Metrics for Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, B

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze137.0ms (2.5%)

Memory

-7.4MiB live, 211.2MiB 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
0%	0%	99.9%	0.1%	0%	0%	0%	5
0%	0%	99.9%	0.1%	0%	0%	0%	6
30.8%	25%	56.2%	0.1%	0%	18.7%	0%	7
30.8%	25%	56.2%	0.1%	0%	18.7%	0%	8
32%	25%	53%	0.1%	0%	21.8%	0%	9
55.8%	37.4%	29.6%	0.1%	0%	32.8%	0%	10
55.8%	37.4%	29.6%	0.1%	0%	32.8%	0%	11
57.8%	37.4%	27.3%	0.1%	0%	35.1%	0%	12

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample1.6s (28.7%)

Memory

31.4MiB live, 1 149.4MiB allocated

Samples

706.0ms	8 256×	0	valid
379.0ms	2 472×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 549.0ms

ival-mult: 314.0ms (57.2% of total)

ival-sqrt: 129.0ms (23.5% of total)

ival-sub: 94.0ms (17.1% of total)

ival-true: 8.0ms (1.5% of total)

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

Bogosity

explain98.0ms (1.8%)

Memory

-1.9MiB live, 276.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
140	-	1	(9.004990910872586e+135 -3.4665972432908886e-158 -1.0738291087363719e-235)	`(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))`
17	-	0	-	`(-.f64 (.f64 y y) (.f64 z z))`
0	-	0	-	`(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))`
0	-	0	-	`y`
0	-	0	-	`(*.f64 z z)`
0	-	0	-	`(*.f64 y y)`
0	-	0	-	`z`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))`	oflow-rescue	130	0
↳	`(*.f64 y y)`	overflow	130
↳	`(-.f64 (.f64 y y) (.f64 z z))`	overflow	130
↳	`(*.f64 z z)`	overflow	17
`-.f64`	`(-.f64 (.f64 y y) (.f64 z z))`	nan-rescue	17	0
↳	`(*.f64 y y)`	overflow	130
↳	`(*.f64 z z)`	overflow	17
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))`	uflow-rescue	9	0
↳	`(*.f64 y y)`	underflow	9
↳	`(-.f64 (.f64 y y) (.f64 z z))`	underflow	9
↳	`(*.f64 z z)`	underflow	103

Confusion

	Predicted +	Predicted -
+	99	1
-	40	116

Precision

0.7122302158273381

Recall

0.99

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	99	0	1
-	40	0	116

Precision?

0.7122302158273381

Recall?

0.99

Freqs

test

number	freq
0	117
1	122
2	17

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

38.0ms

512×

valid

Compiler

Compiled 82 to 28 computations (65.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-mult: 10.0ms (59.4% of total)

ival-sqrt: 4.0ms (23.8% of total)

ival-sub: 2.0ms (11.9% of total)

ival-true: 1.0ms (5.9% of total)

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

preprocess544.0ms (9.8%)

Memory

4.5MiB live, 372.1MiB allocated

Algorithm

1×	egg-herbie

Rules

24 584×	`lower-fma.f64`
24 584×	`lower-fma.f32`
5 200×	`lower-+.f64`
5 200×	`lower-+.f32`
4 138×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	93
1	108	93
2	221	93
3	608	93
4	1655	93
5	2753	93
6	3995	93
7	4670	93
8	5262	93
9	5561	93
10	5651	93
11	5747	93
12	5811	93
13	6963	93
14	7539	93
15	7635	93
16	7731	93
17	7827	93
18	7827	93
0	8	10
0	13	10
1	22	10
2	33	10
3	59	10
4	123	10
5	324	10
6	579	10
7	1254	10
8	2514	10
9	4177	10
10	5039	10
11	5408	10
12	5638	10
13	5752	10
14	5752	10
15	6712	10
16	6872	10
17	7192	10
18	7192	10
19	7592	10
20	7752	10
21	7832	10
22	7832	10
23	7832	10
0	10485	10

Stop Event

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

Calls

Call 1

Inputs
(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Outputs
(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
(.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x)

Symmetry

(abs z)

(abs y)

(negabs x)

Compiler

Compiled 10 to 8 computations (20% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.9%	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 10 to 8 computations (20% saved)

simplify467.0ms (8.4%)

Memory

15.4MiB live, 289.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 y y)
cost-diff	0	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
cost-diff	0	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
cost-diff	128	(-.f64 (.f64 y y) (.f64 z z))

Rules

24 584×	`lower-fma.f64`
24 584×	`lower-fma.f32`
5 200×	`lower-+.f64`
5 200×	`lower-+.f32`
4 138×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	34
0	13	34
1	22	34
2	33	34
3	59	34
4	123	34
5	324	34
6	579	34
7	1254	34
8	2514	34
9	4177	34
10	5039	34
11	5408	34
12	5638	34
13	5752	34
14	5752	34
15	6712	34
16	6872	34
17	7192	34
18	7192	34
19	7592	34
20	7752	34
21	7832	34
22	7832	34
23	7832	34
0	10485	34

Stop Event

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

Calls

Call 1

Inputs
(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
x
(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
(-.f64 (.f64 y y) (.f64 z z))
(*.f64 y y)
y
(*.f64 z z)
z

Outputs
(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
(.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x)
x
(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
(sqrt.f64 (*.f64 (-.f64 y z) (+.f64 z y)))
(-.f64 (.f64 y y) (.f64 z z))
(*.f64 (-.f64 y z) (+.f64 z y))
(*.f64 y y)
y
(*.f64 z z)
z

localize92.0ms (1.7%)

Memory

6.4MiB live, 45.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0.0078125	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
accuracy	3.3945312500000004	(-.f64 (.f64 y y) (.f64 z z))
accuracy	32.39762079405059	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

Samples

86.0ms

256×

valid

Compiler

Compiled 36 to 10 computations (72.2% saved)

Precisions

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

ival-mult: 5.0ms (64.8% of total)

ival-sqrt: 2.0ms (25.9% of total)

ival-sub: 1.0ms (13% of total)

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

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

series72.0ms (1.3%)

Memory

-11.9MiB live, 27.8MiB allocated

Counts

4 → 96

Calls

Call 1

Inputs
#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())
#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())
#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())

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

Calls

9 calls:

Time	Variable		Point	Expression
61.0ms	z	@	0	((- (* y y) (* z z)) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (* y y))
2.0ms	z	@	inf	((- (* y y) (* z z)) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (* y y))
1.0ms	y	@	inf	((- (* y y) (* z z)) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (* y y))
1.0ms	y	@	0	((- (* y y) (* z z)) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (* y y))
1.0ms	x	@	0	((- (* y y) (* z z)) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (* y y))

simplify374.0ms (6.8%)

Memory

-37.1MiB live, 319.9MiB allocated

Algorithm

1×	egg-herbie

Rules

13 108×	`lower-fma.f64`
13 108×	`lower-fma.f32`
5 990×	`lower-*.f64`
5 990×	`lower-*.f32`
3 530×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	205	1489
1	648	1483
2	2455	1426
3	7928	1426
0	8162	1349

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 94

Calls

Call 1

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

Outputs
(pow y 2)
(*.f64 y y)
(+ (* -1 (pow z 2)) (pow y 2))
(*.f64 (+.f64 z y) (-.f64 y z))
(+ (* -1 (pow z 2)) (pow y 2))
(*.f64 (+.f64 z y) (-.f64 y z))
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(.f64 (sqrt.f64 (.f64 (+.f64 z y) (-.f64 y z))) x)
(* x (sqrt (- (pow y 2) (pow z 2))))
(.f64 (sqrt.f64 (.f64 (+.f64 z y) (-.f64 y z))) x)
(* x (sqrt (- (pow y 2) (pow z 2))))
(.f64 (sqrt.f64 (.f64 (+.f64 z y) (-.f64 y z))) x)
(* x (sqrt (- (pow y 2) (pow z 2))))
(.f64 (sqrt.f64 (.f64 (+.f64 z y) (-.f64 y z))) x)

rewrite208.0ms (3.8%)

Memory

20.5MiB live, 327.7MiB allocated

Rules

6 736×	`lower-fma.f64`
6 736×	`lower-fma.f32`
3 592×	`lower-/.f64`
3 592×	`lower-/.f32`
3 504×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	28
0	13	28
1	40	28
2	243	28
3	2153	28
0	9394	28

Stop Event

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

Counts

4 → 332

Calls

Call 1

Inputs
(-.f64 (.f64 y y) (.f64 z z))
(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
(*.f64 y y)

Outputs
(.f64 (exp.f64 (log.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64))))) (exp.f64 (neg.f64 (log.f64 (fma.f64 z z (.f64 y y))))))
(.f64 (exp.f64 (log.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64))))) (exp.f64 (neg.f64 (log.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (*.f64 z z) (pow.f64 y #s(literal 4 binary64)))))))
(*.f64 (exp.f64 (log.f64 (+.f64 z y))) (exp.f64 (log.f64 (-.f64 y z))))
(*.f64 (exp.f64 (log.f64 (-.f64 y z))) (exp.f64 (log.f64 (+.f64 z y))))
(.f64 (pow.f64 (/.f64 (fma.f64 z z (.f64 y y)) (-.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 z #s(literal 8 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 z z (.f64 y y)) (-.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 z #s(literal 12 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (*.f64 z y) #s(literal 4 binary64)) (pow.f64 z #s(literal 8 binary64))) (pow.f64 y #s(literal 8 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (*.f64 z z) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 z #s(literal 12 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 18 binary64)) (pow.f64 z #s(literal 18 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (.f64 z y) #s(literal 6 binary64)) (pow.f64 z #s(literal 12 binary64))) (pow.f64 y #s(literal 12 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64))) (-.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 (+.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) (pow.f64 z #s(literal 4 binary64))) #s(literal 2 binary64)))) (-.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64))) (pow.f64 (*.f64 z y) #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64))) (fma.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 3 binary64)) (pow.f64 z #s(literal 6 binary64)) (pow.f64 y #s(literal 12 binary64)))) (fma.f64 (+.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) (pow.f64 z #s(literal 4 binary64))) (-.f64 (+.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) (pow.f64 z #s(literal 4 binary64))) (pow.f64 y #s(literal 4 binary64))) (pow.f64 y #s(literal 8 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64)))) (.f64 (-.f64 y z) (+.f64 z y)))
(.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64)))) (+.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 (.f64 z y) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))))
(.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal -1 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64))))
(.f64 (pow.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (*.f64 z z) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (*.f64 z z) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)) (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64))))
(.f64 #s(literal 1 binary64) (.f64 (-.f64 y z) (+.f64 z y)))
(.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64)))) (pow.f64 (neg.f64 (fma.f64 z z (.f64 y y))) #s(literal -1 binary64)))
(.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64)))) (pow.f64 (neg.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (*.f64 z z) (pow.f64 y #s(literal 4 binary64)))) #s(literal -1 binary64)))
(*.f64 (-.f64 y z) (+.f64 z y))
(*.f64 (+.f64 z y) (-.f64 y z))
(.f64 (fma.f64 z z (.f64 y y)) (/.f64 (.f64 (-.f64 y z) (+.f64 z y)) (fma.f64 z z (.f64 y y))))
(.f64 (fma.f64 z z (.f64 y y)) (.f64 (.f64 (-.f64 y z) (+.f64 z y)) (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal -1 binary64))))
(.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64))) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal -1 binary64)))
(.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64))) (/.f64 (.f64 (-.f64 y z) (+.f64 z y)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))))
(.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64))) (.f64 (.f64 (-.f64 y z) (+.f64 z y)) (pow.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (*.f64 z z) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64))))
(.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64))) (pow.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (*.f64 z z) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (pow.f64 (*.f64 (-.f64 y z) (+.f64 z y)) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (*.f64 (-.f64 y z) (+.f64 z y)) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (+.f64 (pow.f64 (.f64 z (-.f64 y z)) #s(literal 3 binary64)) (pow.f64 (.f64 y (-.f64 y z)) #s(literal 3 binary64))) (fma.f64 (.f64 z (-.f64 y z)) (.f64 z (-.f64 y z)) (-.f64 (.f64 (.f64 y (-.f64 y z)) (.f64 y (-.f64 y z))) (.f64 (.f64 z (-.f64 y z)) (.f64 y (-.f64 y z))))))
(/.f64 (+.f64 (pow.f64 (.f64 y (-.f64 y z)) #s(literal 3 binary64)) (pow.f64 (.f64 z (-.f64 y z)) #s(literal 3 binary64))) (fma.f64 (.f64 y (-.f64 y z)) (.f64 y (-.f64 y z)) (-.f64 (.f64 (.f64 z (-.f64 y z)) (.f64 z (-.f64 y z))) (.f64 (.f64 y (-.f64 y z)) (.f64 z (-.f64 y z))))))
(/.f64 (+.f64 (pow.f64 (.f64 y (+.f64 z y)) #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 z) (+.f64 z y)) #s(literal 3 binary64))) (fma.f64 (.f64 y (+.f64 z y)) (.f64 y (+.f64 z y)) (-.f64 (.f64 (.f64 (neg.f64 z) (+.f64 z y)) (.f64 (neg.f64 z) (+.f64 z y))) (.f64 (.f64 y (+.f64 z y)) (.f64 (neg.f64 z) (+.f64 z y))))))
(/.f64 (+.f64 (pow.f64 (.f64 (-.f64 y z) z) #s(literal 3 binary64)) (pow.f64 (.f64 (-.f64 y z) y) #s(literal 3 binary64))) (fma.f64 (.f64 (-.f64 y z) z) (.f64 (-.f64 y z) z) (-.f64 (.f64 (.f64 (-.f64 y z) y) (.f64 (-.f64 y z) y)) (.f64 (.f64 (-.f64 y z) z) (.f64 (-.f64 y z) y)))))
(/.f64 (+.f64 (pow.f64 (.f64 (-.f64 y z) y) #s(literal 3 binary64)) (pow.f64 (.f64 (-.f64 y z) z) #s(literal 3 binary64))) (fma.f64 (.f64 (-.f64 y z) y) (.f64 (-.f64 y z) y) (-.f64 (.f64 (.f64 (-.f64 y z) z) (.f64 (-.f64 y z) z)) (.f64 (.f64 (-.f64 y z) y) (.f64 (-.f64 y z) z)))))
(/.f64 (+.f64 (pow.f64 (.f64 (+.f64 z y) y) #s(literal 3 binary64)) (pow.f64 (.f64 (+.f64 z y) (neg.f64 z)) #s(literal 3 binary64))) (fma.f64 (.f64 (+.f64 z y) y) (.f64 (+.f64 z y) y) (-.f64 (.f64 (.f64 (+.f64 z y) (neg.f64 z)) (.f64 (+.f64 z y) (neg.f64 z))) (.f64 (.f64 (+.f64 z y) y) (.f64 (+.f64 z y) (neg.f64 z))))))
(/.f64 (+.f64 (/.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 3 binary64))) (pow.f64 (neg.f64 (/.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 z z (.f64 y y)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 z z (.f64 y y))) #s(literal 2 binary64)) (-.f64 (.f64 (neg.f64 (/.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 z z (.f64 y y)))) (neg.f64 (/.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 z z (.f64 y y))))) (.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 z z (.f64 y y))) (neg.f64 (/.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 z z (*.f64 y y))))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (neg.f64 (/.f64 (pow.f64 z #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64))))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))) #s(literal 2 binary64)) (-.f64 (.f64 (neg.f64 (/.f64 (pow.f64 z #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64))))) (neg.f64 (/.f64 (pow.f64 z #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))))) (.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 z #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))))))))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64))) #s(literal 1 binary64))) (neg.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (*.f64 z z) (pow.f64 y #s(literal 4 binary64)))))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (+.f64 z y))) (neg.f64 (fma.f64 z (+.f64 z y) (.f64 y y))))
(/.f64 (neg.f64 (.f64 (.f64 (-.f64 y z) (+.f64 z y)) (+.f64 z y))) (neg.f64 (+.f64 z y)))
(/.f64 (neg.f64 (.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (-.f64 y z))) (neg.f64 (fma.f64 z (-.f64 z y) (.f64 y y))))
(/.f64 (neg.f64 (.f64 (.f64 (-.f64 y z) (+.f64 z y)) (-.f64 y z))) (neg.f64 (-.f64 y z)))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 z #s(literal 8 binary64))) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal -1 binary64)))) (neg.f64 (+.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 z #s(literal 12 binary64))) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal -1 binary64)))) (neg.f64 (+.f64 (+.f64 (pow.f64 (*.f64 z y) #s(literal 4 binary64)) (pow.f64 z #s(literal 8 binary64))) (pow.f64 y #s(literal 8 binary64)))))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 z #s(literal 12 binary64))) (pow.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (*.f64 z z) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)))) (neg.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64)))))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 y #s(literal 18 binary64)) (pow.f64 z #s(literal 18 binary64))) (pow.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)))) (neg.f64 (+.f64 (+.f64 (pow.f64 (.f64 z y) #s(literal 6 binary64)) (pow.f64 z #s(literal 12 binary64))) (pow.f64 y #s(literal 12 binary64)))))
(/.f64 (neg.f64 (.f64 (-.f64 y z) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))))) (neg.f64 (fma.f64 z (-.f64 z y) (.f64 y y))))
(/.f64 (neg.f64 (.f64 (-.f64 y z) (.f64 (-.f64 y z) (+.f64 z y)))) (neg.f64 (-.f64 y z)))
(/.f64 (neg.f64 (.f64 (+.f64 z y) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))))) (neg.f64 (fma.f64 z (+.f64 z y) (.f64 y y))))
(/.f64 (neg.f64 (.f64 (+.f64 z y) (.f64 (-.f64 y z) (+.f64 z y)))) (neg.f64 (+.f64 z y)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 z z (.f64 y y))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 z z (.f64 y y))) #s(literal 2 binary64)))) (neg.f64 (+.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 z z (.f64 y y))) (/.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 z z (.f64 y y))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 z #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))) #s(literal 2 binary64)))) (neg.f64 (+.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))) (/.f64 (pow.f64 z #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))))))
(/.f64 (neg.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 3 binary64))) (/.f64 (pow.f64 z #s(literal 12 binary64)) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 3 binary64))))) (neg.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 z z (.f64 y y))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 z z (.f64 y y))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 z z (.f64 y y))) (/.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 z z (*.f64 y y))))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 z #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 z #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))) (/.f64 (pow.f64 z #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (*.f64 z z) (pow.f64 y #s(literal 4 binary64)))))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64)))))) (neg.f64 (neg.f64 (neg.f64 (fma.f64 z z (*.f64 y y))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64)))))) (neg.f64 (neg.f64 (neg.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))))))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64))) #s(literal 1 binary64))) (neg.f64 (fma.f64 z z (.f64 y y))))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))))) (neg.f64 (.f64 (fma.f64 z (+.f64 z y) (.f64 y y)) (fma.f64 z (-.f64 z y) (.f64 y y)))))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (.f64 (-.f64 y z) (+.f64 z y)))) (neg.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64)))))
(/.f64 (neg.f64 (.f64 (.f64 (-.f64 y z) (+.f64 z y)) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))))) (neg.f64 (.f64 (+.f64 z y) (fma.f64 z (-.f64 z y) (.f64 y y)))))
(/.f64 (neg.f64 (.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (.f64 (-.f64 y z) (+.f64 z y)))) (neg.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64)))))
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(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 z #s(literal 12 binary64))) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal -1 binary64)))) (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 z y) #s(literal 4 binary64)) (pow.f64 z #s(literal 8 binary64))) (pow.f64 y #s(literal 8 binary64)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 z #s(literal 12 binary64))) (pow.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (*.f64 z z) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)))) (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 y #s(literal 18 binary64)) (pow.f64 z #s(literal 18 binary64))) (pow.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)))) (hypot.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64))) (pow.f64 (.f64 z y) #s(literal 3 binary64))))
(/.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 z (-.f64 z y) (.f64 y y))))
(/.f64 (sqrt.f64 (.f64 (-.f64 y z) (.f64 (-.f64 y z) (+.f64 z y)))) (sqrt.f64 (-.f64 y z)))
(/.f64 (sqrt.f64 (.f64 (+.f64 z y) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 z (+.f64 z y) (.f64 y y))))
(/.f64 (sqrt.f64 (.f64 (+.f64 z y) (.f64 (-.f64 y z) (+.f64 z y)))) (sqrt.f64 (+.f64 z y)))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 z z (.f64 y y))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 z z (.f64 y y))) #s(literal 2 binary64)))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 z z (.f64 y y))) (/.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 z z (.f64 y y))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 z #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))) #s(literal 2 binary64)))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))) (/.f64 (pow.f64 z #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 3 binary64))) (/.f64 (pow.f64 z #s(literal 12 binary64)) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 z z (.f64 y y))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 z z (.f64 y y))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 z z (.f64 y y))) (/.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 z z (*.f64 y y))))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 z #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))) #s(literal 3 binary64)))) (sqrt.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 z #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))) (/.f64 (pow.f64 z #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (*.f64 z z) (pow.f64 y #s(literal 4 binary64)))))))))
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64)))))) (sqrt.f64 (neg.f64 (neg.f64 (fma.f64 z z (*.f64 y y))))))
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64)))))) (sqrt.f64 (neg.f64 (neg.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))))) (sqrt.f64 (.f64 (fma.f64 z (+.f64 z y) (.f64 y y)) (fma.f64 z (-.f64 z y) (.f64 y y)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (.f64 (-.f64 y z) (+.f64 z y)))) (sqrt.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64)))))
(/.f64 (sqrt.f64 (.f64 (.f64 (-.f64 y z) (+.f64 z y)) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))))) (sqrt.f64 (.f64 (+.f64 z y) (fma.f64 z (-.f64 z y) (.f64 y y)))))
(/.f64 (sqrt.f64 (.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (.f64 (-.f64 y z) (+.f64 z y)))) (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 z #s(literal 3/2 binary64))))
(/.f64 (sqrt.f64 (.f64 (.f64 (-.f64 y z) (+.f64 z y)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))))) (sqrt.f64 (.f64 (-.f64 y z) (fma.f64 z (+.f64 z y) (.f64 y y)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 z #s(literal 8 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (+.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (fma.f64 z z (*.f64 y y)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 z #s(literal 12 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (+.f64 (+.f64 (pow.f64 (.f64 z y) #s(literal 4 binary64)) (pow.f64 z #s(literal 8 binary64))) (pow.f64 y #s(literal 8 binary64))) (fma.f64 z z (.f64 y y)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 z #s(literal 12 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64))) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 y #s(literal 18 binary64)) (pow.f64 z #s(literal 18 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (+.f64 (+.f64 (pow.f64 (.f64 z y) #s(literal 6 binary64)) (pow.f64 z #s(literal 12 binary64))) (pow.f64 y #s(literal 12 binary64))) (fma.f64 (fma.f64 z z (.f64 y y)) (*.f64 z z) (pow.f64 y #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 z z (.f64 y y))) (.f64 (fma.f64 z z (.f64 y y)) (pow.f64 z #s(literal 4 binary64))))) (sqrt.f64 (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))) (.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64))) (pow.f64 z #s(literal 6 binary64))))) (sqrt.f64 (pow.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64))) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 (-.f64 y z) (+.f64 z y)) #s(literal 2 binary64))) (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (.f64 (neg.f64 z) z) (.f64 y y))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64))) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (*.f64 z z) (pow.f64 y #s(literal 4 binary64)))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64))) #s(literal 1 binary64))) (hypot.f64 z y))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (pow.f64 (*.f64 (-.f64 y z) (+.f64 z y)) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64))))) (neg.f64 (hypot.f64 z y)))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 z #s(literal 8 binary64)))) (sqrt.f64 (.f64 (fma.f64 z z (.f64 y y)) (+.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64))) (sqrt.f64 (.f64 (fma.f64 z z (.f64 y y)) (+.f64 (+.f64 (pow.f64 (*.f64 z y) #s(literal 4 binary64)) (pow.f64 z #s(literal 8 binary64))) (pow.f64 y #s(literal 8 binary64))))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64))) (sqrt.f64 (.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (*.f64 z z) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (hypot.f64 z y)))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64))))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 z #s(literal 9 binary64))) (sqrt.f64 (.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64))) (+.f64 (+.f64 (pow.f64 (.f64 z y) #s(literal 6 binary64)) (pow.f64 z #s(literal 12 binary64))) (pow.f64 y #s(literal 12 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (-.f64 y z) (+.f64 z y))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (-.f64 y z) (+.f64 z y)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (-.f64 y z) (+.f64 z y)))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64)))) (hypot.f64 z y))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (sqrt.f64 (+.f64 (pow.f64 z #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (neg.f64 (pow.f64 (*.f64 z y) #s(literal 2 binary64)))))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (sqrt.f64 (.f64 (fma.f64 z (-.f64 z y) (.f64 y y)) (fma.f64 z (+.f64 z y) (*.f64 y y)))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (sqrt.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (.f64 z z) (pow.f64 y #s(literal 4 binary64)))))
(sqrt.f64 (*.f64 (-.f64 y z) (+.f64 z y)))
(exp.f64 (fma.f64 (log.f64 (.f64 (-.f64 y z) (+.f64 z y))) #s(literal 1/4 binary64) (.f64 (log.f64 (*.f64 (-.f64 y z) (+.f64 z y))) #s(literal 1/4 binary64))))
(exp.f64 (fma.f64 (log.f64 (-.f64 y z)) #s(literal 1/2 binary64) (*.f64 (log.f64 (+.f64 z y)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 (+.f64 z y)) #s(literal 1/2 binary64) (*.f64 (log.f64 (-.f64 y z)) #s(literal 1/2 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 (-.f64 y z) (+.f64 z y))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (-.f64 y z) (+.f64 z y)) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (-.f64 y z) (+.f64 z y)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (-.f64 y z) (+.f64 z y))) #s(literal 1/2 binary64)))
(*.f64 y y)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 y))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))

eval53.0ms (1%)

Memory: -6.9MiB live, 110.0MiB allocated
Compiler: Compiled 12 357 to 1 728 computations (86% saved)

prune8.0ms (0.1%)

Memory

-14.8MiB live, 24.3MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	422	4	426
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	423	4	427

Accuracy

100.0%

Counts

427 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(.f64 (.f64 x (sqrt.f64 (+.f64 z y))) (sqrt.f64 (-.f64 y z)))
▶	67.3%	(.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x)
▶	99.7%	(.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)))
▶	99.3%	#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 x y))

Compiler

Compiled 36 to 31 computations (13.9% saved)

simplify153.0ms (2.8%)

Memory

13.4MiB live, 179.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

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

Rules

14 604×	`lower-fma.f32`
14 602×	`lower-fma.f64`
2 534×	`lower--.f32`
2 532×	`lower--.f64`
2 148×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	141
0	40	141
1	71	141
2	113	141
3	178	141
4	301	141
5	640	141
6	1555	141
7	3314	141
8	6164	141
0	8299	141

Stop Event

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

Calls

Call 1

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

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

localize77.0ms (1.4%)

Memory

-4.9MiB live, 115.9MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(sqrt.f64 (+.f64 z y))
accuracy	0.015625	(sqrt.f64 (-.f64 y z))
accuracy	0.23046875	(*.f64 x (sqrt.f64 (+.f64 z y)))
accuracy	0.29296875	(.f64 (.f64 x (sqrt.f64 (+.f64 z y))) (sqrt.f64 (-.f64 y z)))
accuracy	0	(+.f64 z y)
accuracy	0	(*.f64 (-.f64 y z) (+.f64 z y))
accuracy	0.0078125	(.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x)
accuracy	32.39762079405059	(sqrt.f64 (*.f64 (-.f64 y z) (+.f64 z y)))
accuracy	0	(/.f64 z y)
accuracy	0	(*.f64 #s(literal -1/2 binary64) z)
accuracy	0.0078125	(.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)))
accuracy	0.32211947271403696	#s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))
accuracy	0	(*.f64 x y)
accuracy	0.47415607649900604	#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 x y))

Samples

63.0ms

256×

valid

Compiler

Compiled 122 to 25 computations (79.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 42.0ms

ival-sqrt: 19.0ms (44.7% of total)

ival-mult: 17.0ms (40% of total)

ival-div: 2.0ms (4.7% of total)

ival-sub: 2.0ms (4.7% of total)

ival-add: 2.0ms (4.7% of total)

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

exact: 0.0ms (0% of total)

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

series50.0ms (0.9%)

Memory

14.7MiB live, 90.1MiB allocated

Counts

16 → 432

Calls

Call 1

Inputs
#s(alt #s(approx (* x (sqrt (- (* y y) (* z z)))) (.f64 x y)) (patch #s(approx ( x (sqrt (- (* y y) (* z z)))) (*.f64 x y)) #<representation binary64>) () ())
#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())
#s(alt (.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))) (patch (.f64 x #s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)) (patch #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y) (patch (fma.f64 (.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -1/2 binary64) z) (patch (.f64 #s(literal -1/2 binary64) z) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x) (patch (.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) (patch (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 y z) (+.f64 z y)) (patch (.f64 (-.f64 y z) (+.f64 z y)) #<representation binary64>) () ())
#s(alt (-.f64 y z) (patch (-.f64 y z) #<representation binary64>) () ())
#s(alt (.f64 (.f64 x (sqrt.f64 (+.f64 z y))) (sqrt.f64 (-.f64 y z))) (patch (.f64 (.f64 x (sqrt.f64 (+.f64 z y))) (sqrt.f64 (-.f64 y z))) #<representation binary64>) () ())
#s(alt (.f64 x (sqrt.f64 (+.f64 z y))) (patch (.f64 x (sqrt.f64 (+.f64 z y))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 z y)) (patch (sqrt.f64 (+.f64 z y)) #<representation binary64>) () ())
#s(alt (+.f64 z y) (patch (+.f64 z y) #<representation binary64>) () ())
#s(alt (/.f64 z y) (patch (/.f64 z y) #<representation binary64>) () ())
#s(alt (sqrt.f64 (-.f64 y z)) (patch (sqrt.f64 (-.f64 y z)) #<representation binary64>) () ())

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

Calls

9 calls:

Time	Variable		Point	Expression
10.0ms	y	@	0	((* x (sqrt (- (* y y) (* z z)))) (* x y) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (* -1/2 z) (/ z y)) y) (* -1/2 z) (* (sqrt (* (- y z) (+ z y))) x) (sqrt (* (- y z) (+ z y))) (* (- y z) (+ z y)) (- y z) (* (* x (sqrt (+ z y))) (sqrt (- y z))) (* x (sqrt (+ z y))) (sqrt (+ z y)) (+ z y) (/ z y) (sqrt (- y z)))
5.0ms	y	@	-inf	((* x (sqrt (- (* y y) (* z z)))) (* x y) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (* -1/2 z) (/ z y)) y) (* -1/2 z) (* (sqrt (* (- y z) (+ z y))) x) (sqrt (* (- y z) (+ z y))) (* (- y z) (+ z y)) (- y z) (* (* x (sqrt (+ z y))) (sqrt (- y z))) (* x (sqrt (+ z y))) (sqrt (+ z y)) (+ z y) (/ z y) (sqrt (- y z)))
4.0ms	z	@	inf	((* x (sqrt (- (* y y) (* z z)))) (* x y) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (* -1/2 z) (/ z y)) y) (* -1/2 z) (* (sqrt (* (- y z) (+ z y))) x) (sqrt (* (- y z) (+ z y))) (* (- y z) (+ z y)) (- y z) (* (* x (sqrt (+ z y))) (sqrt (- y z))) (* x (sqrt (+ z y))) (sqrt (+ z y)) (+ z y) (/ z y) (sqrt (- y z)))
4.0ms	z	@	0	((* x (sqrt (- (* y y) (* z z)))) (* x y) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (* -1/2 z) (/ z y)) y) (* -1/2 z) (* (sqrt (* (- y z) (+ z y))) x) (sqrt (* (- y z) (+ z y))) (* (- y z) (+ z y)) (- y z) (* (* x (sqrt (+ z y))) (sqrt (- y z))) (* x (sqrt (+ z y))) (sqrt (+ z y)) (+ z y) (/ z y) (sqrt (- y z)))
4.0ms	z	@	-inf	((* x (sqrt (- (* y y) (* z z)))) (* x y) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (* -1/2 z) (/ z y)) y) (* -1/2 z) (* (sqrt (* (- y z) (+ z y))) x) (sqrt (* (- y z) (+ z y))) (* (- y z) (+ z y)) (- y z) (* (* x (sqrt (+ z y))) (sqrt (- y z))) (* x (sqrt (+ z y))) (sqrt (+ z y)) (+ z y) (/ z y) (sqrt (- y z)))

simplify189.0ms (3.4%)

Memory

11.3MiB live, 323.9MiB allocated

Algorithm

1×	egg-herbie

Rules

14 636×	`lower-fma.f64`
14 636×	`lower-fma.f32`
7 544×	`lower-*.f64`
7 544×	`lower-*.f32`
5 772×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	902	7530
1	3081	6373
0	9649	5949

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 416

Calls

Call 1

Inputs
(* x y)
(+ (* -1/2 (/ (* x (pow z 2)) y)) (* x y))
(+ (* x y) (* (pow z 2) (+ (* -1/2 (/ x y)) (* -1/8 (/ (* x (pow z 2)) (pow y 3))))))
(+ (* x y) (* (pow z 2) (+ (* -1/2 (/ x y)) (* (pow z 2) (+ (* -1/8 (/ x (pow y 3))) (* -1/16 (/ (* x (pow z 2)) (pow y 5))))))))
(* x y)
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(+ (sqrt z) (* y (+ (* 1/2 (sqrt (/ 1 z))) (* y (+ (* -1/8 (sqrt (/ 1 (pow z 3)))) (* 1/16 (* y (sqrt (/ 1 (pow z 5))))))))))
z
(+ y z)
(+ y z)
(+ y z)
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(* (sqrt z) (sqrt -1))
(+ (* 1/2 (* (/ y (sqrt -1)) (sqrt (/ 1 z)))) (* (sqrt z) (sqrt -1)))
(+ (* y (+ (* -1/8 (* (/ y (pow (sqrt -1) 3)) (sqrt (/ 1 (pow z 3))))) (* 1/2 (* (sqrt (/ 1 z)) (/ 1 (sqrt -1)))))) (* (sqrt z) (sqrt -1)))
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 z)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow z 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ y (pow (sqrt -1) 5)) (sqrt (/ 1 (pow z 5))))))))) (* (sqrt z) (sqrt -1)))
(* x y)
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(* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (* -1/8 (/ (* x (pow z 4)) (pow y 4))))))
(* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (+ (* -1/8 (/ (* x (pow z 4)) (pow y 4))) (* -1/16 (/ (* x (pow z 6)) (pow y 6)))))))
(* x y)
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y
(* y (+ 1 (* -1/2 (/ (pow z 2) (pow y 2)))))
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y
(* y (+ 1 (* -1/2 (/ (pow z 2) (pow y 2)))))
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y
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(pow y 2)
(* (pow y 2) (+ 1 (+ (* -1 (/ z y)) (/ z y))))
(* (pow y 2) (+ 1 (+ (* -1 (/ z y)) (+ (* -1 (/ (pow z 2) (pow y 2))) (/ z y)))))
(* (pow y 2) (+ 1 (+ (* -1 (/ z y)) (+ (* -1 (/ (pow z 2) (pow y 2))) (/ z y)))))
y
(* y (+ 1 (* -1 (/ z y))))
(* y (+ 1 (* -1 (/ z y))))
(* y (+ 1 (* -1 (/ z y))))
(* x y)
(* y (+ x (* 1/2 (/ (* x (+ z (* -1 z))) y))))
(* y (+ x (+ (* 1/2 (/ (* x (+ z (* -1 z))) y)) (* 1/2 (/ (* x (- (* -1 (pow z 2)) (* 1/4 (pow (+ z (* -1 z)) 2)))) (pow y 2))))))
(* y (+ x (+ (* -1/4 (/ (* x (* (+ z (* -1 z)) (- (* -1 (pow z 2)) (* 1/4 (pow (+ z (* -1 z)) 2))))) (pow y 3))) (+ (* 1/2 (/ (* x (+ z (* -1 z))) y)) (* 1/2 (/ (* x (- (* -1 (pow z 2)) (* 1/4 (pow (+ z (* -1 z)) 2)))) (pow y 2)))))))
(* x (sqrt y))
(* y (+ (* 1/2 (* (* x z) (sqrt (/ 1 (pow y 3))))) (* x (sqrt (/ 1 y)))))
(* y (+ (* -1/8 (* (* x (pow z 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (* x z) (sqrt (/ 1 (pow y 3))))) (* x (sqrt (/ 1 y))))))
(* y (+ (* -1/8 (* (* x (pow z 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (* x (pow z 3)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (* x z) (sqrt (/ 1 (pow y 3))))) (* x (sqrt (/ 1 y)))))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (sqrt (/ 1 (pow y 3))) z))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (sqrt (/ 1 (pow y 5))) (pow z 2))) (* 1/2 (* (sqrt (/ 1 (pow y 3))) z)))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (sqrt (/ 1 (pow y 5))) (pow z 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow y 7))) (pow z 3))) (* 1/2 (* (sqrt (/ 1 (pow y 3))) z))))))
y
(* y (+ 1 (/ z y)))
(* y (+ 1 (/ z y)))
(* y (+ 1 (/ z y)))
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* -1/2 (* (sqrt (/ 1 (pow y 3))) z))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 3))) z)) (* -1/8 (* (sqrt (/ 1 (pow y 5))) (pow z 2))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* (sqrt (/ 1 (pow y 3))) z)) (+ (* -1/8 (* (sqrt (/ 1 (pow y 5))) (pow z 2))) (* -1/16 (* (sqrt (/ 1 (pow y 7))) (pow z 3)))))))
(* -1 (* x y))
(* -1 (* y (+ x (* -1/2 (/ (* x (pow z 2)) (pow y 2))))))
(* -1 (* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (* -1/8 (/ (* x (pow z 4)) (pow y 4)))))))
(* -1 (* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (+ (* -1/8 (/ (* x (pow z 4)) (pow y 4))) (* -1/16 (/ (* x (pow z 6)) (pow y 6))))))))
(* x y)
(* x y)
(* x y)
(* x y)
(* -1 (* x y))
(* -1 (* y (+ x (* -1/2 (/ (* x (pow z 2)) (pow y 2))))))
(* -1 (* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (* -1/8 (/ (* x (pow z 4)) (pow y 4)))))))
(* -1 (* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (+ (* -1/8 (/ (* x (pow z 4)) (pow y 4))) (* -1/16 (/ (* x (pow z 6)) (pow y 6))))))))
(* -1 y)
(* -1 (* y (+ 1 (* -1/2 (/ (pow z 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/2 (/ (pow z 2) (pow y 2))) (* -1/8 (/ (pow z 4) (pow y 4)))))))
(* -1 (* y (+ 1 (+ (* -1/2 (/ (pow z 2) (pow y 2))) (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* -1/16 (/ (pow z 6) (pow y 6))))))))
y
(* -1 (* y (- (* 1/2 (/ (pow z 2) (pow y 2))) 1)))
(* -1 (* y (- (* 1/2 (/ (pow z 2) (pow y 2))) 1)))
(* -1 (* y (- (* 1/2 (/ (pow z 2) (pow y 2))) 1)))
(* -1 (* x (* y (pow (sqrt -1) 2))))
(* -1 (* y (+ (* -1/2 (/ (* x (+ z (* -1 z))) y)) (* x (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1 (/ (+ (* -1/2 (/ (* x (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2))))) y)) (* 1/2 (* x (+ z (* -1 z))))) y)) (* x (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* x (* (+ z (* -1 z)) (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2)))))) (* y (pow (sqrt -1) 2)))) (* 1/2 (* x (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2))))))) y)) (* 1/2 (* x (+ z (* -1 z))))) y)) (* x (pow (sqrt -1) 2)))))
(* -1 (* y (pow (sqrt -1) 2)))
(* -1 (* y (+ (* -1/2 (/ (+ z (* -1 z)) y)) (pow (sqrt -1) 2))))
(* -1 (* y (+ (* -1 (/ (+ (* -1/2 (/ (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2)))) y)) (* 1/2 (+ z (* -1 z)))) y)) (pow (sqrt -1) 2))))
(* -1 (* y (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ z (* -1 z)) (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2))))) (* y (pow (sqrt -1) 2)))) (* 1/2 (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2)))))) y)) (* 1/2 (+ z (* -1 z)))) y)) (pow (sqrt -1) 2))))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* -1 (/ z y)) (/ z y))))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 (+ z (* -1 z))) (/ (pow z 2) y)) y))))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 (+ z (* -1 z))) (/ (pow z 2) y)) y))))
y
(* -1 (* y (- (/ z y) 1)))
(* -1 (* y (- (/ z y) 1)))
(* -1 (* y (- (/ z y) 1)))
(* -1 (* x (* y (pow (sqrt -1) 2))))
(* -1 (* y (+ (* -1/2 (/ (* x (+ z (* -1 z))) y)) (* x (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1 (/ (+ (* -1/2 (/ (* x (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2))))) y)) (* 1/2 (* x (+ z (* -1 z))))) y)) (* x (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* x (* (+ z (* -1 z)) (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2)))))) (* y (pow (sqrt -1) 2)))) (* 1/2 (* x (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2))))))) y)) (* 1/2 (* x (+ z (* -1 z))))) y)) (* x (pow (sqrt -1) 2)))))
(* -1 (* (* x (pow (sqrt -1) 2)) (sqrt y)))
(* -1 (* y (+ (* 1/2 (* (* x z) (sqrt (/ 1 (pow y 3))))) (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 y))))))
(* -1 (* y (+ (* -1/8 (* (/ (* x (pow z 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (* x z) (sqrt (/ 1 (pow y 3))))) (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 y)))))))
(* -1 (* y (+ (* -1/8 (* (/ (* x (pow z 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (* x (pow z 3)) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (* x z) (sqrt (/ 1 (pow y 3))))) (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 y))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) z)) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (sqrt (/ 1 (pow y 5))) (/ (pow z 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) z)) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (sqrt (/ 1 (pow y 5))) (/ (pow z 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow y 7))) (/ (pow z 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) z)) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
y
(* -1 (* y (- (* -1 (/ z y)) 1)))
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(/ z y)
(/ z y)
(/ z y)
(/ z y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
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(* -1 (* y (+ (* -1/8 (* (sqrt (/ 1 (pow y 5))) (* (pow z 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (* z (pow (sqrt -1) 2)))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (sqrt (/ 1 (pow y 5))) (* (pow z 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow y 7))) (* (pow z 3) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (* z (pow (sqrt -1) 2)))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(* x (sqrt (- (pow y 2) (pow z 2))))
(* x (sqrt (- (pow y 2) (pow z 2))))
(* x (sqrt (- (pow y 2) (pow z 2))))
(* x (sqrt (- (pow y 2) (pow z 2))))
(* x y)
(* x y)
(* x y)
(* x y)
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(* x (sqrt (- (pow y 2) (pow z 2))))
(* x (sqrt (- (pow y 2) (pow z 2))))
(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (* (+ y z) (- y z))))
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(* x (sqrt (+ y z)))
(* x (sqrt (+ y z)))
(* x (sqrt (+ y z)))
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(* x y)
(* x y)
(* x y)
(* x y)
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(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (* (+ y z) (- y z))))
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(* x (sqrt (+ y z)))
(* x (sqrt (+ y z)))
(* x (sqrt (+ y z)))
(* x (sqrt (+ y z)))
(* x (sqrt (- (pow y 2) (pow z 2))))
(* x (sqrt (- (pow y 2) (pow z 2))))
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(* x (sqrt (- (pow y 2) (pow z 2))))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (sqrt (- (pow y 2) (pow z 2))))
(* x (sqrt (- (pow y 2) (pow z 2))))
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(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (* (+ y z) (- y z))))
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(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (+ y z)))
(* x (sqrt (+ y z)))
(* x (sqrt (+ y z)))
(* x (sqrt (+ y z)))

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

rewrite202.0ms (3.7%)

Memory

-2.4MiB live, 319.3MiB allocated

Rules

8 964×	`lower-fma.f32`
8 962×	`lower-fma.f64`
5 894×	`lower-*.f32`
5 880×	`lower-*.f64`
4 128×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	123
0	40	122
1	127	122
2	803	122
0	8597	122

Stop Event

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

Counts

16 → 747

Calls

Call 1

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

Outputs
#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 y x))
(*.f64 y x)
(*.f64 x y)
(.f64 #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (/.f64 z y) (*.f64 #s(literal -1/2 binary64) z) y)) x)
(.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (/.f64 z y) (*.f64 #s(literal -1/2 binary64) z) y)))
#s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (/.f64 z y) (*.f64 #s(literal -1/2 binary64) z) y))
(.f64 (fma.f64 y y (.f64 #s(literal -1/4 binary64) (pow.f64 (.f64 (/.f64 z y) z) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 y (.f64 (*.f64 (/.f64 z y) z) #s(literal 1/2 binary64)))))
(.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 (/.f64 z y) z) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (neg.f64 y) y))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (/.f64 z y) z) #s(literal 1/2 binary64) y)))
(.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 (/.f64 z y) z) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (pow.f64 (.f64 (/.f64 z y) z) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 y (+.f64 y (.f64 (.f64 (/.f64 z y) z) #s(literal 1/2 binary64))))))))
(.f64 (fma.f64 (pow.f64 (.f64 (/.f64 z y) z) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (neg.f64 y) y)) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 (/.f64 z y) z) #s(literal 1/2 binary64) y)))
(.f64 #s(literal 1 binary64) (fma.f64 (/.f64 z y) (.f64 #s(literal -1/2 binary64) z) y))
(.f64 (fma.f64 (pow.f64 (.f64 (/.f64 z y) z) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 y (+.f64 y (.f64 (.f64 (/.f64 z y) z) #s(literal 1/2 binary64))))) (.f64 (fma.f64 (/.f64 z y) (.f64 #s(literal -1/2 binary64) z) y) (pow.f64 (fma.f64 (pow.f64 (.f64 (/.f64 z y) z) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 y (+.f64 y (.f64 (*.f64 (/.f64 z y) z) #s(literal 1/2 binary64))))) #s(literal -1 binary64))))
(.f64 (fma.f64 (pow.f64 (.f64 (/.f64 z y) z) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z) (fma.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z (neg.f64 y))))))
(.f64 (fma.f64 (pow.f64 (.f64 (/.f64 z y) z) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (fma.f64 (pow.f64 (.f64 (/.f64 z y) z) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 y (+.f64 y (.f64 (.f64 (/.f64 z y) z) #s(literal 1/2 binary64))))) #s(literal -1 binary64)))
(.f64 (fma.f64 (/.f64 z y) (.f64 #s(literal -1/2 binary64) z) y) (.f64 (fma.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z (neg.f64 y)) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 (/.f64 z y) z) #s(literal 1/2 binary64) y))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 z y) (*.f64 #s(literal -1/2 binary64) z) y)) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z) #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 (/.f64 z y) z) #s(literal 1/2 binary64) y))) (fma.f64 (pow.f64 (.f64 (/.f64 z y) z) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 y y)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z) #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 (/.f64 z y) z) #s(literal 1/2 binary64) y))) (+.f64 (pow.f64 (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z) #s(literal 4 binary64)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 (.f64 y (*.f64 (/.f64 z y) #s(literal -1/2 binary64))) z) #s(literal 2 binary64)))))
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(pow.f64 (*.f64 (-.f64 y z) (-.f64 y z)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (-.f64 y z) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (-.f64 y z) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 (neg.f64 z) #s(literal 3/2 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (+.f64 z y) y (*.f64 z z)))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 y z)))) (neg.f64 (sqrt.f64 (+.f64 z y))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (+.f64 z y) y (*.f64 z z)))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64)))) (sqrt.f64 (.f64 (+.f64 z y) (fma.f64 z z (.f64 y y)))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64)))) (sqrt.f64 (.f64 (+.f64 z y) (fma.f64 (.f64 z z) (fma.f64 z z (*.f64 y y)) (pow.f64 y #s(literal 4 binary64))))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 (neg.f64 z) #s(literal 3/2 binary64))) (sqrt.f64 (fma.f64 y y (*.f64 (neg.f64 z) (-.f64 (neg.f64 z) y)))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 (neg.f64 z) #s(literal 3/2 binary64))) (sqrt.f64 (fma.f64 (+.f64 z y) y (*.f64 z z))))
(/.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (*.f64 z z))) (sqrt.f64 (neg.f64 (+.f64 z y))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (+.f64 z y) y (*.f64 z z))) (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 (neg.f64 z) #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 z y)) (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 y z)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 y z))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 y z))) (sqrt.f64 (+.f64 z y)))
(sqrt.f64 (-.f64 y z))
(exp.f64 (-.f64 (.f64 (log.f64 (.f64 (+.f64 z y) (-.f64 y z))) #s(literal 1/2 binary64)) (*.f64 (log.f64 (+.f64 z y)) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (-.f64 y z)) #s(literal 1/2 binary64)))

eval199.0ms (3.6%)

Memory: 2.7MiB live, 430.3MiB allocated
Compiler: Compiled 33 950 to 4 556 computations (86.6% saved)

prune28.0ms (0.5%)

Memory

-14.0MiB live, 109.4MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	1 405	1	1 406
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	1 405	5	1 410

Accuracy

100.0%

Counts

1 410 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.4%	(.f64 (.f64 x (sqrt.f64 (+.f64 z y))) (sqrt.f64 (-.f64 y z)))
✓	67.3%	(.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x)
✓	99.7%	(.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)))
▶	89.0%	#s(approx (* x (sqrt (- (* y y) (* z z)))) (fma.f64 (/.f64 (.f64 (.f64 z z) x) y) #s(literal -1/2 binary64) (*.f64 y x)))
✓	99.3%	#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 x y))

Compiler

Compiled 49 to 41 computations (16.3% saved)

simplify118.0ms (2.1%)

Memory

-2.9MiB live, 151.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (.f64 z z) x)
cost-diff	0	(/.f64 (.f64 (.f64 z z) x) y)
cost-diff	0	#s(approx (* x (sqrt (- (* y y) (* z z)))) (fma.f64 (/.f64 (.f64 (.f64 z z) x) y) #s(literal -1/2 binary64) (*.f64 y x)))
cost-diff	320	(fma.f64 (/.f64 (.f64 (.f64 z z) x) y) #s(literal -1/2 binary64) (*.f64 y x))

Rules

10 156×	`lower-fma.f32`
10 154×	`lower-fma.f64`
2 098×	`lower-*.f32`
2 092×	`lower-*.f64`
1 724×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	57
0	21	57
1	40	57
2	75	57
3	156	55
4	285	55
5	516	55
6	780	55
7	1520	55
8	3215	55
9	6718	55
0	8203	53

Stop Event

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

Calls

Call 1

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

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

localize31.0ms (0.6%)

Memory

16.0MiB live, 54.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.19304738490598392	#s(approx (* x (sqrt (- (* y y) (* z z)))) (fma.f64 (/.f64 (.f64 (.f64 z z) x) y) #s(literal -1/2 binary64) (*.f64 y x)))
accuracy	1.5976562500000002	(fma.f64 (/.f64 (.f64 (.f64 z z) x) y) #s(literal -1/2 binary64) (*.f64 y x))
accuracy	4.122091756952142	(/.f64 (.f64 (.f64 z z) x) y)
accuracy	7.970708838578784	(.f64 (.f64 z z) x)

Samples

23.0ms

256×

valid

Compiler

Compiled 47 to 16 computations (66% saved)

Precisions

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

ival-mult: 9.0ms (61.5% of total)

ival-div: 2.0ms (13.7% of total)

ival-sqrt: 2.0ms (13.7% of total)

ival-sub: 1.0ms (6.8% of total)

ival-add: 1.0ms (6.8% of total)

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

exact: 0.0ms (0% of total)

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

series17.0ms (0.3%)

Memory

-0.7MiB live, 38.1MiB allocated

Counts

4 → 132

Calls

Call 1

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

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

Calls

9 calls:

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

simplify213.0ms (3.8%)

Memory

-20.5MiB live, 268.3MiB allocated

Algorithm

1×	egg-herbie

Rules

24 340×	`lower-fma.f64`
24 340×	`lower-fma.f32`
7 398×	`lower-*.f64`
7 398×	`lower-*.f32`
2 202×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	139	1530
1	448	1472
2	1745	1421
3	6919	1411
0	8259	1348

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

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

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

rewrite167.0ms (3%)

Memory

13.6MiB live, 198.5MiB allocated

Rules

6 326×	`lower-fma.f32`
6 324×	`lower-fma.f64`
4 894×	`lower-*.f32`
4 888×	`lower-*.f64`
2 344×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	47
0	21	47
1	78	47
2	532	47
3	5837	47
0	8218	47

Stop Event

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

Counts

4 → 182

Calls

Call 1

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

Outputs
(.f64 (/.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)) #s(literal 2 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)) #s(literal 3 binary64)) (pow.f64 (.f64 y x) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (/.f64 y (.f64 x (.f64 z z))) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 (.f64 y x) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y) (.f64 y x)))))
(.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 y (.f64 x (.f64 z z))) #s(literal -3 binary64)) (pow.f64 (.f64 y x) #s(literal 3 binary64))) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)) #s(literal 4 binary64)) (pow.f64 (.f64 (fma.f64 y x (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y))) (.f64 y x)) #s(literal 2 binary64)))) (fma.f64 (pow.f64 (/.f64 y (.f64 x (.f64 z z))) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 (.f64 (neg.f64 x) y) (fma.f64 y x (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x (*.f64 z z)) y))))))
(.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 y (.f64 x (.f64 z z))) #s(literal -3 binary64)) (pow.f64 (.f64 y x) #s(literal 3 binary64))) (fma.f64 (pow.f64 (/.f64 y (.f64 x (.f64 z z))) #s(literal -6 binary64)) #s(literal 1/64 binary64) (pow.f64 (.f64 (fma.f64 y x (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y))) (.f64 y x)) #s(literal 3 binary64)))) (fma.f64 (.f64 (fma.f64 y x (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y))) (.f64 y x)) (-.f64 (.f64 (fma.f64 y x (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y))) (.f64 y x)) (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)) #s(literal 2 binary64))) (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (*.f64 z z)) y)) #s(literal 4 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)) #s(literal 2 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)) #s(literal 2 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y) (.f64 y x)))
(.f64 (-.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)) #s(literal 2 binary64))) (pow.f64 (fma.f64 y x (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y))) #s(literal -1 binary64)))
(.f64 (pow.f64 (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y))) #s(literal -1 binary64)) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)) #s(literal 2 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))))
(.f64 (pow.f64 (fma.f64 (pow.f64 (/.f64 y (.f64 x (.f64 z z))) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 (fma.f64 y x (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y))) (.f64 y x))) #s(literal -1 binary64)) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 y (.f64 x (.f64 z z))) #s(literal -3 binary64)) (pow.f64 (*.f64 y x) #s(literal 3 binary64))))
(.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)) #s(literal 2 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64)))) (pow.f64 (neg.f64 (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)))) #s(literal -1 binary64)))
(.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 y (.f64 x (.f64 z z))) #s(literal -3 binary64)) (pow.f64 (.f64 y x) #s(literal 3 binary64)))) (pow.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 y (.f64 x (.f64 z z))) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 (fma.f64 y x (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y))) (*.f64 y x)))) #s(literal -1 binary64)))
(.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)) #s(literal 2 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y))) #s(literal -1 binary64)))
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(fma.f64 (/.f64 #s(literal -1/2 binary64) (neg.f64 y)) (.f64 (.f64 (neg.f64 x) z) z) (*.f64 y x))
(fma.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)) #s(literal 3 binary64)) (pow.f64 (.f64 y x) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (/.f64 y (.f64 x (.f64 z z))) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 (.f64 y x) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y) (.f64 y x)))) (neg.f64 (/.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y))))))
(fma.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)) #s(literal 2 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y) (.f64 y x)) (neg.f64 (/.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y))))))
(fma.f64 (.f64 #s(literal -1/2 binary64) z) (.f64 (/.f64 x y) z) (*.f64 y x))
(fma.f64 (/.f64 (.f64 (.f64 (neg.f64 x) z) z) #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) y) (*.f64 y x))
(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (.f64 z z))) #s(literal 1 binary64)) (pow.f64 y #s(literal -1 binary64)) (*.f64 y x))
(fma.f64 (/.f64 #s(literal -1/2 binary64) y) (.f64 x (.f64 z z)) (*.f64 y x))
(fma.f64 (.f64 (/.f64 x y) #s(literal -1/2 binary64)) (.f64 z z) (*.f64 y x))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 z z) y) (*.f64 y x))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 z z)) (/.f64 x y) (*.f64 y x))
(fma.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x (.f64 z z)) y)) (/.f64 (/.f64 (.f64 x (.f64 z z)) y) (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)))) (neg.f64 (/.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y))))))
(fma.f64 (.f64 (pow.f64 (/.f64 y (.f64 x (.f64 z z))) #s(literal -2 binary64)) #s(literal -1/2 binary64)) (/.f64 #s(literal -1/2 binary64) (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)))) (neg.f64 (/.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y))))))
(fma.f64 (pow.f64 (/.f64 y (.f64 x (.f64 z z))) #s(literal -2 binary64)) (/.f64 #s(literal 1/4 binary64) (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)))) (neg.f64 (/.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (*.f64 z z)) y))))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (/.f64 y (.f64 x (.f64 z z))) #s(literal -2 binary64)) (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)))) (neg.f64 (/.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (*.f64 z z)) y))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (.f64 z z))) (/.f64 #s(literal -1 binary64) y) (.f64 y x))
(fma.f64 (/.f64 x y) (.f64 #s(literal -1/2 binary64) (.f64 z z)) (*.f64 y x))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (.f64 z z))) (pow.f64 y #s(literal -1 binary64)) (.f64 y x))
(fma.f64 (.f64 x z) (.f64 z (/.f64 #s(literal -1/2 binary64) y)) (*.f64 y x))
(fma.f64 (pow.f64 y #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 x (.f64 z z))) (.f64 y x))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)) (.f64 y x))
(fma.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)) #s(literal 2 binary64)) (pow.f64 (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y))))))
(fma.f64 (.f64 (.f64 (neg.f64 x) z) z) (/.f64 #s(literal -1/2 binary64) (neg.f64 y)) (*.f64 y x))
(fma.f64 (.f64 (.f64 (neg.f64 x) z) z) (.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1/2 binary64)) (.f64 y x))
(fma.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 x) (/.f64 (.f64 z z) y)) (*.f64 y x))
(fma.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)) (/.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)) (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)))) (neg.f64 (/.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (*.f64 z z)) y))))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (pow.f64 (/.f64 y (.f64 x (.f64 z z))) #s(literal -2 binary64)) #s(literal -1/2 binary64)) (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)))) (neg.f64 (/.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y))))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y) (*.f64 y x))
(fma.f64 (/.f64 (.f64 x (.f64 z z)) y) (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x (.f64 z z)) y)) (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)))) (neg.f64 (/.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y))))))
(fma.f64 (/.f64 (.f64 x (.f64 z z)) y) #s(literal -1/2 binary64) (*.f64 y x))
(fma.f64 y x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (*.f64 z z)) y)))
(fma.f64 (.f64 x (.f64 z z)) (/.f64 #s(literal -1/2 binary64) y) (*.f64 y x))
(fma.f64 x (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 z z)) y) (*.f64 y x))
(fma.f64 x (.f64 (.f64 #s(literal -1/2 binary64) (.f64 z z)) (pow.f64 y #s(literal -1 binary64))) (.f64 y x))
(fma.f64 x (.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64)) (*.f64 y x))
(fma.f64 x (.f64 (.f64 z z) (/.f64 #s(literal -1/2 binary64) y)) (*.f64 y x))
(fma.f64 x y (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (*.f64 z z)) y)))
(fma.f64 (.f64 z z) (.f64 (.f64 #s(literal -1/2 binary64) x) (pow.f64 y #s(literal -1 binary64))) (.f64 y x))
(fma.f64 (.f64 z z) (.f64 (/.f64 x y) #s(literal -1/2 binary64)) (*.f64 y x))
(fma.f64 z (/.f64 (.f64 (.f64 x z) #s(literal -1/2 binary64)) y) (*.f64 y x))
(fma.f64 z (.f64 (.f64 (.f64 x z) #s(literal -1/2 binary64)) (pow.f64 y #s(literal -1 binary64))) (.f64 y x))
(fma.f64 z (.f64 (.f64 (/.f64 x y) z) #s(literal -1/2 binary64)) (*.f64 y x))
(fma.f64 z (.f64 (.f64 x z) (/.f64 #s(literal -1/2 binary64) y)) (*.f64 y x))
(fma.f64 z (.f64 z (.f64 (/.f64 x y) #s(literal -1/2 binary64))) (*.f64 y x))
(-.f64 (/.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) (fma.f64 y x (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)))) (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)) #s(literal 2 binary64)) (fma.f64 y x (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)))))
(-.f64 (.f64 (pow.f64 (/.f64 y (.f64 x (.f64 z z))) #s(literal -2 binary64)) (/.f64 #s(literal 1/4 binary64) (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y))))) (/.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)))))
(exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y) (.f64 y x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (.f64 (pow.f64 (/.f64 y (.f64 x (.f64 z z))) #s(literal -2 binary64)) (/.f64 #s(literal 1/4 binary64) (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y))))) (neg.f64 (/.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) (fma.f64 (neg.f64 y) x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y))))))
(+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)) (.f64 y x))
(+.f64 (.f64 y x) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y)))
#s(approx (* x (sqrt (- (* y y) (* z z)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 x (.f64 z z)) y) (*.f64 y x)))
(.f64 (pow.f64 (/.f64 y z) #s(literal -1 binary64)) (.f64 x z))
(.f64 (.f64 (pow.f64 y #s(literal -1 binary64)) z) (*.f64 x z))
(.f64 (.f64 #s(literal 1 binary64) x) (/.f64 (*.f64 z z) y))
(.f64 (.f64 #s(literal 1 binary64) z) (*.f64 (/.f64 x y) z))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 z z)) (/.f64 x y))
(.f64 (pow.f64 (/.f64 y (.f64 x (.f64 z z))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 y (.f64 x (*.f64 z z))) #s(literal -1/2 binary64)))
(.f64 (/.f64 (neg.f64 x) #s(literal -1 binary64)) (/.f64 (.f64 z z) y))
(.f64 (/.f64 (neg.f64 z) #s(literal -1 binary64)) (.f64 (/.f64 x y) z))
(.f64 (/.f64 (.f64 (neg.f64 z) z) #s(literal -1 binary64)) (/.f64 x y))
(.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 (.f64 (neg.f64 z) z) y))
(.f64 (/.f64 (.f64 z z) #s(literal -1 binary64)) (/.f64 (neg.f64 x) y))
(.f64 (/.f64 z #s(literal -1 binary64)) (/.f64 (.f64 (neg.f64 x) z) y))
(.f64 (.f64 #s(literal 1 binary64) (.f64 (.f64 (neg.f64 x) z) z)) (/.f64 #s(literal -1 binary64) y))
(.f64 (/.f64 (.f64 z z) y) x)
(.f64 (.f64 (/.f64 x y) z) z)
(.f64 (/.f64 #s(literal -1 binary64) y) (.f64 (*.f64 (neg.f64 x) z) z))
(.f64 (neg.f64 x) (/.f64 (.f64 z z) (neg.f64 y)))
(.f64 (neg.f64 x) (.f64 (*.f64 z z) (/.f64 #s(literal -1 binary64) y)))
(.f64 #s(literal -1 binary64) (.f64 (neg.f64 x) (/.f64 (*.f64 z z) y)))
(.f64 (/.f64 x y) (.f64 z z))
(.f64 (.f64 x z) (*.f64 z (pow.f64 y #s(literal -1 binary64))))
(.f64 (.f64 x z) (/.f64 z y))
(.f64 (neg.f64 z) (/.f64 (.f64 x z) (neg.f64 y)))
(.f64 (neg.f64 z) (.f64 (*.f64 x z) (/.f64 #s(literal -1 binary64) y)))
(.f64 (.f64 (neg.f64 z) z) (*.f64 x (/.f64 #s(literal -1 binary64) y)))
(.f64 (.f64 (neg.f64 z) z) (/.f64 x (neg.f64 y)))
(.f64 (pow.f64 y #s(literal -1 binary64)) (pow.f64 (.f64 x (*.f64 z z)) #s(literal 1 binary64)))
(.f64 (pow.f64 y #s(literal -1 binary64)) (.f64 x (*.f64 z z)))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 x (*.f64 z z)) y))
(.f64 (.f64 (*.f64 (neg.f64 x) z) z) (/.f64 #s(literal -1 binary64) y))
(.f64 (/.f64 (.f64 x (*.f64 z z)) y) #s(literal 1 binary64))
(.f64 (.f64 x (*.f64 z z)) (pow.f64 y #s(literal -1 binary64)))
(.f64 x (.f64 (*.f64 (neg.f64 z) z) (/.f64 #s(literal -1 binary64) y)))
(.f64 x (/.f64 (.f64 z z) y))
(.f64 (.f64 z z) (/.f64 x y))
(.f64 z (.f64 (*.f64 (neg.f64 x) z) (/.f64 #s(literal -1 binary64) y)))
(.f64 z (.f64 (/.f64 x y) z))
(pow.f64 (/.f64 y (.f64 x (.f64 z z))) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 x (.f64 z z)) y) #s(literal 1 binary64))
(/.f64 (.f64 (.f64 z z) #s(literal 1 binary64)) (/.f64 y x))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 z z)) (/.f64 y x))
(/.f64 (/.f64 (.f64 (.f64 (neg.f64 x) z) z) #s(literal -1 binary64)) y)
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (*.f64 (neg.f64 x) z) z)) (neg.f64 y))
(/.f64 (.f64 (.f64 (*.f64 (neg.f64 x) z) z) #s(literal 1 binary64)) (neg.f64 y))
(/.f64 #s(literal -1 binary64) (/.f64 (/.f64 (/.f64 y z) z) (neg.f64 x)))
(/.f64 (pow.f64 y #s(literal -1 binary64)) (pow.f64 (.f64 x (.f64 z z)) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 y (.f64 x (.f64 z z))))
(/.f64 (.f64 (.f64 (neg.f64 x) z) z) (neg.f64 y))
(/.f64 (.f64 x (.f64 z z)) y)
(/.f64 (*.f64 z z) (/.f64 y x))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 y (.f64 x (.f64 z z)))))
(neg.f64 (.f64 #s(literal 1 binary64) (.f64 (neg.f64 x) (/.f64 (*.f64 z z) y))))
(neg.f64 (.f64 (neg.f64 x) (/.f64 (.f64 z z) y)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 y)) (.f64 (neg.f64 x) (/.f64 (.f64 z z) y)))
(-.f64 #s(literal 0 binary64) (.f64 (neg.f64 x) (/.f64 (.f64 z z) y)))
(exp.f64 (.f64 (log.f64 (/.f64 y (.f64 x (*.f64 z z)))) #s(literal -1 binary64)))
(.f64 (neg.f64 (neg.f64 z)) (.f64 x z))
(.f64 (neg.f64 (.f64 (neg.f64 z) z)) x)
(.f64 (neg.f64 (neg.f64 x)) (.f64 z z))
(.f64 (neg.f64 x) (.f64 (neg.f64 z) z))
(.f64 #s(literal -1 binary64) (.f64 (*.f64 (neg.f64 x) z) z))
(.f64 (.f64 x z) (*.f64 z #s(literal 1 binary64)))
(.f64 (.f64 x z) z)
(.f64 (neg.f64 z) (.f64 (neg.f64 x) z))
(.f64 (.f64 (neg.f64 z) z) (neg.f64 x))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 z z)))
(.f64 (.f64 x (*.f64 z z)) #s(literal 1 binary64))
(.f64 x (.f64 (*.f64 z z) #s(literal 1 binary64)))
(.f64 x (neg.f64 (.f64 (neg.f64 z) z)))
(.f64 x (.f64 z z))
(.f64 (.f64 z z) (*.f64 x #s(literal 1 binary64)))
(.f64 (.f64 z z) (neg.f64 (neg.f64 x)))
(.f64 (.f64 z z) x)
(.f64 z (.f64 (*.f64 x z) #s(literal 1 binary64)))
(.f64 z (neg.f64 (.f64 (neg.f64 x) z)))
(.f64 z (.f64 x z))
(neg.f64 (.f64 (.f64 (neg.f64 x) z) z))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 (neg.f64 x) z) z))

eval51.0ms (0.9%)

Memory: 3.8MiB live, 94.9MiB allocated
Compiler: Compiled 7 036 to 827 computations (88.2% saved)

prune9.0ms (0.2%)

Memory

-16.3MiB live, 22.4MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	314	0	314
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	314	5	319

Accuracy

100.0%

Counts

319 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.4%	(.f64 (.f64 x (sqrt.f64 (+.f64 z y))) (sqrt.f64 (-.f64 y z)))
✓	67.3%	(.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x)
✓	99.7%	(.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)))
✓	89.0%	#s(approx (* x (sqrt (- (* y y) (* z z)))) (fma.f64 (/.f64 (.f64 (.f64 z z) x) y) #s(literal -1/2 binary64) (*.f64 y x)))
✓	99.3%	#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 x y))

Compiler

Compiled 108 to 71 computations (34.3% saved)

regimes21.0ms (0.4%)

Memory

12.3MiB live, 50.9MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

8 calls:

4.0ms	z
2.0ms	x
2.0ms	y
2.0ms	(-.f64 (.f64 y y) (.f64 z z))
2.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`y`
99.7%	1	`z`
99.7%	1	`(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))`
99.7%	1	`(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))`
99.7%	1	`(-.f64 (.f64 y y) (.f64 z z))`
99.7%	1	`(*.f64 y y)`
99.7%	1	`(*.f64 z z)`

Compiler

Compiled 34 to 38 computations (-11.8% saved)

regimes13.0ms (0.2%)

Memory

-10.4MiB live, 34.7MiB allocated

Accuracy

Total -20.6b remaining (-4352.9%)

Threshold costs -20.6b (-4352.9%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 x y))
(.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x)

Outputs
#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 x y))

Calls

8 calls:

3.0ms	y
2.0ms	x
1.0ms	z
1.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
1.0ms	(-.f64 (.f64 y y) (.f64 z z))

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`y`
99.3%	1	`z`
99.3%	1	`(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))`
99.3%	1	`(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))`
99.3%	1	`(-.f64 (.f64 y y) (.f64 z z))`
99.3%	1	`(*.f64 y y)`
99.3%	1	`(*.f64 z z)`

Compiler

Compiled 34 to 38 computations (-11.8% saved)

simplify22.0ms (0.4%)

Memory

30.5MiB live, 69.6MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`-commutative-binary64-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	33
1	19	33

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness213.0ms (3.8%)

Memory

-37.6MiB live, 167.2MiB allocated

Rules

13 108×	`lower-fma.f64`
13 108×	`lower-fma.f32`
5 990×	`lower-*.f64`
5 990×	`lower-*.f32`
3 530×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	205	1489
1	648	1483
2	2455	1426
3	7928	1426
0	8162	1349

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 28 to 23 computations (17.9% saved)

preprocess120.0ms (2.2%)

Memory

18.0MiB live, 138.9MiB allocated

Remove

(negabs x)

(abs z)

Compiler

Compiled 352 to 282 computations (19.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze137.0ms (2.5%)

sample1.6s (28.7%)

explain98.0ms (1.8%)

preprocess544.0ms (9.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify467.0ms (8.4%)

localize92.0ms (1.7%)

series72.0ms (1.3%)

simplify374.0ms (6.8%)

rewrite208.0ms (3.8%)

eval53.0ms (1%)

prune8.0ms (0.1%)

simplify153.0ms (2.8%)

localize77.0ms (1.4%)

series50.0ms (0.9%)

simplify189.0ms (3.4%)

rewrite202.0ms (3.7%)

eval199.0ms (3.6%)

prune28.0ms (0.5%)

simplify118.0ms (2.1%)

localize31.0ms (0.6%)

series17.0ms (0.3%)

simplify213.0ms (3.8%)

rewrite167.0ms (3%)

eval51.0ms (0.9%)

prune9.0ms (0.2%)

regimes21.0ms (0.4%)

regimes13.0ms (0.2%)

simplify22.0ms (0.4%)

soundness213.0ms (3.8%)

preprocess120.0ms (2.2%)

end0.0ms (0%)

Profiling