Metrics for bug366, discussion (missed optimization)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze32.0ms (0.8%)

Memory

-13.6MiB live, 65.6MiB 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)

sample1.4s (34.3%)

Memory

-8.4MiB live, 1 274.6MiB allocated

Samples

1.1s	8 256×	0	valid
32.0ms	657×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 570.0ms

ival-mult: 265.0ms (46.5% of total)

ival-sub: 181.0ms (31.8% of total)

ival-sqrt: 113.0ms (19.8% of total)

ival-true: 7.0ms (1.2% of total)

ival-assert: 4.0ms (0.7% of total)

Bogosity

explain107.0ms (2.6%)

Memory

10.3MiB live, 167.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
117	-	-	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
13	-	-	`(-.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	105	0
↳	`(*.f64 b b)`	overflow	13
↳	`(-.f64 (.f64 a a) (.f64 b b))`	overflow	105
↳	`(*.f64 a a)`	overflow	105
`-.f64`	`(-.f64 (.f64 a a) (.f64 b b))`	nan-rescue	13	0
↳	`(*.f64 a a)`	overflow	105
↳	`(*.f64 b b)`	overflow	13
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`	uflow-rescue	12	0
↳	`(*.f64 b b)`	underflow	122
↳	`(-.f64 (.f64 a a) (.f64 b b))`	underflow	12
↳	`(*.f64 a a)`	underflow	12

Confusion

	Predicted +	Predicted -
+	117	0
-	0	139

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	117	0	0
-	0	0	139

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	139
1	104
2	13

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 58 to 22 computations (62.1% saved)

Precisions

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

ival-mult: 7.0ms (49.3% of total)

ival-sqrt: 4.0ms (28.2% of total)

ival-sub: 2.0ms (14.1% of total)

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

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

preprocess424.0ms (10.3%)

Memory

-4.2MiB live, 269.5MiB allocated

Algorithm

1×	egg-herbie

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 b a)))

Symmetry

(abs b)

(abs a)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	57.0%	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify342.0ms (8.3%)

Memory

-12.2MiB live, 192.3MiB 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))

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

localize54.0ms (1.3%)

Memory

27.5MiB live, 102.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 b b)
accuracy	0	(*.f64 a a)
accuracy	2.5898437500000004	(-.f64 (.f64 a a) (.f64 b b))
accuracy	27.241348465738422	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Samples

15.0ms

256×

valid

Compiler

Compiled 25 to 8 computations (68% saved)

Precisions

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

ival-mult: 5.0ms (61.5% of total)

ival-sqrt: 2.0ms (24.6% of total)

ival-sub: 1.0ms (12.3% of total)

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

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

series7.0ms (0.2%)

Memory

10.8MiB live, 10.8MiB 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 (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 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 (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 (* -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 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 (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 (* -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 (* 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 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 (* -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 (* 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 (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 (.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 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 (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 (.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 (* -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 (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>) () ())) ())

Calls

6 calls:

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

simplify161.0ms (3.9%)

Memory

-20.9MiB live, 172.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	119	757
1	332	757
2	1128	744
3	4541	722
0	8122	682

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 70

Calls

Call 1

Inputs
(pow a 2)
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
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)))))
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 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))
(* 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))))))))
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 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 (* 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 b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(- (pow a 2) (pow b 2))
(- (pow a 2) (pow b 2))
(* 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)))))))
(pow a 2)
(pow a 2)
(pow a 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)))))
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)))))))
(pow a 2)
(pow a 2)
(pow a 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)))))
(* -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))))))))
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)

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

rewrite230.0ms (5.6%)

Memory

26.0MiB live, 262.6MiB allocated

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
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval74.0ms (1.8%)

Memory: 3.3MiB live, 76.3MiB allocated
Compiler: Compiled 10 807 to 1 293 computations (88% saved)

prune9.0ms (0.2%)

Memory

-26.9MiB live, 23.3MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	393	3	396
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	394	3	397

Accuracy

100.0%

Counts

397 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	57.4%	(sqrt.f64 #s(approx (- (* a a) (* b b)) (*.f64 a a)))
▶	100.0%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a))
▶	1.1%	#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify145.0ms (3.5%)

Memory

23.3MiB live, 181.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	77
0	23	77
1	41	77
2	63	77
3	98	77
4	163	77
5	367	77
6	622	77
7	1329	77
8	2689	77
9	4895	77
10	7027	77
0	8053	77

Stop Event

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

Calls

Call 1

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

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

localize36.0ms (0.9%)

Memory

-13.6MiB live, 61.8MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 a a)
accuracy	0	#s(approx (- (* a a) (* b b)) (*.f64 a a))
accuracy	27.241348465738422	(sqrt.f64 #s(approx (- (* a a) (* b b)) (*.f64 a a)))
accuracy	0	(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)
accuracy	0	(/.f64 #s(literal -1/2 binary64) a)
accuracy	0	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a))
accuracy	0.1640625	(*.f64 (/.f64 #s(literal -1/2 binary64) a) b)
accuracy	0	(neg.f64 a)
accuracy	63.2693058534996	#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))

Samples

28.0ms

256×

valid

Compiler

Compiled 60 to 14 computations (76.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-mult: 11.0ms (60% of total)

ival-div: 2.0ms (10.9% of total)

ival-sqrt: 2.0ms (10.9% of total)

ival-add: 1.0ms (5.5% of total)

ival-sub: 1.0ms (5.5% of total)

ival-neg: 1.0ms (5.5% of total)

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

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

exact: 0.0ms (0% of total)

series14.0ms (0.3%)

Memory

27.8MiB live, 27.8MiB allocated

Counts

9 → 180

Calls

Call 1

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

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

Calls

6 calls:

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

simplify295.0ms (7.2%)

Memory

-32.5MiB live, 246.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	132	2145
1	360	2145
2	1198	2106
3	4782	2034
0	8311	1911

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 171

Calls

Call 1

Inputs
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)))))
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)))))
a
(+ a (* -1/2 (/ (pow b 2) a)))
(+ a (* -1/2 (/ (pow b 2) a)))
(+ a (* -1/2 (/ (pow b 2) a)))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
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)))))
(pow a 2)
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(* 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))))))))
(* 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))))))))
(* -1/2 (/ (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 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b 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 (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 (* 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 (* 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)))))))))
(* -1/2 (/ (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 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -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 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)))))))
(* -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)))))))
(* -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)
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(/ -1/2 a)
(/ -1/2 a)
(/ -1/2 a)
(/ -1/2 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)))))))
(* -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)
(pow a 2)
(pow a 2)
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 a)
(* -1 a)
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)))))))
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)))))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(/ -1/2 a)
(/ -1/2 a)
(/ -1/2 a)
(/ -1/2 a)
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)))))))
(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)
(pow a 2)
(pow a 2)
(* -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))))))))
(* -1 a)
(* -1 a)
(* -1 a)
(* -1 a)
(* -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
(* -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 a)
(/ -1/2 a)
(/ -1/2 a)
(/ -1/2 a)
(* -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))))))))
(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)
(pow a 2)
(pow a 2)

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

rewrite158.0ms (3.9%)

Memory

31.1MiB live, 265.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	72
0	23	72
1	78	72
2	482	72
3	5136	72
0	8983	72

Stop Event

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

Counts

9 → 216

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval96.0ms (2.3%)

Memory: -5.1MiB live, 80.7MiB allocated
Compiler: Compiled 6 356 to 900 computations (85.8% saved)

prune17.0ms (0.4%)

Memory

4.8MiB live, 41.0MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	387	0	387
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	387	3	390

Accuracy

100.0%

Counts

390 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	57.4%	(sqrt.f64 #s(approx (- (* a a) (* b b)) (*.f64 a a)))
✓	100.0%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a))
✓	1.1%	#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))

Compiler

Compiled 42 to 31 computations (26.2% saved)

regimes14.0ms (0.4%)

Memory

-11.0MiB live, 27.1MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

6 calls:

4.0ms	(-.f64 (.f64 a a) (.f64 b b))
2.0ms	b
2.0ms	a
2.0ms	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
2.0ms	(*.f64 a a)

Results

Accuracy	Segments	Branch
100.0%	1	`a`
100.0%	1	`b`
100.0%	1	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
100.0%	1	`(-.f64 (.f64 a a) (.f64 b b))`
100.0%	1	`(*.f64 a a)`
100.0%	1	`(*.f64 b b)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes63.0ms (1.5%)

Memory

-30.5MiB live, 29.0MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

6 calls:

37.0ms	b
19.0ms	a
2.0ms	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
1.0ms	(-.f64 (.f64 a a) (.f64 b b))
1.0ms	(*.f64 a a)

Results

Accuracy	Segments	Branch
57.4%	1	`a`
57.4%	1	`b`
57.4%	1	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
57.4%	1	`(-.f64 (.f64 a a) (.f64 b b))`
57.4%	1	`(*.f64 a a)`
57.4%	1	`(*.f64 b b)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes8.0ms (0.2%)

Memory

13.3MiB live, 13.3MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

6 calls:

1.0ms	a
1.0ms	b
1.0ms	(-.f64 (.f64 a a) (.f64 b b))
1.0ms	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
1.0ms	(*.f64 a a)

Results

Accuracy	Segments	Branch
1.1%	1	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
1.1%	1	`(-.f64 (.f64 a a) (.f64 b b))`
1.1%	1	`(*.f64 b b)`
1.1%	1	`b`
1.1%	1	`(*.f64 a a)`
1.1%	1	`a`

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify29.0ms (0.7%)

Memory

-2.5MiB live, 36.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	40
1	21	40
2	23	40
3	24	40

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness337.0ms (8.2%)

Memory

-3.0MiB live, 190.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	119	757
1	332	757
2	1128	744
3	4541	722
0	8122	682

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 31 to 25 computations (19.4% saved)

preprocess44.0ms (1.1%)

Memory: 17.1MiB live, 94.4MiB allocated
Remove: (abs b)
Compiler: Compiled 130 to 96 computations (26.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze32.0ms (0.8%)

sample1.4s (34.3%)

explain107.0ms (2.6%)

preprocess424.0ms (10.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify342.0ms (8.3%)

localize54.0ms (1.3%)

series7.0ms (0.2%)

simplify161.0ms (3.9%)

rewrite230.0ms (5.6%)

eval74.0ms (1.8%)

prune9.0ms (0.2%)

simplify145.0ms (3.5%)

localize36.0ms (0.9%)

series14.0ms (0.3%)

simplify295.0ms (7.2%)

rewrite158.0ms (3.9%)

eval96.0ms (2.3%)

prune17.0ms (0.4%)

regimes14.0ms (0.4%)

regimes63.0ms (1.5%)

regimes8.0ms (0.2%)

simplify29.0ms (0.7%)

soundness337.0ms (8.2%)

preprocess44.0ms (1.1%)

end0.0ms (0%)

Profiling