))))) (+.f64 a (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 b b) a))))
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(.f64 (sqrt.f64 (.f64 (fma.f64 b (.f64 b b) (.f64 a (.f64 a a))) (.f64 (fma.f64 a (+.f64 a b) (.f64 b b)) (-.f64 a b)))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 b (.f64 b (fma.f64 a a (.f64 b b))) (.f64 a (.f64 a (.f64 a a))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 (fma.f64 b (.f64 b b) (.f64 a (.f64 a a))) (.f64 (fma.f64 a (+.f64 a b) (.f64 b b)) (-.f64 a b)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 b (.f64 b (fma.f64 a a (.f64 b b))) (.f64 a (.f64 a (.f64 a a)))))))
(.f64 (sqrt.f64 (.f64 (fma.f64 b (.f64 b b) (.f64 a (.f64 a a))) (.f64 (fma.f64 a (+.f64 a b) (.f64 b b)) (-.f64 a b)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 b (.f64 b (fma.f64 a a (.f64 b b))) (.f64 a (.f64 a (.f64 a a)))))))
(.f64 (sqrt.f64 (.f64 (.f64 (-.f64 a b) (+.f64 a b)) (fma.f64 a a (.f64 b b)))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a a (*.f64 b b))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 (.f64 (-.f64 a b) (+.f64 a b)) (fma.f64 a a (.f64 b b)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a a (*.f64 b b)))))
(.f64 (sqrt.f64 (.f64 (.f64 (-.f64 a b) (+.f64 a b)) (fma.f64 a a (.f64 b b)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 a a (*.f64 b b)))))
(.f64 (pow.f64 (.f64 (-.f64 a b) (+.f64 a b)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (-.f64 a b) (+.f64 a b)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (-.f64 a b) #s(literal 1/4 binary64)) (.f64 (pow.f64 (-.f64 a b) #s(literal 1/4 binary64)) (sqrt.f64 (+.f64 a b))))
(.f64 (pow.f64 (+.f64 a b) #s(literal 1/4 binary64)) (.f64 (pow.f64 (+.f64 a b) #s(literal 1/4 binary64)) (sqrt.f64 (-.f64 a b))))
(.f64 (.f64 (sqrt.f64 (-.f64 a b)) (pow.f64 (+.f64 a b) #s(literal 1/4 binary64))) (pow.f64 (+.f64 a b) #s(literal 1/4 binary64)))
(.f64 (.f64 (sqrt.f64 (+.f64 a b)) (pow.f64 (-.f64 a b) #s(literal 1/4 binary64))) (pow.f64 (-.f64 a b) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (-.f64 a b)) #s(literal 1/2 binary64)))
(exp.f64 (-.f64 (.f64 (log.f64 (.f64 (-.f64 a b) (+.f64 a b))) #s(literal 1/2 binary64)) (*.f64 (log.f64 (+.f64 a b)) #s(literal 1/2 binary64))))
(sqrt.f64 (-.f64 a b))
(/.f64 (sqrt.f64 (*.f64 (-.f64 a b) (+.f64 a b))) (sqrt.f64 (+.f64 a b)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 a b))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 a b)) (sqrt.f64 (*.f64 (-.f64 a b) (+.f64 a b)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 a (+.f64 a b) (.f64 b b))) (sqrt.f64 (.f64 (fma.f64 a (+.f64 a b) (*.f64 b b)) (-.f64 a b)))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 b (.f64 b b) (.f64 a (.f64 a a))) (.f64 (fma.f64 a (+.f64 a b) (.f64 b b)) (-.f64 a b)))) (sqrt.f64 (.f64 (+.f64 a b) (fma.f64 b (.f64 b (fma.f64 a a (.f64 b b))) (.f64 a (.f64 a (.f64 a a)))))))
(/.f64 (sqrt.f64 (.f64 (.f64 (-.f64 a b) (+.f64 a b)) (fma.f64 a a (.f64 b b)))) (sqrt.f64 (.f64 (+.f64 a b) (fma.f64 a a (*.f64 b b)))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 a (+.f64 a b) (.f64 b b)) (-.f64 a b))) (sqrt.f64 (fma.f64 a (+.f64 a b) (*.f64 b b))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 a (+.f64 a b) (.f64 b b)) (-.f64 a b))) (sqrt.f64 (fma.f64 a a (*.f64 (neg.f64 b) (-.f64 (neg.f64 b) a)))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 a b) (-.f64 b a))) (sqrt.f64 (neg.f64 (+.f64 a b))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 a (+.f64 a b) (.f64 b b)) (-.f64 b a))) (sqrt.f64 (neg.f64 (fma.f64 a (+.f64 a b) (*.f64 b b)))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (-.f64 a b) (+.f64 a b)))) (neg.f64 (sqrt.f64 (+.f64 a b))))
(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 a (+.f64 a b) (.f64 b b)) (-.f64 a b)))) (neg.f64 (sqrt.f64 (fma.f64 a (+.f64 a b) (*.f64 b b)))))
(pow.f64 (-.f64 a b) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (-.f64 a b) (-.f64 a b)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (-.f64 a b) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 (-.f64 a b))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (.f64 (-.f64 a b) (+.f64 a b))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 a b)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 (-.f64 a b) (+.f64 a b))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 a b))))
(.f64 (sqrt.f64 (.f64 (-.f64 a b) (+.f64 a b))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 a b))))
(*.f64 (sqrt.f64 (-.f64 a b)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (-.f64 a b)) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 a b)) (pow.f64 (/.f64 (-.f64 a b) (+.f64 a b)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 a b)) (sqrt.f64 (/.f64 (-.f64 a b) (+.f64 a b))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 a b)))
(.f64 (sqrt.f64 (.f64 (fma.f64 a (+.f64 a b) (.f64 b b)) (-.f64 a b))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a (+.f64 a b) (.f64 b b))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 (fma.f64 a (+.f64 a b) (.f64 b b)) (-.f64 a b))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a (+.f64 a b) (.f64 b b)))))
(.f64 (sqrt.f64 (.f64 (fma.f64 a (+.f64 a b) (.f64 b b)) (-.f64 a b))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 a (+.f64 a b) (.f64 b b)))))
(*.f64 (pow.f64 (-.f64 a b) #s(literal 1/4 binary64)) (pow.f64 (-.f64 a b) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 a b)))
(.f64 (pow.f64 (.f64 (/.f64 (-.f64 a b) (fma.f64 b (-.f64 b a) (.f64 a a))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 b (-.f64 b a) (.f64 a a))))
(.f64 (sqrt.f64 (.f64 (/.f64 (-.f64 a b) (fma.f64 b (-.f64 b a) (.f64 a a))) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 b (-.f64 b a) (.f64 a a))))
(*.f64 (/.f64 (sqrt.f64 (-.f64 a b)) (pow.f64 (+.f64 a b) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (+.f64 a b)) (pow.f64 (+.f64 a b) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 (+.f64 a b)) (pow.f64 (+.f64 a b) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (-.f64 a b)) (pow.f64 (+.f64 a b) #s(literal 1/4 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 (-.f64 a b) (+.f64 a b)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 a b) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 (-.f64 a b) (+.f64 a b)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 a b) #s(literal 1/4 binary64))))
(exp.f64 (*.f64 (log.f64 (+.f64 a b)) #s(literal 1/2 binary64)))
(exp.f64 (-.f64 (.f64 (log.f64 (.f64 (-.f64 a b) (+.f64 a b))) #s(literal 1/2 binary64)) (*.f64 (log.f64 (-.f64 a b)) #s(literal 1/2 binary64))))
(hypot.f64 (pow.f64 b #s(literal 1/2 binary64)) (pow.f64 a #s(literal 1/2 binary64)))
(hypot.f64 (pow.f64 a #s(literal 1/2 binary64)) (pow.f64 b #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 a b))
(/.f64 (sqrt.f64 (*.f64 (-.f64 a b) (+.f64 a b))) (sqrt.f64 (-.f64 a b)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 a b))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (*.f64 (-.f64 a b) (+.f64 a b)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 b (-.f64 b a) (.f64 a a))) (sqrt.f64 (fma.f64 b (.f64 b b) (.f64 a (.f64 a a))))))
(/.f64 (sqrt.f64 (fma.f64 b (.f64 b b) (.f64 a (.f64 a a)))) (sqrt.f64 (fma.f64 b (-.f64 b a) (.f64 a a))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 b (.f64 b b) (.f64 a (.f64 a a))) (.f64 (fma.f64 a (+.f64 a b) (.f64 b b)) (-.f64 a b)))) (sqrt.f64 (.f64 (-.f64 a b) (fma.f64 b (.f64 b (fma.f64 a a (.f64 b b))) (.f64 a (.f64 a (.f64 a a)))))))
(/.f64 (sqrt.f64 (.f64 (.f64 (-.f64 a b) (+.f64 a b)) (fma.f64 a a (.f64 b b)))) (sqrt.f64 (.f64 (-.f64 a b) (fma.f64 a a (*.f64 b b)))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 a b) (-.f64 b a))) (sqrt.f64 (-.f64 b a)))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 b (.f64 b b) (.f64 a (.f64 a a))))) (sqrt.f64 (neg.f64 (fma.f64 b (-.f64 b a) (.f64 a a)))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (-.f64 a b) (+.f64 a b)))) (neg.f64 (sqrt.f64 (-.f64 a b))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 b (.f64 b b) (.f64 a (.f64 a a))))) (neg.f64 (sqrt.f64 (fma.f64 b (-.f64 b a) (.f64 a a)))))
(pow.f64 (+.f64 a b) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 a b) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 a b) (+.f64 a b)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 a b))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (.f64 (-.f64 a b) (+.f64 a b))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 a b)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 (-.f64 a b) (+.f64 a b))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 a b))))
(.f64 (sqrt.f64 (.f64 (-.f64 a b) (+.f64 a b))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 a b))))
(*.f64 (sqrt.f64 (-.f64 a b)) (pow.f64 (/.f64 (+.f64 a b) (-.f64 a b)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (/.f64 (+.f64 a b) (-.f64 a b))))
(*.f64 (sqrt.f64 (+.f64 a b)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (+.f64 a b)) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 a b)))
(.f64 (sqrt.f64 (fma.f64 b (.f64 b b) (.f64 a (.f64 a a)))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 b (-.f64 b a) (*.f64 a a))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 b (.f64 b b) (.f64 a (.f64 a a)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 b (-.f64 b a) (*.f64 a a)))))
(.f64 (sqrt.f64 (fma.f64 b (.f64 b b) (.f64 a (.f64 a a)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 b (-.f64 b a) (*.f64 a a)))))
(*.f64 (pow.f64 (+.f64 a b) #s(literal 1/4 binary64)) (pow.f64 (+.f64 a b) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 a b)))
(.f64 (pow.f64 (.f64 (/.f64 (+.f64 a b) (fma.f64 a (+.f64 a b) (.f64 b b))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 a (+.f64 a b) (.f64 b b))))
(.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 a b) (fma.f64 a (+.f64 a b) (.f64 b b))) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 a (+.f64 a b) (.f64 b b))))
(*.f64 (/.f64 (sqrt.f64 (-.f64 a b)) (pow.f64 (-.f64 a b) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (+.f64 a b)) (pow.f64 (-.f64 a b) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 (+.f64 a b)) (pow.f64 (-.f64 a b) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (-.f64 a b)) (pow.f64 (-.f64 a b) #s(literal 1/4 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 (-.f64 a b) (+.f64 a b)) #s(literal 1/4 binary64)) (pow.f64 (-.f64 a b) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 (-.f64 a b) (+.f64 a b)) #s(literal 1/4 binary64)) (pow.f64 (-.f64 a b) #s(literal 1/4 binary64))))

eval270.0ms (3.7%)

Memory: -4.7MiB live, 425.9MiB allocated
Compiler: Compiled 42 953 to 3 907 computations (90.9% saved)

prune209.0ms (2.8%)

Memory

36.6MiB live, 433.4MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	1 624	2	1 626
Fresh	0	0	0
Picked	2	3	5
Done	0	0	0
Total	1 626	5	1 631

Accuracy

100.0%

Counts

1 631 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 a b)))
▶	72.0%	(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 #s(approx (+ a b) (fma.f64 b (/.f64 a b) b))))
✓	56.3%	(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 a b)))
▶	99.5%	#s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a)
✓	99.9%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a))

Compiler

Compiled 51 to 29 computations (43.1% saved)

simplify214.0ms (2.9%)

Memory

-32.8MiB live, 211.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 a b)
cost-diff	0	(sqrt.f64 (-.f64 a b))
cost-diff	0	(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 #s(approx (+ a b) (fma.f64 b (/.f64 a b) b))))
cost-diff	896	(fma.f64 b (/.f64 a b) b)
cost-diff	0	#s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a)

Rules

4 976×	`lower-*.f32`
4 974×	`lower-*.f64`
4 264×	`lower-fma.f32`
4 262×	`lower-fma.f64`
1 748×	`cube-prod`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	15	67
0	22	64
1	31	64
2	41	64
3	52	61
4	69	55
5	100	55
6	206	55
7	564	55
8	2367	55
9	3873	55
10	5003	55
11	5818	55
12	6376	55
13	7015	55
14	7824	55
0	8416	55

Stop Event

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

Calls

Call 1

Inputs
#s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a)
a
(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 #s(approx (+ a b) (fma.f64 b (/.f64 a b) b))))
(sqrt.f64 (-.f64 a b))
(-.f64 a b)
a
b
(sqrt.f64 #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)))
#s(approx (+ a b) (fma.f64 b (/.f64 a b) b))
(fma.f64 b (/.f64 a b) b)
(/.f64 a b)

Outputs
#s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a)
a
(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 #s(approx (+ a b) (fma.f64 b (/.f64 a b) b))))
(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 #s(approx (+ a b) (+.f64 a b))))
(sqrt.f64 (-.f64 a b))
(-.f64 a b)
a
b
(sqrt.f64 #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)))
(sqrt.f64 #s(approx (+ a b) (+.f64 a b)))
#s(approx (+ a b) (fma.f64 b (/.f64 a b) b))
#s(approx (+ a b) (+.f64 a b))
(fma.f64 b (/.f64 a b) b)
(+.f64 a b)
(/.f64 a b)

localize38.0ms (0.5%)

Memory

-5.1MiB live, 79.3MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0	#s(approx (+ a b) (fma.f64 b (/.f64 a b) b))
accuracy	0.00390625	(sqrt.f64 (-.f64 a b))
accuracy	0.5	(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 #s(approx (+ a b) (fma.f64 b (/.f64 a b) b))))
accuracy	17.631469225675673	(fma.f64 b (/.f64 a b) b)
accuracy	0.3117451951916497	#s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a)

Samples

23.0ms

256×

valid

Compiler

Compiled 47 to 12 computations (74.5% saved)

Precisions

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

ival-mult: 3.0ms (24.5% of total)

ival-sqrt: 3.0ms (24.5% of total)

ival-sub: 2.0ms (16.3% of total)

ival-div: 2.0ms (16.3% of total)

ival-add: 2.0ms (16.3% of total)

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

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

series5.0ms (0.1%)

Memory

10.8MiB live, 10.8MiB allocated

Counts

6 → 144

Calls

Call 1

Inputs
#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a) #<representation binary64>) () ())
#s(alt (fma.f64 b (/.f64 a b) b) (patch (fma.f64 b (/.f64 a b) b) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)))) (patch (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())
#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())
#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())

Outputs
#s(alt (* b (sqrt -1)) (taylor 0 a) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1))) (taylor 0 a) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a) #<representation binary64>) () ())) ())
#s(alt (+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1))) (taylor 0 a) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a) #<representation binary64>) () ())) ())
#s(alt (+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1))) (taylor 0 a) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a) #<representation binary64>) () ())) ())
#s(alt a (taylor inf a) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a) #<representation binary64>) () ())) ())
#s(alt (* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a)))) (taylor inf a) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))) (taylor -inf b) (#s(alt (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)))) (patch (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b))))) (taylor -inf b) (#s(alt (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)))) (patch (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b))))) (taylor -inf b) (#s(alt (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)))) (patch (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt b) (sqrt -1)) (taylor 0 a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1))) (taylor 0 a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1))) (taylor 0 a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1))) (taylor 0 a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (sqrt a) (taylor inf a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* a (+ (sqrt (/ 1 a)) (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)))) (taylor inf a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2)))))) (taylor inf a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* -1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3))))))) (taylor inf a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt a) (pow (sqrt -1) 2))) (taylor -inf a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))) (taylor -inf a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))) (taylor -inf a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (* (pow b 3) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))) (taylor -inf a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (sqrt a) (taylor 0 b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt a) (* -1/2 (* (sqrt (/ 1 a)) b))) (taylor 0 b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* -1/8 (* (sqrt (/ 1 (pow a 3))) b))))) (taylor 0 b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* -1/16 (* (sqrt (/ 1 (pow a 5))) b))))))) (taylor 0 b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt b) (sqrt -1)) (taylor inf b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* b (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))) (taylor inf b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))) (taylor inf b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))) (taylor inf b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt b) (sqrt -1))) (taylor -inf b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))) (taylor -inf b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))) (taylor -inf b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))) (taylor -inf b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 b) (taylor 0 a) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (- a b) (taylor 0 a) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (- a b) (taylor 0 a) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (- a b) (taylor 0 a) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt a (taylor inf a) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (* a (+ 1 (* -1 (/ b a)))) (taylor inf a) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (* a (+ 1 (* -1 (/ b a)))) (taylor inf a) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (* a (+ 1 (* -1 (/ b a)))) (taylor inf a) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt a (taylor -inf a) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (- (/ b a) 1))) (taylor -inf a) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (- (/ b a) 1))) (taylor -inf a) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (- (/ b a) 1))) (taylor -inf a) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt a (taylor 0 b) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (+ a (* -1 b)) (taylor 0 b) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (+ a (* -1 b)) (taylor 0 b) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (+ a (* -1 b)) (taylor 0 b) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (* -1 b) (taylor inf b) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (* b (- (/ a b) 1)) (taylor inf b) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (* b (- (/ a b) 1)) (taylor inf b) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (* b (- (/ a b) 1)) (taylor inf b) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (* -1 b) (taylor -inf b) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ 1 (* -1 (/ a b))))) (taylor -inf b) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ 1 (* -1 (/ a b))))) (taylor -inf b) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ 1 (* -1 (/ a b))))) (taylor -inf b) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt b (taylor 0 a) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt (+ a b) (taylor 0 a) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt (+ a b) (taylor 0 a) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt (+ a b) (taylor 0 a) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt a (taylor inf a) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt (* a (+ 1 (/ b a))) (taylor inf a) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt (* a (+ 1 (/ b a))) (taylor inf a) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt (* a (+ 1 (/ b a))) (taylor inf a) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt a (taylor -inf a) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (- (* -1 (/ b a)) 1))) (taylor -inf a) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (- (* -1 (/ b a)) 1))) (taylor -inf a) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (- (* -1 (/ b a)) 1))) (taylor -inf a) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt a (taylor 0 b) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt (+ a b) (taylor 0 b) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt (+ a b) (taylor 0 b) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt (+ a b) (taylor 0 b) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt b (taylor inf b) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt (* b (+ 1 (/ a b))) (taylor inf b) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt (* b (+ 1 (/ a b))) (taylor inf b) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt (* b (+ 1 (/ a b))) (taylor inf b) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt b (taylor -inf b) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (- (* -1 (/ a b)) 1))) (taylor -inf b) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (- (* -1 (/ a b)) 1))) (taylor -inf b) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (- (* -1 (/ a b)) 1))) (taylor -inf b) (#s(alt #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) (patch #s(approx (+ a b) (fma.f64 b (/.f64 a b) b)) #<representation binary64>) () ())) ())

Calls

36 calls:

Time	Variable		Point	Expression
0.0ms	b	@	inf	(+ (* b (/ a b)) b)
0.0ms	a	@	0	(* (sqrt (- a b)) (sqrt (+ a b)))
0.0ms	b	@	-inf	(+ (* b (/ a b)) b)
0.0ms	b	@	0	(+ (* b (/ a b)) b)
0.0ms	a	@	-inf	(+ (* b (/ a b)) b)

simplify198.0ms (2.7%)

Memory

29.0MiB live, 257.5MiB allocated

Algorithm

1×	egg-herbie

Rules

7 536×	`lower-fma.f64`
7 536×	`lower-fma.f32`
3 640×	`lower-*.f64`
3 640×	`lower-*.f32`
2 398×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	343	2033
1	1137	1608
2	4835	1359
0	8874	1276

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 125

Calls

Call 1

Inputs
(* b (sqrt -1))
(+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))
a
(* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))
(* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))
(* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))
(* -1 (* a (pow (sqrt -1) 2)))
(* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
a
(+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))
(+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))
(+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))
(* b (sqrt -1))
(* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))
(* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))
(* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
a
(+ a b)
(+ a b)
(+ a b)
b
(* b (+ 1 (/ a b)))
(* b (+ 1 (/ a b)))
(* b (+ 1 (/ a b)))
b
(* -1 (* b (- (* -1 (/ a b)) 1)))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(* -1 (* b (- (* -1 (/ a b)) 1)))
b
(+ a b)
(+ a b)
(+ a b)
a
(* a (+ 1 (/ b a)))
(* a (+ 1 (/ b a)))
(* a (+ 1 (/ b a)))
a
(* -1 (* a (- (* -1 (/ b a)) 1)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(* b (sqrt -1))
(+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))
a
(* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))
(* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))
(* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))
(* -1 (* a (pow (sqrt -1) 2)))
(* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
a
(+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))
(+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))
(+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))
(* b (sqrt -1))
(* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))
(* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))
(* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* (sqrt b) (sqrt -1))
(+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1)))
(+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1)))
(+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1)))
(sqrt a)
(* a (+ (sqrt (/ 1 a)) (* -1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* -1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3)))))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (* (pow b 3) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(sqrt a)
(+ (sqrt a) (* -1/2 (* (sqrt (/ 1 a)) b)))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)))))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* -1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(* (sqrt b) (sqrt -1))
(* b (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(* -1 (* (sqrt b) (sqrt -1)))
(* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
(* -1 b)
(- a b)
(- a b)
(- a b)
a
(* a (+ 1 (* -1 (/ b a))))
(* a (+ 1 (* -1 (/ b a))))
(* a (+ 1 (* -1 (/ b a))))
a
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (- (/ b a) 1)))
a
(+ a (* -1 b))
(+ a (* -1 b))
(+ a (* -1 b))
(* -1 b)
(* b (- (/ a b) 1))
(* b (- (/ a b) 1))
(* b (- (/ a b) 1))
(* -1 b)
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
b
(+ a b)
(+ a b)
(+ a b)
a
(* a (+ 1 (/ b a)))
(* a (+ 1 (/ b a)))
(* a (+ 1 (/ b a)))
a
(* -1 (* a (- (* -1 (/ b a)) 1)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
a
(+ a b)
(+ a b)
(+ a b)
b
(* b (+ 1 (/ a b)))
(* b (+ 1 (/ a b)))
(* b (+ 1 (/ a b)))
b
(* -1 (* b (- (* -1 (/ a b)) 1)))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(* -1 (* b (- (* -1 (/ a b)) 1)))

Outputs
(* b (sqrt -1))
(*.f64 b (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))
(fma.f64 b (sqrt.f64 #s(literal -1 binary64)) #s(literal 0 binary64))
(+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))
(fma.f64 (.f64 a (/.f64 a (.f64 b (sqrt.f64 #s(literal -1 binary64))))) #s(literal 1/2 binary64) (*.f64 b (sqrt.f64 #s(literal -1 binary64))))
(+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))
(fma.f64 (.f64 a (/.f64 a (.f64 b (sqrt.f64 #s(literal -1 binary64))))) #s(literal 1/2 binary64) (*.f64 b (sqrt.f64 #s(literal -1 binary64))))
a
(* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))
a
(* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))
(fma.f64 a (/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (.f64 b b))) (*.f64 a a)) a)
(* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))
(fma.f64 a (/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (.f64 b b))) (*.f64 a a)) a)
(* -1 (* a (pow (sqrt -1) 2)))
a
(* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))
a
(* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(fma.f64 a (/.f64 (/.f64 (.f64 (.f64 b b) #s(literal -1/2 binary64)) a) a) a)
(* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(fma.f64 a (/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (.f64 b b))) (*.f64 a a)) a)
a
(+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))
a
(+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))
(fma.f64 b (/.f64 (*.f64 b #s(literal -1/2 binary64)) a) a)
(+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))
(fma.f64 b (/.f64 (*.f64 b #s(literal -1/2 binary64)) a) a)
(* b (sqrt -1))
(*.f64 b (sqrt.f64 #s(literal -1 binary64)))
(* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))
(fma.f64 b (sqrt.f64 #s(literal -1 binary64)) #s(literal 0 binary64))
(* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))
(.f64 b (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 a a) (.f64 b (.f64 b (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 #s(literal -1 binary64))))
(* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))
(.f64 b (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 a a) (.f64 b (.f64 b (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* b (sqrt -1)))
(neg.f64 (*.f64 b (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))
(neg.f64 (*.f64 b (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(neg.f64 (.f64 b (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 (.f64 (.f64 a a) #s(literal -1/2 binary64)) (.f64 b (sqrt.f64 #s(literal -1 binary64)))) b))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(.f64 (neg.f64 b) (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (*.f64 a a)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 b)) b)))
a
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
b
(* b (+ 1 (/ a b)))
(fma.f64 b (/.f64 a b) b)
(* b (+ 1 (/ a b)))
(fma.f64 b (/.f64 a b) b)
(* b (+ 1 (/ a b)))
(fma.f64 b (/.f64 a b) b)
b
(* -1 (* b (- (* -1 (/ a b)) 1)))
(fma.f64 b (/.f64 a b) b)
(* -1 (* b (- (* -1 (/ a b)) 1)))
(fma.f64 b (/.f64 a b) b)
(* -1 (* b (- (* -1 (/ a b)) 1)))
(fma.f64 b (/.f64 a b) b)
b
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
a
(* a (+ 1 (/ b a)))
(fma.f64 a (/.f64 b a) a)
(* a (+ 1 (/ b a)))
(fma.f64 a (/.f64 b a) a)
(* a (+ 1 (/ b a)))
(fma.f64 a (/.f64 b a) a)
a
(* -1 (* a (- (* -1 (/ b a)) 1)))
(fma.f64 a (/.f64 b a) a)
(* -1 (* a (- (* -1 (/ b a)) 1)))
(fma.f64 a (/.f64 b a) a)
(* -1 (* a (- (* -1 (/ b a)) 1)))
(fma.f64 a (/.f64 b a) a)
(* b (sqrt -1))
(*.f64 b (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))
(fma.f64 b (sqrt.f64 #s(literal -1 binary64)) #s(literal 0 binary64))
(+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))
(fma.f64 (.f64 a (/.f64 a (.f64 b (sqrt.f64 #s(literal -1 binary64))))) #s(literal 1/2 binary64) (*.f64 b (sqrt.f64 #s(literal -1 binary64))))
(+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))
(fma.f64 (.f64 a (/.f64 a (.f64 b (sqrt.f64 #s(literal -1 binary64))))) #s(literal 1/2 binary64) (*.f64 b (sqrt.f64 #s(literal -1 binary64))))
a
(* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))
a
(* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))
(fma.f64 a (/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (.f64 b b))) (*.f64 a a)) a)
(* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))
(fma.f64 a (/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (.f64 b b))) (*.f64 a a)) a)
(* -1 (* a (pow (sqrt -1) 2)))
a
(* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))
a
(* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(fma.f64 a (/.f64 (/.f64 (.f64 (.f64 b b) #s(literal -1/2 binary64)) a) a) a)
(* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(fma.f64 a (/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (.f64 b b))) (*.f64 a a)) a)
a
(+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))
a
(+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))
(fma.f64 b (/.f64 (*.f64 b #s(literal -1/2 binary64)) a) a)
(+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))
(fma.f64 b (/.f64 (*.f64 b #s(literal -1/2 binary64)) a) a)
(* b (sqrt -1))
(*.f64 b (sqrt.f64 #s(literal -1 binary64)))
(* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))
(fma.f64 b (sqrt.f64 #s(literal -1 binary64)) #s(literal 0 binary64))
(* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))
(.f64 b (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 a a) (.f64 b (.f64 b (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 #s(literal -1 binary64))))
(* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))
(.f64 b (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 a a) (.f64 b (.f64 b (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* b (sqrt -1)))
(neg.f64 (*.f64 b (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))
(neg.f64 (*.f64 b (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(neg.f64 (.f64 b (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 (.f64 (.f64 a a) #s(literal -1/2 binary64)) (.f64 b (sqrt.f64 #s(literal -1 binary64)))) b))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(.f64 (neg.f64 b) (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (*.f64 a a)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 b)) b)))
(* (sqrt b) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 b))
(+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1)))
(fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (sqrt.f64 #s(literal -1 binary64))) (.f64 #s(literal 1/2 binary64) a) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 b)))
(+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1)))
(fma.f64 a (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (sqrt.f64 #s(literal -1 binary64))) (.f64 a (.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 b)))
(+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1)))
(fma.f64 a (fma.f64 a (fma.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (/.f64 (.f64 #s(literal 1/16 binary64) a) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 b)))
(sqrt a)
(sqrt.f64 a)
(* a (+ (sqrt (/ 1 a)) (* -1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))))))
(.f64 a (fma.f64 b (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 (.f64 b b) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* -1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3)))))))
(.f64 a (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (fma.f64 b (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) (.f64 (.f64 b (.f64 b b)) #s(literal -1/16 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 (.f64 b b) #s(literal -1/8 binary64)))))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(sqrt.f64 a)
(* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(neg.f64 (.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal -1/2 binary64)) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(neg.f64 (.f64 a (fma.f64 (.f64 (.f64 b b) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64))))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal -1/2 binary64)) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (* (pow b 3) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(neg.f64 (.f64 a (fma.f64 (.f64 b (.f64 b b)) (.f64 #s(literal -1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64))))) (fma.f64 (.f64 (.f64 b b) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64))))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (*.f64 b #s(literal -1/2 binary64)) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))))))
(sqrt a)
(sqrt.f64 a)
(+ (sqrt a) (* -1/2 (* (sqrt (/ 1 a)) b)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 b #s(literal -1/2 binary64)) (sqrt.f64 a))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)))))
(fma.f64 b (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 b #s(literal -1/8 binary64)))) (sqrt.f64 a))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* -1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(fma.f64 b (fma.f64 b (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 b #s(literal -1/16 binary64)))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))) (sqrt.f64 a))
(* (sqrt b) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 b))
(* b (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))
(.f64 b (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 a (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(.f64 b (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 a a)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 a (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (*.f64 b b)))))))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(.f64 b (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 a a)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 7 binary64)))) (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 a (.f64 a a))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 a (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)))))))
(* -1 (* (sqrt b) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 b))
(* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(.f64 (neg.f64 b) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) a)))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(.f64 (neg.f64 b) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 #s(literal -1/8 binary64) (.f64 a (.f64 (sqrt.f64 #s(literal -1 binary64)) a))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) a))))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
(.f64 (neg.f64 b) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 #s(literal -1/8 binary64) (.f64 a (.f64 (sqrt.f64 #s(literal -1 binary64)) a))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 7 binary64)))) (.f64 #s(literal 1/16 binary64) (.f64 a (.f64 a (.f64 (sqrt.f64 #s(literal -1 binary64)) a)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 b (.f64 b b)))) (.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) a)))))))
(* -1 b)
(neg.f64 b)
(- a b)
(-.f64 a b)
(- a b)
(-.f64 a b)
(- a b)
(-.f64 a b)
a
(* a (+ 1 (* -1 (/ b a))))
(fma.f64 a (/.f64 b (neg.f64 a)) a)
(* a (+ 1 (* -1 (/ b a))))
(fma.f64 a (/.f64 b (neg.f64 a)) a)
(* a (+ 1 (* -1 (/ b a))))
(fma.f64 a (/.f64 b (neg.f64 a)) a)
a
(* -1 (* a (- (/ b a) 1)))
(fma.f64 a (/.f64 b (neg.f64 a)) a)
(* -1 (* a (- (/ b a) 1)))
(fma.f64 a (/.f64 b (neg.f64 a)) a)
(* -1 (* a (- (/ b a) 1)))
(fma.f64 a (/.f64 b (neg.f64 a)) a)
a
(+ a (* -1 b))
(-.f64 a b)
(+ a (* -1 b))
(-.f64 a b)
(+ a (* -1 b))
(-.f64 a b)
(* -1 b)
(neg.f64 b)
(* b (- (/ a b) 1))
(fma.f64 b (/.f64 a b) (neg.f64 b))
(* b (- (/ a b) 1))
(fma.f64 b (/.f64 a b) (neg.f64 b))
(* b (- (/ a b) 1))
(fma.f64 b (/.f64 a b) (neg.f64 b))
(* -1 b)
(neg.f64 b)
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(fma.f64 b (/.f64 a b) (neg.f64 b))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(fma.f64 b (/.f64 a b) (neg.f64 b))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(fma.f64 b (/.f64 a b) (neg.f64 b))
b
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
a
(* a (+ 1 (/ b a)))
(fma.f64 a (/.f64 b a) a)
(* a (+ 1 (/ b a)))
(fma.f64 a (/.f64 b a) a)
(* a (+ 1 (/ b a)))
(fma.f64 a (/.f64 b a) a)
a
(* -1 (* a (- (* -1 (/ b a)) 1)))
(fma.f64 a (/.f64 b a) a)
(* -1 (* a (- (* -1 (/ b a)) 1)))
(fma.f64 a (/.f64 b a) a)
(* -1 (* a (- (* -1 (/ b a)) 1)))
(fma.f64 a (/.f64 b a) a)
a
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
b
(* b (+ 1 (/ a b)))
(fma.f64 b (/.f64 a b) b)
(* b (+ 1 (/ a b)))
(fma.f64 b (/.f64 a b) b)
(* b (+ 1 (/ a b)))
(fma.f64 b (/.f64 a b) b)
b
(* -1 (* b (- (* -1 (/ a b)) 1)))
(fma.f64 b (/.f64 a b) b)
(* -1 (* b (- (* -1 (/ a b)) 1)))
(fma.f64 b (/.f64 a b) b)
(* -1 (* b (- (* -1 (/ a b)) 1)))
(fma.f64 b (/.f64 a b) b)

rewrite162.0ms (2.2%)

Memory

-39.2MiB live, 258.1MiB allocated

Rules

3 714×	`lower-*.f32`
3 712×	`lower-*.f64`
3 410×	`lower-fma.f32`
3 408×	`lower-fma.f64`
3 210×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	50
0	22	48
1	73	48
2	480	39
0	8632	39

Stop Event

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

Counts

6 → 371

Calls

Call 1

Inputs
#s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a)
(fma.f64 b (/.f64 a b) b)
(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 #s(approx (+ a b) (fma.f64 b (/.f64 a b) b))))
(sqrt.f64 (-.f64 a b))
(-.f64 a b)
#s(approx (+ a b) (fma.f64 b (/.f64 a b) b))

Outputs
#s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a)
(+.f64 a b)
(+.f64 b a)
(+.f64 (/.f64 (.f64 a a) (-.f64 a b)) (neg.f64 (/.f64 (.f64 b b) (-.f64 a b))))
(+.f64 (.f64 (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64)) (.f64 a a)) (.f64 (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64)) (.f64 b (+.f64 a b))))
(+.f64 (.f64 (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64)) (.f64 b (+.f64 a b))) (.f64 (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64)) (.f64 a a)))
(+.f64 (.f64 (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64)) (fma.f64 a a (.f64 b b))) (.f64 (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64)) (.f64 a b)))
(+.f64 (.f64 (.f64 a a) (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64))) (.f64 (.f64 b (+.f64 a b)) (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64))))
(+.f64 (.f64 (.f64 b (+.f64 a b)) (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64))) (.f64 (.f64 a a) (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64))))
(+.f64 (.f64 (fma.f64 a a (.f64 b b)) (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64))) (.f64 (.f64 a b) (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64))))
(+.f64 (-.f64 a #s(literal 0 binary64)) b)
(-.f64 a (neg.f64 b))
(-.f64 (/.f64 (.f64 a a) (-.f64 a b)) (/.f64 (.f64 b b) (-.f64 a b)))
(-.f64 (/.f64 (.f64 b b) (-.f64 b a)) (/.f64 (.f64 a a) (-.f64 b a)))
(fma.f64 a #s(literal 1 binary64) b)
(fma.f64 a (/.f64 a (-.f64 a b)) (neg.f64 (/.f64 (*.f64 b b) (-.f64 a b))))
(fma.f64 b (/.f64 a b) b)
(fma.f64 b #s(literal 1 binary64) a)
(fma.f64 b (/.f64 (/.f64 (.f64 a a) b) (-.f64 a b)) (neg.f64 (/.f64 (.f64 b b) (-.f64 a b))))
(fma.f64 (/.f64 a b) b b)
(fma.f64 (/.f64 a b) (/.f64 (.f64 a b) (-.f64 a b)) (neg.f64 (/.f64 (.f64 b b) (-.f64 a b))))
(fma.f64 (neg.f64 a) (*.f64 (/.f64 #s(literal -1 binary64) b) b) b)
(fma.f64 (neg.f64 a) (/.f64 b (neg.f64 b)) b)
(fma.f64 (.f64 a a) (/.f64 #s(literal 1 binary64) (-.f64 a b)) (neg.f64 (/.f64 (.f64 b b) (-.f64 a b))))
(fma.f64 (.f64 a a) (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64)) (.f64 (.f64 b (+.f64 a b)) (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (*.f64 b (+.f64 a b)))) #s(literal 1 binary64))))
(fma.f64 (.f64 b b) (/.f64 (/.f64 (.f64 a a) (.f64 b b)) (-.f64 a b)) (neg.f64 (/.f64 (.f64 b b) (-.f64 a b))))
(fma.f64 (.f64 b (+.f64 a b)) (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64)) (.f64 (.f64 a a) (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (*.f64 b (+.f64 a b)))) #s(literal 1 binary64))))
(fma.f64 #s(literal 1 binary64) a b)
(fma.f64 #s(literal 1 binary64) b a)
(fma.f64 (/.f64 #s(literal 1 binary64) b) (*.f64 a b) b)
(fma.f64 (*.f64 a b) (/.f64 #s(literal 1 binary64) b) b)
(fma.f64 (.f64 a b) (/.f64 (/.f64 a b) (-.f64 a b)) (neg.f64 (/.f64 (.f64 b b) (-.f64 a b))))
(fma.f64 #s(literal -1 binary64) (neg.f64 a) b)
(fma.f64 #s(literal -1 binary64) (neg.f64 b) a)
(fma.f64 (*.f64 a (neg.f64 b)) (/.f64 #s(literal -1 binary64) b) b)
(fma.f64 (fma.f64 a a (.f64 b b)) (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64)) (.f64 (.f64 a b) (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (*.f64 b (+.f64 a b)))) #s(literal 1 binary64))))
(fma.f64 (/.f64 (.f64 a a) (.f64 b b)) (/.f64 (.f64 b b) (-.f64 a b)) (neg.f64 (/.f64 (.f64 b b) (-.f64 a b))))
(fma.f64 (/.f64 (.f64 a a) b) (/.f64 b (-.f64 a b)) (neg.f64 (/.f64 (.f64 b b) (-.f64 a b))))
(fma.f64 (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64)) (.f64 a a) (.f64 (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64)) (*.f64 b (+.f64 a b))))
(fma.f64 (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64)) (.f64 b (+.f64 a b)) (.f64 (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64)) (*.f64 a a)))
(fma.f64 (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64)) (fma.f64 a a (.f64 b b)) (.f64 (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64)) (*.f64 a b)))
(fma.f64 (/.f64 (.f64 a a) (.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b))))) (fma.f64 a a (.f64 b (+.f64 a b))) (neg.f64 (/.f64 (*.f64 b b) (-.f64 a b))))
(fma.f64 (/.f64 (.f64 a a) (.f64 (+.f64 a b) (-.f64 a b))) (+.f64 a b) (neg.f64 (/.f64 (*.f64 b b) (-.f64 a b))))
(fma.f64 (/.f64 a (.f64 (+.f64 a b) (-.f64 a b))) (/.f64 a (/.f64 #s(literal 1 binary64) (+.f64 a b))) (neg.f64 (/.f64 (.f64 b b) (-.f64 a b))))
(fma.f64 (/.f64 a (.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b))))) (/.f64 a (/.f64 #s(literal 1 binary64) (fma.f64 a a (.f64 b (+.f64 a b))))) (neg.f64 (/.f64 (.f64 b b) (-.f64 a b))))
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(/.f64 (.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b))))) (.f64 (+.f64 a b) (.f64 (fma.f64 a a (.f64 b (-.f64 b a))) (fma.f64 a a (.f64 b (+.f64 a b))))))
(/.f64 (.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b))))) (.f64 (+.f64 a b) (fma.f64 (.f64 b b) (fma.f64 a a (.f64 b b)) (.f64 a (.f64 a (.f64 a a))))))
(/.f64 (.f64 (fma.f64 a a (.f64 b b)) (.f64 (+.f64 a b) (-.f64 a b))) (.f64 (+.f64 a b) (fma.f64 a a (*.f64 b b))))
(/.f64 (.f64 (-.f64 a b) (fma.f64 a (.f64 a a) (.f64 b (.f64 b b)))) (fma.f64 a (.f64 a a) (.f64 b (*.f64 b b))))
(/.f64 (.f64 (-.f64 a b) (.f64 (+.f64 a b) (-.f64 a b))) (*.f64 (+.f64 a b) (-.f64 a b)))
(/.f64 (.f64 (+.f64 a b) (.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b))))) (.f64 (+.f64 a b) (fma.f64 a a (*.f64 b (+.f64 a b)))))
(/.f64 (.f64 (+.f64 a b) (.f64 (+.f64 a b) (-.f64 a b))) (*.f64 (+.f64 a b) (+.f64 a b)))
(/.f64 (.f64 (/.f64 (-.f64 a b) (fma.f64 a a (.f64 b (-.f64 b a)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 a a (*.f64 b (-.f64 b a)))))
(/.f64 (-.f64 (.f64 (.f64 a (.f64 a a)) (fma.f64 a a (.f64 b (+.f64 a b)))) (.f64 (fma.f64 a a (.f64 b (+.f64 a b))) (.f64 b (.f64 b b)))) (.f64 (fma.f64 a a (.f64 b (+.f64 a b))) (fma.f64 a a (*.f64 b (+.f64 a b)))))
(/.f64 (-.f64 (.f64 (.f64 a a) (+.f64 a b)) (.f64 (+.f64 a b) (.f64 b b))) (*.f64 (+.f64 a b) (+.f64 a b)))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b))))) (fma.f64 a a (.f64 b (+.f64 a b))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (fma.f64 a a (.f64 b (+.f64 a b))) (-.f64 b a))) (neg.f64 (fma.f64 a a (.f64 b (+.f64 a b)))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (+.f64 a b) (-.f64 b a))) (neg.f64 (+.f64 a b)))
(/.f64 (.f64 (.f64 (+.f64 a b) (-.f64 a b)) (.f64 (fma.f64 a a (.f64 b (+.f64 a b))) (-.f64 b a))) (.f64 (.f64 (+.f64 a b) (-.f64 a b)) (neg.f64 (fma.f64 a a (*.f64 b (+.f64 a b))))))
(/.f64 (.f64 (.f64 (+.f64 a b) (-.f64 a b)) (.f64 (+.f64 a b) (-.f64 b a))) (.f64 (*.f64 (+.f64 a b) (-.f64 a b)) (neg.f64 (+.f64 a b))))
(/.f64 (.f64 (.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64)) (fma.f64 a a (.f64 b (+.f64 a b))))
(/.f64 (.f64 (.f64 (.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) (.f64 (+.f64 a b) (-.f64 a b))) #s(literal 1 binary64)) (.f64 (+.f64 a b) (.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b))))))
(/.f64 (.f64 (.f64 (+.f64 a b) (.f64 (-.f64 a b) (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))))) #s(literal 1 binary64)) (.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (+.f64 a b)))
(/.f64 (.f64 (.f64 (+.f64 a b) (-.f64 a b)) (fma.f64 a a (.f64 b (-.f64 b a)))) (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))))
(/.f64 (.f64 (.f64 (.f64 (+.f64 a b) (-.f64 a b)) (.f64 (+.f64 a b) (-.f64 a b))) #s(literal 1 binary64)) (.f64 (+.f64 a b) (.f64 (+.f64 a b) (-.f64 a b))))
(/.f64 (.f64 (.f64 (fma.f64 a a (.f64 b b)) (.f64 (+.f64 a b) (-.f64 a b))) #s(literal 1 binary64)) (.f64 (fma.f64 a a (.f64 b b)) (+.f64 a b)))
(/.f64 (.f64 (.f64 (-.f64 a b) (fma.f64 a (.f64 a a) (.f64 b (.f64 b b)))) #s(literal 1 binary64)) (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))))
(/.f64 (.f64 (.f64 (-.f64 a b) (.f64 (+.f64 a b) (-.f64 a b))) #s(literal 1 binary64)) (.f64 (+.f64 a b) (-.f64 a b)))
(/.f64 (.f64 (.f64 (+.f64 a b) (.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b))))) #s(literal 1 binary64)) (.f64 (fma.f64 a a (.f64 b (+.f64 a b))) (+.f64 a b)))
(/.f64 (.f64 (.f64 (+.f64 a b) (.f64 (+.f64 a b) (-.f64 a b))) #s(literal 1 binary64)) (.f64 (+.f64 a b) (+.f64 a b)))
(/.f64 (.f64 (.f64 (+.f64 a b) (-.f64 a b)) (fma.f64 a (.f64 (.f64 a a) (.f64 a (.f64 a a))) (.f64 (.f64 b (-.f64 b a)) (.f64 (.f64 b (-.f64 b a)) (.f64 b (-.f64 b a)))))) (.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (fma.f64 (.f64 b (-.f64 b a)) (-.f64 (.f64 b (-.f64 b a)) (.f64 a a)) (.f64 a (.f64 a (*.f64 a a))))))
(/.f64 (.f64 (.f64 (+.f64 a b) (-.f64 a b)) (.f64 (fma.f64 a a (.f64 b (-.f64 b a))) (-.f64 (.f64 a a) (.f64 b (-.f64 b a))))) (.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (-.f64 (.f64 a a) (.f64 b (-.f64 b a)))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 a (.f64 a a)) (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a)))) (.f64 (.f64 b (.f64 b b)) (.f64 (.f64 b (.f64 b b)) (.f64 b (.f64 b b))))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 b (.f64 b b)) (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a)))) (fma.f64 a a (*.f64 b (+.f64 a b)))))
(/.f64 (.f64 (.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b))))) #s(literal 1 binary64)) (.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (fma.f64 a a (.f64 b (+.f64 a b)))))
(/.f64 (.f64 (.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b))))) #s(literal 1 binary64)) (.f64 (.f64 (fma.f64 a a (.f64 b (-.f64 b a))) (fma.f64 a a (*.f64 b (+.f64 a b)))) (+.f64 a b)))
(/.f64 (.f64 (.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b))))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 b b) (fma.f64 a a (.f64 b b)) (.f64 a (.f64 a (*.f64 a a)))) (+.f64 a b)))
(/.f64 (neg.f64 (*.f64 (+.f64 a b) (-.f64 b a))) (+.f64 a b))
(/.f64 (neg.f64 (.f64 (fma.f64 a a (.f64 b (+.f64 a b))) (-.f64 b a))) (neg.f64 (neg.f64 (fma.f64 a a (*.f64 b (+.f64 a b))))))
(/.f64 (/.f64 (.f64 (+.f64 a b) (-.f64 a b)) (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64))) (fma.f64 a a (.f64 b (+.f64 a b))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 a (.f64 a a)) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 b (.f64 b b)) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 a (.f64 a a)) (fma.f64 a a (.f64 b (+.f64 a b)))) (/.f64 (.f64 a (.f64 a a)) (fma.f64 a a (.f64 b (+.f64 a b)))) (fma.f64 (/.f64 (.f64 b (.f64 b b)) (fma.f64 a a (.f64 b (+.f64 a b)))) (/.f64 (.f64 b (.f64 b b)) (fma.f64 a a (.f64 b (+.f64 a b)))) (.f64 (/.f64 (.f64 a (.f64 a a)) (fma.f64 a a (.f64 b (+.f64 a b)))) (/.f64 (.f64 b (.f64 b b)) (fma.f64 a a (*.f64 b (+.f64 a b))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 a a) (+.f64 a b)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 b b) (+.f64 a b)) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 a a) (+.f64 a b)) (/.f64 (.f64 a a) (+.f64 a b)) (fma.f64 (/.f64 (.f64 b b) (+.f64 a b)) (/.f64 (.f64 b b) (+.f64 a b)) (.f64 (/.f64 (.f64 a a) (+.f64 a b)) (/.f64 (*.f64 b b) (+.f64 a b))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 a (.f64 a a)) (fma.f64 a a (.f64 b (+.f64 a b)))) (/.f64 (.f64 a (.f64 a a)) (fma.f64 a a (.f64 b (+.f64 a b))))) (.f64 (/.f64 (.f64 b (.f64 b b)) (fma.f64 a a (.f64 b (+.f64 a b)))) (/.f64 (.f64 b (.f64 b b)) (fma.f64 a a (.f64 b (+.f64 a b)))))) (fma.f64 a (/.f64 (.f64 a a) (fma.f64 a a (.f64 b (+.f64 a b)))) (/.f64 (.f64 b (.f64 b b)) (fma.f64 a a (*.f64 b (+.f64 a b))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 a a) (+.f64 a b)) (/.f64 (.f64 a a) (+.f64 a b))) (.f64 (/.f64 (.f64 b b) (+.f64 a b)) (/.f64 (.f64 b b) (+.f64 a b)))) (fma.f64 a (/.f64 a (+.f64 a b)) (/.f64 (*.f64 b b) (+.f64 a b))))
(/.f64 (.f64 (.f64 (/.f64 (-.f64 a b) (fma.f64 a a (.f64 b (-.f64 b a)))) #s(literal 1 binary64)) (fma.f64 a (.f64 (.f64 a a) (.f64 a (.f64 a a))) (.f64 (.f64 b (-.f64 b a)) (.f64 (.f64 b (-.f64 b a)) (.f64 b (-.f64 b a)))))) (fma.f64 (.f64 b (-.f64 b a)) (-.f64 (.f64 b (-.f64 b a)) (.f64 a a)) (.f64 a (.f64 a (.f64 a a)))))
(/.f64 (.f64 (.f64 (/.f64 (-.f64 a b) (fma.f64 a a (.f64 b (-.f64 b a)))) #s(literal 1 binary64)) (.f64 (fma.f64 a a (.f64 b (-.f64 b a))) (-.f64 (.f64 a a) (.f64 b (-.f64 b a))))) (-.f64 (.f64 a a) (*.f64 b (-.f64 b a))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 a (.f64 a a)) (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a)))) (.f64 (.f64 b (.f64 b b)) (.f64 (.f64 b (.f64 b b)) (.f64 b (.f64 b b))))) (/.f64 #s(literal 1 binary64) (fma.f64 a a (.f64 b (+.f64 a b))))) (fma.f64 (.f64 b (.f64 b b)) (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a)))))
(/.f64 (.f64 (.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b))))) (/.f64 #s(literal 1 binary64) (fma.f64 a a (.f64 b (+.f64 a b))))) (fma.f64 a (.f64 a a) (.f64 b (*.f64 b b))))
(/.f64 (.f64 (.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b))))) (/.f64 #s(literal 1 binary64) (+.f64 a b))) (.f64 (fma.f64 a a (.f64 b (-.f64 b a))) (fma.f64 a a (.f64 b (+.f64 a b)))))
(/.f64 (.f64 (.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b))))) (/.f64 #s(literal 1 binary64) (+.f64 a b))) (fma.f64 (.f64 b b) (fma.f64 a a (.f64 b b)) (.f64 a (.f64 a (.f64 a a)))))
(/.f64 (.f64 (.f64 (.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) (.f64 (+.f64 a b) (-.f64 a b))) (/.f64 #s(literal 1 binary64) (+.f64 a b))) (.f64 (-.f64 a b) (fma.f64 a a (*.f64 b (+.f64 a b)))))
(/.f64 (.f64 (.f64 (+.f64 a b) (.f64 (-.f64 a b) (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))))) (/.f64 #s(literal 1 binary64) (+.f64 a b))) (fma.f64 a (.f64 a a) (.f64 b (*.f64 b b))))
(/.f64 (.f64 (.f64 (.f64 (+.f64 a b) (-.f64 a b)) (.f64 (+.f64 a b) (-.f64 a b))) (/.f64 #s(literal 1 binary64) (+.f64 a b))) (*.f64 (+.f64 a b) (-.f64 a b)))
(/.f64 (.f64 (.f64 (fma.f64 a a (.f64 b b)) (.f64 (+.f64 a b) (-.f64 a b))) (/.f64 #s(literal 1 binary64) (+.f64 a b))) (fma.f64 a a (*.f64 b b)))
(/.f64 (.f64 (.f64 (-.f64 a b) (fma.f64 a (.f64 a a) (.f64 b (.f64 b b)))) (/.f64 #s(literal 1 binary64) (+.f64 a b))) (fma.f64 a a (.f64 b (-.f64 b a))))
(/.f64 (.f64 (.f64 (-.f64 a b) (*.f64 (+.f64 a b) (-.f64 a b))) (/.f64 #s(literal 1 binary64) (+.f64 a b))) (-.f64 a b))
(/.f64 (/.f64 (*.f64 (+.f64 a b) (-.f64 a b)) (+.f64 (/.f64 a b) #s(literal 1 binary64))) b)
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 a b)) #s(literal -1 binary64))
(*.f64 b (+.f64 (/.f64 a b) #s(literal -1 binary64)))
(.f64 (+.f64 a b) (.f64 (-.f64 a b) (/.f64 #s(literal 1 binary64) (+.f64 a b))))
(*.f64 (+.f64 a b) (/.f64 (-.f64 a b) (+.f64 a b)))
(*.f64 (-.f64 a b) #s(literal 1 binary64))
(.f64 (fma.f64 a a (.f64 b (-.f64 b a))) (.f64 (/.f64 (-.f64 a b) (fma.f64 a a (.f64 b (-.f64 b a)))) #s(literal 1 binary64)))
(.f64 (.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) (/.f64 #s(literal 1 binary64) (fma.f64 a a (.f64 b (+.f64 a b)))))
(.f64 (fma.f64 a a (.f64 b (+.f64 a b))) (/.f64 (-.f64 a b) (fma.f64 a a (*.f64 b (+.f64 a b)))))
(.f64 (fma.f64 a a (.f64 b (+.f64 a b))) (.f64 (-.f64 a b) (/.f64 #s(literal 1 binary64) (fma.f64 a a (.f64 b (+.f64 a b))))))
(*.f64 #s(literal 1 binary64) (-.f64 a b))
(.f64 (.f64 (+.f64 a b) (-.f64 a b)) (/.f64 #s(literal 1 binary64) (+.f64 a b)))
(.f64 (.f64 (fma.f64 a a (.f64 b (+.f64 a b))) (-.f64 b a)) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 a a (.f64 b (+.f64 a b))))))
(.f64 (.f64 (+.f64 a b) (-.f64 b a)) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 a b))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 a b)) (/.f64 (-.f64 a b) (/.f64 #s(literal 1 binary64) (-.f64 a b))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 a b)) (.f64 (+.f64 a b) (-.f64 a b)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a a (.f64 b (+.f64 a b)))) (.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))))
(.f64 (.f64 (/.f64 (-.f64 a b) (fma.f64 a a (.f64 b (-.f64 b a)))) #s(literal 1 binary64)) (fma.f64 a a (.f64 b (-.f64 b a))))
(.f64 (.f64 #s(literal 1 binary64) (.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b))))) (/.f64 #s(literal 1 binary64) (fma.f64 a a (*.f64 b (+.f64 a b)))))
(*.f64 (/.f64 (+.f64 a b) (+.f64 (/.f64 a b) #s(literal 1 binary64))) (/.f64 (-.f64 a b) b))
(*.f64 (/.f64 (-.f64 a b) #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 (/.f64 (+.f64 a b) #s(literal 1 binary64)) (/.f64 (-.f64 a b) (+.f64 a b)))
(.f64 (/.f64 (+.f64 a b) (fma.f64 a (.f64 a a) (.f64 b (.f64 b b)))) (/.f64 (-.f64 a b) (/.f64 #s(literal 1 binary64) (fma.f64 a a (*.f64 b (-.f64 b a))))))
(.f64 (/.f64 (+.f64 a b) (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64))) (/.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))))
(.f64 (/.f64 (-.f64 a b) (fma.f64 a (.f64 a a) (.f64 b (.f64 b b)))) (/.f64 (+.f64 a b) (/.f64 #s(literal 1 binary64) (fma.f64 a a (*.f64 b (-.f64 b a))))))
(.f64 (/.f64 (-.f64 a b) (.f64 (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) #s(literal 1 binary64))) (/.f64 (+.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))))
(.f64 (.f64 #s(literal 1 binary64) (.f64 (/.f64 (-.f64 a b) (fma.f64 a a (.f64 b (-.f64 b a)))) #s(literal 1 binary64))) (fma.f64 a a (*.f64 b (-.f64 b a))))
(.f64 (/.f64 (.f64 (+.f64 a b) (-.f64 a b)) (*.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a))
(.f64 (/.f64 (.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) (fma.f64 a (.f64 (.f64 a a) (.f64 a (.f64 a a))) (.f64 (.f64 b (+.f64 a b)) (.f64 (.f64 b (+.f64 a b)) (.f64 b (+.f64 a b)))))) (fma.f64 (.f64 b (+.f64 a b)) (-.f64 (.f64 b (+.f64 a b)) (.f64 a a)) (.f64 a (.f64 a (.f64 a a)))))
(.f64 (/.f64 (.f64 (-.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b)))) (.f64 (fma.f64 a a (.f64 b (+.f64 a b))) (-.f64 (.f64 a a) (.f64 b (+.f64 a b))))) (-.f64 (.f64 a a) (*.f64 b (+.f64 a b))))
(.f64 (/.f64 (.f64 (+.f64 a b) (-.f64 a b)) (neg.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))))) (neg.f64 (fma.f64 a a (.f64 b (-.f64 b a)))))
#s(approx (+ a b) (+.f64 a b))

eval131.0ms (1.8%)

Memory: -4.7MiB live, 112.3MiB allocated
Compiler: Compiled 13 798 to 1 592 computations (88.5% saved)

prune762.0ms (10.4%)

Memory

5.0MiB live, 122.8MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	496	0	496
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	496	5	501

Accuracy

100.0%

Counts

501 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 a b)))
✓	72.0%	(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 #s(approx (+ a b) (fma.f64 b (/.f64 a b) b))))
✓	56.3%	(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 a b)))
✓	99.5%	#s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a)
✓	99.9%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a))

Compiler

Compiled 110 to 52 computations (52.7% saved)

regimes17.0ms (0.2%)

Memory

27.8MiB live, 27.8MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

6 calls:

3.0ms	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
3.0ms	b
3.0ms	a
3.0ms	(-.f64 (.f64 a a) (.f64 b b))
3.0ms	(*.f64 a a)

Results

Accuracy	Segments	Branch
99.9%	1	`a`
99.9%	1	`b`
99.9%	1	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
99.9%	1	`(-.f64 (.f64 a a) (.f64 b b))`
99.9%	1	`(*.f64 a a)`
99.9%	1	`(*.f64 b b)`

Compiler

Compiled 35 to 21 computations (40% saved)

regimes490.0ms (6.7%)

Memory

-21.7MiB live, 23.4MiB allocated

Accuracy

Total -63.0b remaining (-20217.2%)

Threshold costs -63b (-20217.2%)

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a)
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
(sqrt.f64 #s(approx (- (* a a) (* b b)) (*.f64 a a)))
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 a b)))

Outputs
#s(approx (* (sqrt (- a b)) (sqrt (+ a b))) a)

Calls

6 calls:

480.0ms	(*.f64 a a)
2.0ms	a
2.0ms	b
2.0ms	(-.f64 (.f64 a a) (.f64 b b))
2.0ms	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Results

Accuracy	Segments	Branch
99.5%	1	`a`
99.5%	1	`b`
99.5%	1	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
99.5%	1	`(-.f64 (.f64 a a) (.f64 b b))`
99.5%	1	`(*.f64 a a)`
99.5%	1	`(*.f64 b b)`

Compiler

Compiled 35 to 21 computations (40% saved)

simplify5.0ms (0.1%)

Memory

8.0MiB live, 8.0MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	28
1	18	28

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness476.0ms (6.5%)

Memory

18.8MiB live, 212.3MiB allocated

Rules

21 296×	`lower-fma.f64`
21 296×	`lower-fma.f32`
11 938×	`lower-fma.f64`
11 938×	`lower-fma.f32`
6 736×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	575	5151
1	1871	4359
2	7607	4351
0	8057	4106
0	6	21
0	10	21
1	36	21
2	239	21
3	2135	21
0	9378	21
0	119	753
1	332	753
2	1125	740
3	4532	722
0	8248	682

Stop Event

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

Compiler

Compiled 45 to 25 computations (44.4% saved)

preprocess68.0ms (0.9%)

Memory: -31.3MiB live, 46.6MiB allocated
Remove: (abs b)
Compiler: Compiled 142 to 78 computations (45.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze30.0ms (0.4%)

sample809.0ms (11%)

explain113.0ms (1.5%)

preprocess783.0ms (10.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify580.0ms (7.9%)

localize36.0ms (0.5%)

series6.0ms (0.1%)

simplify415.0ms (5.6%)

rewrite373.0ms (5.1%)

eval90.0ms (1.2%)

prune64.0ms (0.9%)

simplify203.0ms (2.8%)

localize92.0ms (1.3%)

series35.0ms (0.5%)

simplify342.0ms (4.6%)

rewrite332.0ms (4.5%)

eval270.0ms (3.7%)

prune209.0ms (2.8%)

simplify214.0ms (2.9%)

localize38.0ms (0.5%)

series5.0ms (0.1%)

simplify198.0ms (2.7%)

rewrite162.0ms (2.2%)

eval131.0ms (1.8%)

prune762.0ms (10.4%)

regimes17.0ms (0.2%)

regimes490.0ms (6.7%)

simplify5.0ms (0.1%)

soundness476.0ms (6.5%)

preprocess68.0ms (0.9%)

end0.0ms (0%)

Profiling