Metrics for Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze55.0ms (0.8%)

Memory

5.2MiB live, 42.9MiB 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
50%	49.9%	49.9%	0.1%	0%	0%	0%	4
50%	49.9%	49.9%	0.1%	0%	0%	0%	5
50%	49.9%	49.9%	0.1%	0%	0%	0%	6
66.7%	49.9%	25%	0.1%	0%	25%	0%	7
66.7%	49.9%	25%	0.1%	0%	25%	0%	8
66.7%	49.9%	25%	0.1%	0%	25%	0%	9
80%	49.9%	12.5%	0.1%	0%	37.4%	0%	10
80%	49.9%	12.5%	0.1%	0%	37.4%	0%	11
80%	49.9%	12.5%	0.1%	0%	37.4%	0%	12

Compiler

Compiled 12 to 12 computations (0% saved)

sample1.4s (18.5%)

Memory

5.3MiB live, 1 512.0MiB allocated

Samples

796.0ms	8 256×	0	valid
193.0ms	2 013×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 602.0ms

ival-div: 322.0ms (53.5% of total)

ival-mult: 124.0ms (20.6% of total)

ival-sqrt: 76.0ms (12.6% of total)

ival-add: 60.0ms (10% of total)

exact: 9.0ms (1.5% of total)

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

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

Bogosity

explain180.0ms (2.5%)

Memory

30.7MiB live, 188.8MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))`
-	-	`#s(literal 1 binary64)`
-	-	`z`
-	-	`(sqrt.f64 z)`
-	-	`(+.f64 x (*.f64 y (sqrt.f64 z)))`
-	-	`(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z))))`
-	-	`y`
-	-	`#s(literal 2 binary64)`
-	-	`(*.f64 y (sqrt.f64 z))`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

33.0ms

512×

valid

Compiler

Compiled 74 to 34 computations (54.1% saved)

Precisions

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

ival-mult: 6.0ms (34.9% of total)

ival-sqrt: 4.0ms (23.3% of total)

ival-div: 3.0ms (17.5% of total)

ival-add: 2.0ms (11.6% of total)

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

exact: 0.0ms (0% of total)

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

preprocess71.0ms (1%)

Memory

-7.1MiB live, 69.2MiB allocated

Algorithm

1×	egg-herbie

Rules

482×	`unsub-neg`
354×	`distribute-lft-neg-in`
312×	`cancel-sign-sub-inv`
270×	`distribute-rgt-in`
236×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	78
1	112	74
2	311	74
3	600	74
4	932	74
5	1348	74
6	1744	74
7	2055	74
8	2168	74
9	2252	74
10	2288	74
11	2292	74
12	2292	74
0	10	8
0	16	8
1	27	8
2	37	8
3	39	8
0	39	7

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 10 to 10 computations (0% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z))))

Compiler

Compiled 10 to 10 computations (0% saved)

simplify4.0ms (0.1%)

Memory

9.0MiB live, 9.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 y (sqrt.f64 z))
cost-diff	0	(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z))))
cost-diff	128	(+.f64 x (*.f64 y (sqrt.f64 z)))
cost-diff	704	(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))

Rules

32×	`lower-*.f32`
28×	`lower-*.f64`
20×	`lower-fma.f64`
20×	`lower-fma.f32`
16×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
0	16	26
1	27	26
2	37	26
3	39	26
0	39	24

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize29.0ms (0.4%)

Memory

-32.0MiB live, 50.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z))))
accuracy	0	(sqrt.f64 z)
accuracy	0.00390625	(+.f64 x (*.f64 y (sqrt.f64 z)))
accuracy	0.25	(*.f64 y (sqrt.f64 z))

Samples

21.0ms

256×

valid

Compiler

Compiled 32 to 12 computations (62.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 5.0ms (49.4% of total)

ival-div: 2.0ms (19.8% of total)

ival-sqrt: 2.0ms (19.8% of total)

ival-add: 1.0ms (9.9% of total)

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

exact: 0.0ms (0% of total)

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

series10.0ms (0.1%)

Memory

24.3MiB live, 24.3MiB allocated

Counts

5 → 108

Calls

Call 1

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

Outputs
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation:binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation:binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation:binary64>) () ())) ())
#s(alt (sqrt z) (taylor 0 z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor inf z) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z))) (taylor inf z) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z))) (taylor inf z) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* z (+ (* y (sqrt (/ 1 z))) (/ x z))) (taylor inf z) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (* y (sqrt z))) (taylor inf z) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) (taylor inf z) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) (taylor inf z) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z)))) (taylor inf z) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor inf z) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor inf z) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor inf z) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor inf z) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (sqrt z) (taylor inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation:binary64>) () ())) ())
#s(alt (sqrt z) (taylor inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation:binary64>) () ())) ())
#s(alt (sqrt z) (taylor inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation:binary64>) () ())) ())
#s(alt (sqrt z) (taylor inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) (taylor -inf z) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) (taylor -inf z) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) (taylor -inf z) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))) (taylor -inf z) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z))) (taylor -inf z) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) (taylor -inf z) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) (taylor -inf z) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))) (taylor -inf z) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) (taylor -inf z) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) (taylor -inf z) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) (taylor -inf z) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z))) (taylor -inf z) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt z) (pow (sqrt -1) 2))) (taylor -inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt z) (pow (sqrt -1) 2))) (taylor -inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt z) (pow (sqrt -1) 2))) (taylor -inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* (sqrt z) (pow (sqrt -1) 2))) (taylor -inf z) (#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation:binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 y) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 y) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 y) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 y) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) (taylor 0 y) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) (taylor 0 y) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) (taylor 0 y) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 y) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 y) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 y) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 y) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor inf y) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* y (+ (sqrt z) (/ x y))) (taylor inf y) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* y (+ (sqrt z) (/ x y))) (taylor inf y) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* y (+ (sqrt z) (/ x y))) (taylor inf y) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (* y (sqrt z))) (taylor inf y) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) (taylor inf y) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) (taylor inf y) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y)))) (taylor inf y) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor inf y) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor inf y) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor inf y) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor inf y) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor -inf y) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) (taylor -inf y) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) (taylor -inf y) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y))))) (taylor -inf y) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (* y (sqrt z))) (taylor -inf y) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) (taylor -inf y) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) (taylor -inf y) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y))))) (taylor -inf y) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor -inf y) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor -inf y) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor -inf y) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor -inf y) (#s(alt (.f64 y (sqrt.f64 z)) (patch (.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 x) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 x) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 x) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 x) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (* y (sqrt z))) (taylor 0 x) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) (taylor 0 x) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) (taylor 0 x) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (+ (* 1/2 x) (* 1/2 (* y (sqrt z)))) (taylor 0 x) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (* (/ y x) (sqrt z)))) (taylor inf x) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (* (/ y x) (sqrt z)))) (taylor inf x) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (* (/ y x) (sqrt z)))) (taylor inf x) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) (taylor inf x) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) (taylor inf x) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z))))) (taylor inf x) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1))) (taylor -inf x) (#s(alt (+.f64 x (.f64 y (sqrt.f64 z))) (patch (+.f64 x (.f64 y (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z)))) #<representation:binary64>) () ())) ())

Calls

9 calls:

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

simplify160.0ms (2.2%)

Memory

-34.5MiB live, 187.9MiB allocated

Algorithm

1×	egg-herbie

Rules

5 642×	`lower-fma.f64`
5 642×	`lower-fma.f32`
3 660×	`lower-*.f64`
3 660×	`lower-*.f32`
1 856×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	646
1	251	646
2	797	646
3	2298	622
4	5069	622
5	7549	622
0	8141	566

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 105

Calls

Call 1

Inputs
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* 1/2 (+ x (* y (sqrt z))))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(* y (sqrt z))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* z (+ (* y (sqrt (/ 1 z))) (/ x z)))
(* 1/2 (* y (sqrt z)))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* z (+ (* 1/2 (* y (sqrt (/ 1 z)))) (* 1/2 (/ x z))))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1 (* z (+ (* -1 (/ x z)) (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(* -1/2 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* z (+ (* -1/2 (/ x z)) (* 1/2 (* (* y (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (* y (pow (sqrt -1) 2)) (sqrt z)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
x
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* 1/2 x)
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* y (+ (sqrt z) (/ x y)))
(* 1/2 (* y (sqrt z)))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (+ (* 1/2 (sqrt z)) (* 1/2 (/ x y))))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* -1 (* y (+ (* -1 (sqrt z)) (* -1 (/ x y)))))
(* 1/2 (* y (sqrt z)))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1/2 (sqrt z)) (* -1/2 (/ x y)))))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(* y (sqrt z))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(+ x (* y (sqrt z)))
(* 1/2 (* y (sqrt z)))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
(+ (* 1/2 x) (* 1/2 (* y (sqrt z))))
x
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
(* x (+ 1 (* (/ y x) (sqrt z))))
(* 1/2 x)
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
(* x (+ 1/2 (* 1/2 (* (/ y x) (sqrt z)))))
x
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* -1 (* x (- (* -1 (* (/ y x) (sqrt z))) 1)))
(* 1/2 x)
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))
(* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2)))

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

rewrite184.0ms (2.5%)

Memory

21.2MiB live, 339.2MiB allocated

Rules

7 460×	`lower-fma.f64`
7 460×	`lower-fma.f32`
4 298×	`lower-*.f32`
4 294×	`lower-*.f64`
4 222×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
0	16	21
1	41	21
2	234	21
3	2001	21
0	8162	19

Stop Event

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

Counts

5 → 272

Calls

Call 1

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

Outputs
#s(literal 1/2 binary64)
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (.f64 (sqrt.f64 z) y)))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (.f64 (sqrt.f64 z) y)))) (fma.f64 (pow.f64 z #s(literal 9/2 binary64)) (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 3 binary64))) (pow.f64 (.f64 (*.f64 (sqrt.f64 z) y) x) #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 x (.f64 (sqrt.f64 z) y)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (hypot.f64 (.f64 (sqrt.f64 z) y) x) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 x (.f64 (sqrt.f64 z) y)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (.f64 (.f64 z y) y) (hypot.f64 (.f64 (sqrt.f64 z) y) x) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 (neg.f64 z) (.f64 y y) (.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 3 binary64)))) (fma.f64 y (fma.f64 z y (.f64 (sqrt.f64 z) x)) (.f64 x x)))
(.f64 (/.f64 (fma.f64 (pow.f64 z #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 z (pow.f64 (.f64 y (-.f64 (.f64 (sqrt.f64 z) y) x)) #s(literal 2 binary64))))) (-.f64 (.f64 x x) (.f64 y (-.f64 (.f64 z y) (.f64 (sqrt.f64 z) x)))))
(.f64 (/.f64 (fma.f64 (pow.f64 z #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 y (-.f64 (.f64 z y) (.f64 (sqrt.f64 z) x))) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (.f64 y (-.f64 (.f64 z y) (.f64 (sqrt.f64 z) x))) (-.f64 (.f64 y (-.f64 (.f64 z y) (.f64 (sqrt.f64 z) x))) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (fma.f64 (neg.f64 z) (.f64 y y) (.f64 x x)) (fma.f64 (neg.f64 z) (.f64 y y) (*.f64 x x))) (fma.f64 (sqrt.f64 z) y x))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))) (-.f64 x (.f64 (sqrt.f64 z) y))) (pow.f64 (hypot.f64 (.f64 (sqrt.f64 z) y) x) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 6 binary64))) (-.f64 x (.f64 (sqrt.f64 z) y))) (pow.f64 (fma.f64 (.f64 (.f64 z y) y) (hypot.f64 (.f64 (sqrt.f64 z) y) x) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 6 binary64))) (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (.f64 (sqrt.f64 z) y))))) (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 (pow.f64 z #s(literal 9/2 binary64)) (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (.f64 (sqrt.f64 z) y))))) (pow.f64 (-.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 3 binary64))) (pow.f64 (.f64 (*.f64 (sqrt.f64 z) y) x) #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 (fma.f64 (pow.f64 z #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y)))) #s(literal -1 binary64)))
(.f64 (-.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x (.f64 (sqrt.f64 z) y)))) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 z y) (/.f64 y (-.f64 x (.f64 (sqrt.f64 z) y)))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 x (-.f64 x (.f64 (sqrt.f64 z) y))) (.f64 (.f64 z y) (/.f64 y (-.f64 x (.f64 (sqrt.f64 z) y)))))))
(.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 x (.f64 (sqrt.f64 z) y)) #s(literal 3 binary64))) (.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (/.f64 z (-.f64 x (.f64 (sqrt.f64 z) y))) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x (.f64 (sqrt.f64 z) y)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (.f64 z y) (/.f64 y (-.f64 x (.f64 (sqrt.f64 z) y)))) #s(literal 2 binary64)) (.f64 (.f64 x (/.f64 x (-.f64 x (.f64 (sqrt.f64 z) y)))) (.f64 (.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))))))))
(.f64 (neg.f64 (fma.f64 (.f64 z y) y (.f64 (neg.f64 x) x))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (.f64 (sqrt.f64 z) y) x))))
(.f64 (neg.f64 (neg.f64 (fma.f64 (neg.f64 z) (.f64 y y) (.f64 x x)))) (pow.f64 (-.f64 x (.f64 (sqrt.f64 z) y)) #s(literal -1 binary64)))
(.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 z #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (pow.f64 (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (.f64 (sqrt.f64 z) y)))) #s(literal -1 binary64)))
(.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (hypot.f64 (.f64 (sqrt.f64 z) y) x) (-.f64 x (.f64 (sqrt.f64 z) y)))))
(.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 6 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 (.f64 z y) y) (hypot.f64 (.f64 (sqrt.f64 z) y) x) (pow.f64 x #s(literal 4 binary64))) (-.f64 x (.f64 (sqrt.f64 z) y)))))
(.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 6 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 3 binary64))) (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (.f64 (sqrt.f64 z) y)))))))
(.f64 (.f64 (fma.f64 (pow.f64 z #s(literal 9/2 binary64)) (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 3 binary64))) (pow.f64 (.f64 (.f64 (sqrt.f64 z) y) x) #s(literal 3 binary64))) (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y)))))))
(.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x (.f64 (sqrt.f64 z) y))) (.f64 (-.f64 x (.f64 (sqrt.f64 z) y)) (.f64 (.f64 z y) y))) (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 x (*.f64 (sqrt.f64 z) y)) #s(literal 2 binary64))))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal -1 binary64)))))
(.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x (.f64 (sqrt.f64 z) y)) (hypot.f64 (*.f64 (sqrt.f64 z) y) x))))
(.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x (.f64 (sqrt.f64 z) y)) (fma.f64 (.f64 (.f64 z y) y) (hypot.f64 (*.f64 (sqrt.f64 z) y) x) (pow.f64 x #s(literal 4 binary64))))))
(.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (.f64 (sqrt.f64 z) y)))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (*.f64 (sqrt.f64 z) y) #s(literal 3 binary64))))))
(.f64 (fma.f64 (.f64 z y) y (.f64 (neg.f64 x) x)) (pow.f64 (-.f64 (.f64 (sqrt.f64 z) y) x) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 x (.f64 (sqrt.f64 z) y)) #s(literal -1 binary64)) (fma.f64 (neg.f64 z) (.f64 y y) (.f64 x x)))
(.f64 (pow.f64 (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (.f64 (sqrt.f64 z) y)))) #s(literal -1 binary64)) (fma.f64 (pow.f64 z #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(.f64 (fma.f64 (pow.f64 z #s(literal 9/2 binary64)) (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (.f64 (sqrt.f64 z) y)))) (-.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 3 binary64))) (pow.f64 (.f64 (.f64 (sqrt.f64 z) y) x) #s(literal 3 binary64))))))
(.f64 (neg.f64 (fma.f64 (neg.f64 z) (.f64 y y) (.f64 x x))) (pow.f64 (neg.f64 (-.f64 x (.f64 (sqrt.f64 z) y))) #s(literal -1 binary64)))
(.f64 (neg.f64 (fma.f64 (pow.f64 z #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (neg.f64 (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (.f64 (sqrt.f64 z) y))))) #s(literal -1 binary64)))
(.f64 (fma.f64 (neg.f64 z) (.f64 y y) (.f64 x x)) (pow.f64 (-.f64 x (.f64 (sqrt.f64 z) y)) #s(literal -1 binary64)))
(.f64 (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (.f64 (sqrt.f64 z) y)))) (/.f64 (fma.f64 (sqrt.f64 z) y x) (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y))))))
(.f64 (fma.f64 (pow.f64 z #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (.f64 z y) y (.f64 x (-.f64 x (.f64 (sqrt.f64 z) y)))) #s(literal -1 binary64)))
(.f64 (fma.f64 (sqrt.f64 z) y x) (/.f64 (-.f64 x (.f64 (sqrt.f64 z) y)) (-.f64 x (*.f64 (sqrt.f64 z) y))))
(*.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 z) y x))
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eval44.0ms (0.6%)

Memory: 5.7MiB live, 87.2MiB allocated
Compiler: Compiled 9 324 to 939 computations (89.9% saved)

prune41.0ms (0.6%)

Memory

-1.8MiB live, 35.8MiB allocated

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	366	11	377
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	367	11	378

Accuracy

100.0%

Counts

378 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(fma.f64 (pow.f64 z #s(literal 1/4 binary64)) (.f64 (pow.f64 z #s(literal 1/4 binary64)) (.f64 y #s(literal 1/2 binary64))) (*.f64 x #s(literal 1/2 binary64)))
	55.3%	(/.f64 (.f64 (fma.f64 (.f64 z y) y (.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)) (-.f64 (.f64 (sqrt.f64 z) y) x))
▶	55.2%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (sqrt.f64 z) y) x) (.f64 (fma.f64 (.f64 z y) y (.f64 (neg.f64 x) x)) #s(literal 1/2 binary64))))
▶	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))))
▶	99.8%	(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
	88.4%	(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (fma.f64 x (/.f64 x (-.f64 x (.f64 (sqrt.f64 z) y))) (neg.f64 (.f64 (.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))))))
	99.6%	(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 z))))))
▶	99.8%	(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (sqrt.f64 z))))
	93.6%	#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (.f64 (fma.f64 (.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #s(literal 1/2 binary64)))
	48.2%	#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 z) y)))
▶	53.5%	#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 286 to 232 computations (18.9% saved)

simplify439.0ms (6%)

Memory

-10.9MiB live, 268.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (sqrt.f64 z) y)
cost-diff	0	(-.f64 (*.f64 (sqrt.f64 z) y) x)
cost-diff	0	(/.f64 (-.f64 (.f64 (sqrt.f64 z) y) x) (.f64 (fma.f64 (.f64 z y) y (.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (sqrt.f64 z) y) x) (.f64 (fma.f64 (.f64 z y) y (.f64 (neg.f64 x) x)) #s(literal 1/2 binary64))))
cost-diff	0	(fma.f64 (sqrt.f64 z) y x)
cost-diff	0	(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
cost-diff	320	(/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)))
cost-diff	1088	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))))
cost-diff	0	(sqrt.f64 z)
cost-diff	0	(fma.f64 (sqrt.f64 z) y x)
cost-diff	0	(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
cost-diff	0	#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))
cost-diff	0	(sqrt.f64 z)
cost-diff	0	(*.f64 y (sqrt.f64 z))
cost-diff	0	(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (sqrt.f64 z))))
cost-diff	128	(+.f64 x (*.f64 y (sqrt.f64 z)))

Rules

28 192×	`lower-fma.f32`
28 188×	`lower-fma.f64`
3 132×	`lower-*.f32`
3 116×	`lower-*.f64`
2 560×	`lower-+.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	182
0	48	175
1	91	173
2	173	171
3	381	171
4	870	171
5	1822	171
6	3562	171
7	5389	171
8	6205	171
9	6564	171
10	6684	171
11	6711	171
12	7024	171
13	7259	171
14	7363	171
15	7518	171
16	7625	171
17	7626	171
18	7626	171
19	7626	171
0	8664	171

Stop Event

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

Calls

Call 1

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

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

localize75.0ms (1%)

Memory

17.9MiB live, 128.6MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.17578125	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (sqrt.f64 z) y) x) (.f64 (fma.f64 (.f64 z y) y (.f64 (neg.f64 x) x)) #s(literal 1/2 binary64))))
accuracy	0.25	(*.f64 (sqrt.f64 z) y)
accuracy	2.234366742816681	(fma.f64 (.f64 z y) y (.f64 (neg.f64 x) x))
accuracy	28.51280426495442	(/.f64 (-.f64 (.f64 (sqrt.f64 z) y) x) (.f64 (fma.f64 (.f64 z y) y (.f64 (neg.f64 x) x)) #s(literal 1/2 binary64)))
accuracy	0	(sqrt.f64 z)
accuracy	0.12890625	(fma.f64 (sqrt.f64 z) y x)
accuracy	0.17578125	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))))
accuracy	0.3397126371810252	(/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64)))
accuracy	0	(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
accuracy	0	(sqrt.f64 z)
accuracy	0.12890625	(fma.f64 (sqrt.f64 z) y x)
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	29.778004456179165	#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))
accuracy	0	(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (sqrt.f64 z))))
accuracy	0	(sqrt.f64 z)
accuracy	0.00390625	(+.f64 x (*.f64 y (sqrt.f64 z)))
accuracy	0.25	(*.f64 y (sqrt.f64 z))

Samples

52.0ms

256×

valid

Compiler

Compiled 192 to 29 computations (84.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-mult: 18.0ms (50.4% of total)

ival-div: 10.0ms (28% of total)

ival-add: 4.0ms (11.2% of total)

ival-sqrt: 2.0ms (5.6% of total)

ival-sub: 1.0ms (2.8% of total)

ival-neg: 1.0ms (2.8% of total)

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

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

exact: 0.0ms (0% of total)

series50.0ms (0.7%)

Memory

1.9MiB live, 87.1MiB allocated

Counts

15 → 468

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
8.0ms	z	@	0	((+ x (* y (sqrt z))) (* 1/2 (+ x (* y (sqrt z)))) (* y (sqrt z)) (sqrt z) (* (/ 1 2) (+ x (* y (sqrt z)))) (* 1/2 x) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ 1 (/ 1 (* (+ (* (sqrt z) y) x) 1/2))) (/ 1 (* (+ (* (sqrt z) y) x) 1/2)) (/ 1 (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2))) (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (- (* (sqrt z) y) x) (* (sqrt z) y) (+ (* (* z y) y) (* (neg x) x)))
5.0ms	y	@	-inf	((+ x (* y (sqrt z))) (* 1/2 (+ x (* y (sqrt z)))) (* y (sqrt z)) (sqrt z) (* (/ 1 2) (+ x (* y (sqrt z)))) (* 1/2 x) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ 1 (/ 1 (* (+ (* (sqrt z) y) x) 1/2))) (/ 1 (* (+ (* (sqrt z) y) x) 1/2)) (/ 1 (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2))) (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (- (* (sqrt z) y) x) (* (sqrt z) y) (+ (* (* z y) y) (* (neg x) x)))
5.0ms	z	@	inf	((+ x (* y (sqrt z))) (* 1/2 (+ x (* y (sqrt z)))) (* y (sqrt z)) (sqrt z) (* (/ 1 2) (+ x (* y (sqrt z)))) (* 1/2 x) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ 1 (/ 1 (* (+ (* (sqrt z) y) x) 1/2))) (/ 1 (* (+ (* (sqrt z) y) x) 1/2)) (/ 1 (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2))) (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (- (* (sqrt z) y) x) (* (sqrt z) y) (+ (* (* z y) y) (* (neg x) x)))
5.0ms	z	@	-inf	((+ x (* y (sqrt z))) (* 1/2 (+ x (* y (sqrt z)))) (* y (sqrt z)) (sqrt z) (* (/ 1 2) (+ x (* y (sqrt z)))) (* 1/2 x) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ 1 (/ 1 (* (+ (* (sqrt z) y) x) 1/2))) (/ 1 (* (+ (* (sqrt z) y) x) 1/2)) (/ 1 (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2))) (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (- (* (sqrt z) y) x) (* (sqrt z) y) (+ (* (* z y) y) (* (neg x) x)))
5.0ms	x	@	0	((+ x (* y (sqrt z))) (* 1/2 (+ x (* y (sqrt z)))) (* y (sqrt z)) (sqrt z) (* (/ 1 2) (+ x (* y (sqrt z)))) (* 1/2 x) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ 1 (/ 1 (* (+ (* (sqrt z) y) x) 1/2))) (/ 1 (* (+ (* (sqrt z) y) x) 1/2)) (/ 1 (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2))) (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (- (* (sqrt z) y) x) (* (sqrt z) y) (+ (* (* z y) y) (* (neg x) x)))

simplify518.0ms (7.1%)

Memory

0.4MiB live, 148.3MiB allocated

Algorithm

1×	egg-herbie

Rules

7 430×	`lower-fma.f64`
7 430×	`lower-fma.f32`
6 178×	`lower-*.f64`
6 178×	`lower-*.f32`
2 040×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	518	5414
1	1682	5144
2	5623	5013
0	8143	4760

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 462

Calls

Call 1

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

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

rewrite333.0ms (4.5%)

Memory

15.5MiB live, 371.0MiB allocated

Rules

5 922×	`lower-fma.f32`
5 918×	`lower-fma.f64`
4 340×	`lower-*.f32`
4 324×	`lower-*.f64`
4 066×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	124
0	48	95
1	159	91
2	981	91
0	9033	91

Stop Event

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

Counts

15 → 1 486

Calls

Call 1

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

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

eval336.0ms (4.6%)

Memory: 7.6MiB live, 541.1MiB allocated
Compiler: Compiled 68 124 to 3 984 computations (94.2% saved)

prune48.0ms (0.7%)

Memory

14.8MiB live, 174.0MiB allocated

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	2 350	5	2 355
Fresh	5	1	6
Picked	2	3	5
Done	0	0	0
Total	2 357	9	2 366

Accuracy

100.0%

Counts

2 366 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	47.7%	(/.f64 #s(literal 1 binary64) #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (*.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))))
✓	99.8%	(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
	88.4%	(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (fma.f64 x (/.f64 x (-.f64 x (.f64 (sqrt.f64 z) y))) (neg.f64 (.f64 (.f64 z y) (/.f64 y (-.f64 x (*.f64 (sqrt.f64 z) y)))))))
▶	93.6%	(.f64 #s(approx (+ ( (sqrt z) y) x) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)) #s(literal 1/2 binary64))
▶	86.9%	(.f64 #s(approx (+ ( (sqrt z) y) x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) x)) #s(literal 1/2 binary64))
▶	48.2%	(.f64 #s(approx (+ ( (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
▶	70.1%	(.f64 #s(literal 1/2 binary64) (+.f64 x (/.f64 (-.f64 (.f64 (.f64 z y) y) #s(literal 0 binary64)) (-.f64 (.f64 (sqrt.f64 z) y) #s(literal 0 binary64)))))
✓	99.8%	(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (sqrt.f64 z))))
✓	53.5%	#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 193 to 163 computations (15.5% saved)

simplify148.0ms (2%)

Memory

-24.3MiB live, 170.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	128	(+.f64 x (/.f64 (-.f64 (.f64 (.f64 z y) y) #s(literal 0 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) #s(literal 0 binary64))))
cost-diff	192	(-.f64 (*.f64 (sqrt.f64 z) y) #s(literal 0 binary64))
cost-diff	192	(-.f64 (.f64 (.f64 z y) y) #s(literal 0 binary64))
cost-diff	640	(/.f64 (-.f64 (.f64 (.f64 z y) y) #s(literal 0 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) #s(literal 0 binary64)))
cost-diff	0	(/.f64 #s(literal 2 binary64) y)
cost-diff	0	(*.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))
cost-diff	0	#s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (*.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z))))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (*.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))))
cost-diff	0	(fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64))
cost-diff	0	#s(approx (+ (* (sqrt z) y) x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) x))
cost-diff	0	(.f64 #s(approx (+ ( (sqrt z) y) x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) x)) #s(literal 1/2 binary64))
cost-diff	1024	(*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) x)
cost-diff	0	(sqrt.f64 z)
cost-diff	0	(*.f64 (sqrt.f64 z) y)
cost-diff	0	#s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y))
cost-diff	0	(.f64 #s(approx (+ ( (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
cost-diff	0	(*.f64 z y)
cost-diff	0	(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
cost-diff	0	#s(approx (+ (* (sqrt z) y) x) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x))
cost-diff	0	(.f64 #s(approx (+ ( (sqrt z) y) x) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)) #s(literal 1/2 binary64))

Rules

8 992×	`lower-fma.f32`
8 988×	`lower-fma.f64`
3 440×	`lower-*.f32`
3 422×	`lower-*.f64`
2 266×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	311
0	67	295
1	121	293
2	246	287
3	582	281
4	1403	272
5	3565	272
6	6744	272
0	8208	261

Stop Event

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

Calls

Call 1

Inputs
(.f64 #s(approx (+ ( (sqrt z) y) x) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(*.f64 z y)
z
y
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(/.f64 #s(literal 1 binary64) z)
#s(literal 1 binary64)
x
#s(literal 1/2 binary64)
(.f64 #s(approx (+ ( (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y))
(*.f64 (sqrt.f64 z) y)
(sqrt.f64 z)
z
y
#s(literal 1/2 binary64)
(.f64 #s(approx (+ ( (sqrt z) y) x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) x)) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) x))
(*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) x)
(fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64))
(/.f64 y x)
y
x
(sqrt.f64 z)
z
#s(literal 1 binary64)
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (*.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))))
#s(literal 1 binary64)
#s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (*.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z))))
(*.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))
(/.f64 #s(literal 2 binary64) y)
#s(literal 2 binary64)
y
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(/.f64 #s(literal 1 binary64) z)
z
(.f64 #s(literal 1/2 binary64) (+.f64 x (/.f64 (-.f64 (.f64 (.f64 z y) y) #s(literal 0 binary64)) (-.f64 (.f64 (sqrt.f64 z) y) #s(literal 0 binary64)))))
#s(literal 1/2 binary64)
(+.f64 x (/.f64 (-.f64 (.f64 (.f64 z y) y) #s(literal 0 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) #s(literal 0 binary64))))
x
(/.f64 (-.f64 (.f64 (.f64 z y) y) #s(literal 0 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) #s(literal 0 binary64)))
(-.f64 (.f64 (.f64 z y) y) #s(literal 0 binary64))
(.f64 (.f64 z y) y)
(*.f64 z y)
z
y
#s(literal 0 binary64)
(-.f64 (*.f64 (sqrt.f64 z) y) #s(literal 0 binary64))
(*.f64 (sqrt.f64 z) y)
(sqrt.f64 z)

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

localize102.0ms (1.4%)

Memory

-3.5MiB live, 147.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(+.f64 x (/.f64 (-.f64 (.f64 (.f64 z y) y) #s(literal 0 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) #s(literal 0 binary64))))
accuracy	0.13671875	(.f64 (.f64 z y) y)
accuracy	0.25	(*.f64 (sqrt.f64 z) y)
accuracy	29.554939792444657	(/.f64 (-.f64 (.f64 (.f64 z y) y) #s(literal 0 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) #s(literal 0 binary64)))
accuracy	0.17578125	(/.f64 #s(literal 1 binary64) #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (*.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))))
accuracy	0.28125	(*.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))
accuracy	0.3828067452792989	(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
accuracy	33.17091095101119	#s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (*.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z))))
accuracy	0	(sqrt.f64 z)
accuracy	0	#s(approx (+ (* (sqrt z) y) x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) x))
accuracy	1.6934100031621182	(fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64))
accuracy	6.675198340183721	(*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) x)
accuracy	0	(.f64 #s(approx (+ ( (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
accuracy	0	(sqrt.f64 z)
accuracy	0.25	(*.f64 (sqrt.f64 z) y)
accuracy	33.0592613530402	#s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y))
accuracy	0	(*.f64 z y)
accuracy	0	#s(approx (+ (* (sqrt z) y) x) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x))
accuracy	0.3828067452792989	(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
accuracy	3.885037998247241	(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)

Samples

76.0ms

256×

valid

Compiler

Compiled 248 to 37 computations (85.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-mult: 16.0ms (39% of total)

ival-div: 10.0ms (24.4% of total)

ival-add: 6.0ms (14.6% of total)

ival-sqrt: 4.0ms (9.7% of total)

ival-sub: 3.0ms (7.3% of total)

ival-neg: 1.0ms (2.4% of total)

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

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

exact: 0.0ms (0% of total)

series53.0ms (0.7%)

Memory

1.0MiB live, 76.8MiB allocated

Counts

22 → 636

Calls

Call 1

Inputs
#s(alt (.f64 #s(approx (+ ( (sqrt z) y) x) (fma.f64 (.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ (* (sqrt z) y) x) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)) #s(literal 1/2 binary64)) #<representation:binary64>) () ())
#s(alt #s(approx (+ (* (sqrt z) y) x) (fma.f64 (.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)) (patch #s(approx (+ ( (sqrt z) y) x) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)) #<representation:binary64>) () ())
#s(alt (fma.f64 (.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) (patch (fma.f64 (.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x) #<representation:binary64>) () ())
#s(alt (.f64 z y) (patch (.f64 z y) #<representation:binary64>) () ())
#s(alt (.f64 #s(approx (+ ( (sqrt z) y) x) (.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64)) #<representation:binary64>) () ())
#s(alt #s(approx (+ (* (sqrt z) y) x) (.f64 (sqrt.f64 z) y)) (patch #s(approx (+ ( (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #<representation:binary64>) () ())
#s(alt (.f64 (sqrt.f64 z) y) (patch (.f64 (sqrt.f64 z) y) #<representation:binary64>) () ())
#s(alt (sqrt.f64 z) (patch (sqrt.f64 z) #<representation:binary64>) () ())
#s(alt (.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) x) #<representation:binary64>) () ())
#s(alt (.f64 #s(approx (+ ( (sqrt z) y) x) (.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) x)) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) x)) #s(literal 1/2 binary64)) #<representation:binary64>) () ())
#s(alt #s(approx (+ (* (sqrt z) y) x) (.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) x)) (patch #s(approx (+ ( (sqrt z) y) x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) x)) #<representation:binary64>) () ())
#s(alt (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) #<representation:binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z))))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (- ( (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (*.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z))))) #<representation:binary64>) () ())
#s(alt #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))) (patch #s(approx (/ (- ( (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (*.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))) #<representation:binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) (patch (.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) #<representation:binary64>) () ())
#s(alt (/.f64 #s(literal 2 binary64) y) (patch (/.f64 #s(literal 2 binary64) y) #<representation:binary64>) () ())
#s(alt (/.f64 (-.f64 (.f64 (.f64 z y) y) #s(literal 0 binary64)) (-.f64 (.f64 (sqrt.f64 z) y) #s(literal 0 binary64))) (patch (/.f64 (-.f64 (.f64 (.f64 z y) y) #s(literal 0 binary64)) (-.f64 (.f64 (sqrt.f64 z) y) #s(literal 0 binary64))) #<representation:binary64>) () ())
#s(alt (-.f64 (.f64 (.f64 z y) y) #s(literal 0 binary64)) (patch (-.f64 (.f64 (.f64 z y) y) #s(literal 0 binary64)) #<representation:binary64>) () ())
#s(alt (-.f64 (.f64 (sqrt.f64 z) y) #s(literal 0 binary64)) (patch (-.f64 (.f64 (sqrt.f64 z) y) #s(literal 0 binary64)) #<representation:binary64>) () ())
#s(alt (+.f64 x (/.f64 (-.f64 (.f64 (.f64 z y) y) #s(literal 0 binary64)) (-.f64 (.f64 (sqrt.f64 z) y) #s(literal 0 binary64)))) (patch (+.f64 x (/.f64 (-.f64 (.f64 (.f64 z y) y) #s(literal 0 binary64)) (-.f64 (.f64 (sqrt.f64 z) y) #s(literal 0 binary64)))) #<representation:binary64>) () ())
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) #<representation:binary64>) () ())
#s(alt (.f64 (.f64 z y) y) (patch (.f64 (.f64 z y) y) #<representation:binary64>) () ())

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

Calls

9 calls:

Time	Variable		Point	Expression
6.0ms	x	@	-inf	((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (+ (* (* z y) (sqrt (/ 1 z))) x) (* z y) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (sqrt z) (* (+ (* (/ y x) (sqrt z)) 1) x) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (+ (* (/ y x) (sqrt z)) 1) (/ 1 (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2))) (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (* (/ 2 y) (sqrt (/ 1 z))) (/ 2 y) (/ (- (* (* z y) y) 0) (- (* (sqrt z) y) 0)) (- (* (* z y) y) 0) (- (* (sqrt z) y) 0) (+ x (/ (- (* (* z y) y) 0) (- (* (sqrt z) y) 0))) (sqrt (/ 1 z)) (* (* z y) y))
5.0ms	z	@	-inf	((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (+ (* (* z y) (sqrt (/ 1 z))) x) (* z y) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (sqrt z) (* (+ (* (/ y x) (sqrt z)) 1) x) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (+ (* (/ y x) (sqrt z)) 1) (/ 1 (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2))) (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (* (/ 2 y) (sqrt (/ 1 z))) (/ 2 y) (/ (- (* (* z y) y) 0) (- (* (sqrt z) y) 0)) (- (* (* z y) y) 0) (- (* (sqrt z) y) 0) (+ x (/ (- (* (* z y) y) 0) (- (* (sqrt z) y) 0))) (sqrt (/ 1 z)) (* (* z y) y))
4.0ms	z	@	inf	((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (+ (* (* z y) (sqrt (/ 1 z))) x) (* z y) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (sqrt z) (* (+ (* (/ y x) (sqrt z)) 1) x) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (+ (* (/ y x) (sqrt z)) 1) (/ 1 (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2))) (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (* (/ 2 y) (sqrt (/ 1 z))) (/ 2 y) (/ (- (* (* z y) y) 0) (- (* (sqrt z) y) 0)) (- (* (* z y) y) 0) (- (* (sqrt z) y) 0) (+ x (/ (- (* (* z y) y) 0) (- (* (sqrt z) y) 0))) (sqrt (/ 1 z)) (* (* z y) y))
3.0ms	z	@	0	((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (+ (* (* z y) (sqrt (/ 1 z))) x) (* z y) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (sqrt z) (* (+ (* (/ y x) (sqrt z)) 1) x) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (+ (* (/ y x) (sqrt z)) 1) (/ 1 (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2))) (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (* (/ 2 y) (sqrt (/ 1 z))) (/ 2 y) (/ (- (* (* z y) y) 0) (- (* (sqrt z) y) 0)) (- (* (* z y) y) 0) (- (* (sqrt z) y) 0) (+ x (/ (- (* (* z y) y) 0) (- (* (sqrt z) y) 0))) (sqrt (/ 1 z)) (* (* z y) y))
3.0ms	y	@	-inf	((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (+ (* (* z y) (sqrt (/ 1 z))) x) (* z y) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (sqrt z) y) (sqrt z) (* (+ (* (/ y x) (sqrt z)) 1) x) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (+ (* (/ y x) (sqrt z)) 1) (/ 1 (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2))) (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (* (/ 2 y) (sqrt (/ 1 z))) (/ 2 y) (/ (- (* (* z y) y) 0) (- (* (sqrt z) y) 0)) (- (* (* z y) y) 0) (- (* (sqrt z) y) 0) (+ x (/ (- (* (* z y) y) 0) (- (* (sqrt z) y) 0))) (sqrt (/ 1 z)) (* (* z y) y))

simplify202.0ms (2.8%)

Memory

-0.3MiB live, 231.5MiB allocated

Algorithm

1×	egg-herbie

Rules

8 628×	`lower-fma.f64`
8 628×	`lower-fma.f32`
6 762×	`lower-*.f64`
6 762×	`lower-*.f32`
2 840×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	398	5720
1	1270	5468
2	4460	5256
0	8793	4965

Stop Event

1×	iter limit
1×	node limit

Counts

636 → 618

Calls

Call 1

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

rewrite233.0ms (3.2%)

Memory

16.9MiB live, 325.0MiB allocated

Rules

8 360×	`lower-fma.f32`
8 356×	`lower-fma.f64`
3 730×	`lower-/.f32`
3 720×	`lower-/.f64`
3 584×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	247
0	65	226
1	237	213
2	1842	189
0	9677	177

Stop Event

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

Counts

22 → 1 207

Calls

Call 1

Inputs
(.f64 #s(approx (+ ( (sqrt z) y) x) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x))
(fma.f64 (*.f64 z y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) x)
(*.f64 z y)
(.f64 #s(approx (+ ( (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (*.f64 (sqrt.f64 z) y))
(*.f64 (sqrt.f64 z) y)
(sqrt.f64 z)
(*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) x)
(.f64 #s(approx (+ ( (sqrt z) y) x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) x)) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) x))
(fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (*.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))))
#s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (*.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z))))
(*.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))
(/.f64 #s(literal 2 binary64) y)
(/.f64 (-.f64 (.f64 (.f64 z y) y) #s(literal 0 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) #s(literal 0 binary64)))
(-.f64 (.f64 (.f64 z y) y) #s(literal 0 binary64))
(-.f64 (*.f64 (sqrt.f64 z) y) #s(literal 0 binary64))
(+.f64 x (/.f64 (-.f64 (.f64 (.f64 z y) y) #s(literal 0 binary64)) (-.f64 (*.f64 (sqrt.f64 z) y) #s(literal 0 binary64))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) z))
(.f64 (.f64 z y) y)

Outputs
(.f64 #s(literal 1/2 binary64) #s(approx (+ ( (sqrt z) y) x) (fma.f64 (sqrt.f64 z) y x)))
(.f64 #s(approx (+ ( (sqrt z) y) x) (fma.f64 (sqrt.f64 z) y x)) #s(literal 1/2 binary64))
#s(approx (+ (* (sqrt z) y) x) (fma.f64 (sqrt.f64 z) y x))
(.f64 (/.f64 (fma.f64 (.f64 y z) y (.f64 (neg.f64 x) x)) (-.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (fma.f64 (sqrt.f64 z) y x) (.f64 (.f64 y z) y)))
(.f64 (/.f64 (fma.f64 (.f64 y z) y (.f64 (neg.f64 x) x)) (fma.f64 (.f64 y z) y (*.f64 (neg.f64 x) x))) (fma.f64 (sqrt.f64 z) y x))
(.f64 (-.f64 (.f64 x x) (.f64 (.f64 y z) y)) (pow.f64 (-.f64 x (*.f64 (sqrt.f64 z) y)) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (.f64 y y) z (.f64 x (-.f64 x (.f64 (sqrt.f64 z) y)))) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (-.f64 (hypot.f64 x (.f64 (sqrt.f64 z) y)) (.f64 (.f64 (sqrt.f64 z) y) x)) #s(literal -1 binary64)))
(.f64 (fma.f64 (.f64 y z) y (.f64 (neg.f64 x) x)) (pow.f64 (-.f64 (.f64 (sqrt.f64 z) y) x) #s(literal -1 binary64)))
(pow.f64 (/.f64 (fma.f64 (.f64 y y) z (.f64 x (-.f64 x (*.f64 (sqrt.f64 z) y)))) (fma.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 x (.f64 (sqrt.f64 z) y)) (-.f64 (.f64 x x) (.f64 (.f64 y z) y))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (hypot.f64 x (.f64 (sqrt.f64 z) y)) (.f64 (*.f64 (sqrt.f64 z) y) x)) (fma.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 y z) y) (-.f64 (.f64 (sqrt.f64 z) y) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x x) (-.f64 (.f64 (sqrt.f64 z) y) x)) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 y z) y) (-.f64 (.f64 (sqrt.f64 z) y) x)) (/.f64 (.f64 (.f64 y z) y) (-.f64 (.f64 (sqrt.f64 z) y) x)) (fma.f64 (/.f64 (.f64 x x) (-.f64 (.f64 (sqrt.f64 z) y) x)) (/.f64 (.f64 x x) (-.f64 (.f64 (sqrt.f64 z) y) x)) (.f64 (/.f64 (.f64 (.f64 y z) y) (-.f64 (.f64 (sqrt.f64 z) y) x)) (/.f64 (.f64 x x) (-.f64 (*.f64 (sqrt.f64 z) y) x))))))
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(/.f64 (neg.f64 (.f64 (.f64 (sqrt.f64 z) y) #s(literal 1 binary64))) (neg.f64 (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 6 binary64)))) (neg.f64 (neg.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64)))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64)) (.f64 y z)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))) (.f64 y #s(literal 0 binary64))) (.f64 y (pow.f64 (*.f64 (sqrt.f64 z) y) #s(literal 4 binary64))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64)) y) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))) (.f64 (.f64 y z) #s(literal 0 binary64))) (.f64 (.f64 y z) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64)) z) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))) (.f64 (.f64 y y) #s(literal 0 binary64))) (.f64 (.f64 y y) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))))
(/.f64 (-.f64 (.f64 (neg.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 6 binary64))) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))) (.f64 (neg.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))) #s(literal 0 binary64))) (.f64 (neg.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))))
(/.f64 (-.f64 (.f64 (neg.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))) (.f64 (.f64 (neg.f64 z) (.f64 y y)) #s(literal 0 binary64))) (neg.f64 (pow.f64 (*.f64 (sqrt.f64 z) y) #s(literal 6 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 y z) y) #s(literal 5 binary64)) (.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64)) #s(literal 0 binary64))) (pow.f64 (.f64 (.f64 y z) y) #s(literal 4 binary64)))
(/.f64 (-.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64)) (.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal -2 binary64)) #s(literal 0 binary64))) (.f64 (*.f64 y z) y))
(/.f64 (-.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64)) (.f64 (/.f64 (.f64 (.f64 y z) y) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))) #s(literal 0 binary64))) (.f64 (/.f64 (.f64 (.f64 y z) y) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64)) (.f64 y z)) (.f64 (.f64 y z) y)) (.f64 y #s(literal 0 binary64))) (.f64 y (.f64 (*.f64 y z) y)))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64)) y) (.f64 (.f64 y z) y)) (.f64 (.f64 y z) #s(literal 0 binary64))) (.f64 (.f64 y z) (.f64 (.f64 y z) y)))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64)) z) (.f64 (.f64 y z) y)) (.f64 (.f64 y y) #s(literal 0 binary64))) (.f64 (.f64 y y) (.f64 (.f64 y z) y)))
(/.f64 (-.f64 (.f64 (neg.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 6 binary64))) (.f64 (.f64 y z) y)) (.f64 (neg.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))) #s(literal 0 binary64))) (.f64 (neg.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))) (.f64 (.f64 y z) y)))
(/.f64 (-.f64 (.f64 (neg.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))) (.f64 (.f64 y z) y)) (.f64 (.f64 (neg.f64 z) (.f64 y y)) #s(literal 0 binary64))) (.f64 (.f64 (neg.f64 z) (.f64 y y)) (.f64 (.f64 y z) y)))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 y z) y) #s(literal 4 binary64)) (.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64)) #s(literal 0 binary64))) (pow.f64 (*.f64 (sqrt.f64 z) y) #s(literal 6 binary64)))
(/.f64 (-.f64 (.f64 (.f64 y z) y) (.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal -2 binary64)) #s(literal 0 binary64))) (.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal -2 binary64)) (.f64 (.f64 y z) y)))
(/.f64 (-.f64 (.f64 (.f64 y z) y) (.f64 (/.f64 (.f64 (.f64 y z) y) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))) #s(literal 0 binary64))) (.f64 (/.f64 (.f64 (.f64 y z) y) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))) (.f64 (.f64 y z) y)))
(/.f64 (/.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64)) (.f64 y z)) y)
(/.f64 (/.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64)) y) (.f64 y z))
(/.f64 (/.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64)) z) (.f64 y y))
(/.f64 (.f64 (.f64 (sqrt.f64 z) y) #s(literal 1 binary64)) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y))
(/.f64 (.f64 (.f64 (neg.f64 z) (.f64 y y)) (.f64 (sqrt.f64 z) y)) (*.f64 (neg.f64 y) (sqrt.f64 z)))
(/.f64 (.f64 (.f64 (sqrt.f64 z) y) (.f64 (neg.f64 z) (.f64 y y))) (*.f64 (neg.f64 y) (sqrt.f64 z)))
(/.f64 (.f64 (.f64 (sqrt.f64 z) y) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 3 binary64))) (.f64 (*.f64 y z) y))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 y z) y) #s(literal 4 binary64)) #s(literal 0 binary64)) (pow.f64 (*.f64 (sqrt.f64 z) y) #s(literal 6 binary64)))
(/.f64 (neg.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))) (.f64 (neg.f64 z) (*.f64 y y)))
(/.f64 (.f64 (.f64 (neg.f64 z) (.f64 y y)) (.f64 (.f64 y z) y)) (.f64 (.f64 (neg.f64 y) (sqrt.f64 z)) (.f64 (sqrt.f64 z) y)))
(/.f64 (.f64 (.f64 (neg.f64 z) (.f64 y y)) #s(literal 1 binary64)) (.f64 (*.f64 (neg.f64 y) (sqrt.f64 z)) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)))
(/.f64 (.f64 (.f64 (.f64 y z) y) (.f64 (neg.f64 z) (.f64 y y))) (.f64 (.f64 (sqrt.f64 z) y) (.f64 (neg.f64 y) (sqrt.f64 z))))
(/.f64 (.f64 (.f64 (.f64 y z) y) #s(literal 1 binary64)) (.f64 (*.f64 (sqrt.f64 z) y) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (neg.f64 z) (.f64 y y))) (.f64 (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y) (*.f64 (neg.f64 y) (sqrt.f64 z))))
(/.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 5 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 3 binary64)))
(/.f64 (pow.f64 (.f64 (neg.f64 y) (sqrt.f64 z)) #s(literal 3 binary64)) (.f64 (neg.f64 y) (sqrt.f64 z)))
(/.f64 (neg.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 6 binary64))) (neg.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64))))
(/.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64)) (.f64 (*.f64 y z) y))
(/.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 6 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64)))
(/.f64 (.f64 (.f64 y z) y) (.f64 (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y) (.f64 (sqrt.f64 z) y)))
(/.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 3 binary64)) (.f64 (sqrt.f64 z) y))
(/.f64 (*.f64 (neg.f64 y) (sqrt.f64 z)) (neg.f64 (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)))
(/.f64 (.f64 (neg.f64 z) (.f64 y y)) (neg.f64 (.f64 (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y) (.f64 (sqrt.f64 z) y))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 (.f64 y z) y) (pow.f64 (*.f64 (sqrt.f64 z) y) #s(literal 4 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (*.f64 (sqrt.f64 z) y) #s(literal -2 binary64))))
(/.f64 (*.f64 (sqrt.f64 z) y) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 y z) y) (pow.f64 (*.f64 (sqrt.f64 z) y) #s(literal 4 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (sqrt.f64 z) y) #s(literal -2 binary64)))
(fma.f64 (pow.f64 (/.f64 z (sqrt.f64 z)) #s(literal 2 binary64)) (pow.f64 (/.f64 (*.f64 y y) y) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (/.f64 z y) #s(literal 2 binary64)) (pow.f64 (/.f64 (*.f64 y y) (sqrt.f64 z)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (/.f64 (*.f64 y z) y) #s(literal 2 binary64)) (pow.f64 (/.f64 y (sqrt.f64 z)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (/.f64 y (sqrt.f64 z)) #s(literal 2 binary64)) (pow.f64 (/.f64 (*.f64 y z) y) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (/.f64 y (sqrt.f64 z)) #s(literal 2 binary64)) (*.f64 z z) #s(literal 0 binary64))
(fma.f64 (pow.f64 (/.f64 y y) #s(literal 2 binary64)) (.f64 (.f64 y z) y) #s(literal 0 binary64))
(fma.f64 (pow.f64 (.f64 y z) #s(literal 2 binary64)) (pow.f64 (/.f64 y (.f64 (sqrt.f64 z) y)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (.f64 y z) #s(literal 2 binary64)) (pow.f64 (.f64 y (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (*.f64 y z) #s(literal 2 binary64)) (pow.f64 z #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 z z) (pow.f64 (/.f64 y (sqrt.f64 z)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 z z) (pow.f64 (/.f64 (.f64 y y) (*.f64 (sqrt.f64 z) y)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 z z) (pow.f64 (.f64 (*.f64 y y) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 (sqrt.f64 z) y) (pow.f64 z #s(literal -1/2 binary64))) (*.f64 y z) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 (sqrt.f64 z) y) (*.f64 y z)) (pow.f64 z #s(literal -1/2 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 (sqrt.f64 z) y) z) (/.f64 y (sqrt.f64 z)) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 (sqrt.f64 z) y) (sqrt.f64 z)) y #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 (sqrt.f64 z) y) y) (sqrt.f64 z) #s(literal 0 binary64))
(fma.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal -2 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 y y) (pow.f64 (.f64 z (pow.f64 z #s(literal -1/2 binary64))) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 y y) (pow.f64 (/.f64 (.f64 y z) (*.f64 (sqrt.f64 z) y)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 y y) (pow.f64 (.f64 (*.f64 y z) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 y y) z #s(literal 0 binary64))
(fma.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 z) y)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 4 binary64)) (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal -2 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 6 binary64)) (pow.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal -2 binary64)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (.f64 (sqrt.f64 z) y) #s(literal 6 binary64)) (pow.f64 (.f64 (*.f64 y z) y) #s(literal -2 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 y z) y) (pow.f64 (/.f64 y y) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 y z) y) (.f64 (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y) (.f64 (sqrt.f64 z) y)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (*.f64 (sqrt.f64 z) y) #s(literal 3 binary64)) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y) #s(literal 0 binary64))
(fma.f64 (.f64 (neg.f64 y) (sqrt.f64 z)) (.f64 (neg.f64 y) (sqrt.f64 z)) #s(literal 0 binary64))
(fma.f64 (.f64 (sqrt.f64 z) y) (.f64 (sqrt.f64 z) y) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 z) (.f64 y (.f64 (sqrt.f64 z) y)) #s(literal 0 binary64))
(fma.f64 (pow.f64 z #s(literal -1/2 binary64)) (.f64 (.f64 y z) (*.f64 (sqrt.f64 z) y)) #s(literal 0 binary64))
(fma.f64 (pow.f64 z #s(literal -1 binary64)) (pow.f64 (*.f64 y z) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 y z) y) #s(literal 0 binary64))
(fma.f64 (.f64 y z) (.f64 (pow.f64 z #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 z) y)) #s(literal 0 binary64))
(fma.f64 (*.f64 y z) y #s(literal 0 binary64))
(fma.f64 y (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) y)) #s(literal 0 binary64))
(fma.f64 y (*.f64 y z) #s(literal 0 binary64))
(fma.f64 z (.f64 (/.f64 y (sqrt.f64 z)) (.f64 (sqrt.f64 z) y)) #s(literal 0 binary64))
(fma.f64 z (*.f64 y y) #s(literal 0 binary64))
(-.f64 (.f64 (.f64 y z) y) (/.f64 #s(literal 0 binary64) (/.f64 (pow.f64 z #s(literal -1/2 binary64)) y)))
(-.f64 (.f64 (.f64 y z) y) (/.f64 #s(literal 0 binary64) (.f64 (.f64 y z) y)))
(-.f64 (.f64 (.f64 y z) y) (/.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (sqrt.f64 z) y) #s(literal 4 binary64))))
(-.f64 (.f64 (.f64 y z) y) #s(literal 0 binary64))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 z) y)) #s(literal 2 binary64)))
(+.f64 (.f64 (.f64 y z) y) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (.f64 (.f64 y z) y))

eval272.0ms (3.7%)

Memory: 30.6MiB live, 484.3MiB allocated
Compiler: Compiled 41 286 to 5 278 computations (87.2% saved)

prune54.0ms (0.7%)

Memory

-33.4MiB live, 143.1MiB allocated

Pruning

9 alts after pruning (4 fresh and 5 done)

	Pruned	Kept	Total
New	2 090	4	2 094
Fresh	1	0	1
Picked	3	2	5
Done	0	3	3
Total	2 094	9	2 103

Accuracy

100.0%

Counts

2 103 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.1%	(/.f64 #s(literal 1 binary64) #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 z)) y)))
▶	48.1%	(/.f64 #s(literal 1 binary64) #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 z))))
✓	99.8%	(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
▶	42.3%	(.f64 #s(approx (+ ( (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) #s(literal 1/2 binary64))
✓	86.9%	(.f64 #s(approx (+ ( (sqrt z) y) x) (*.f64 (fma.f64 (/.f64 y x) (sqrt.f64 z) #s(literal 1 binary64)) x)) #s(literal 1/2 binary64))
▶	41.5%	(.f64 #s(approx (+ ( (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64))
✓	48.2%	(.f64 #s(approx (+ ( (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
✓	99.8%	(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (sqrt.f64 z))))
✓	53.5%	#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 74 to 78 computations (-5.4% saved)

simplify261.0ms (3.6%)

Memory

17.6MiB live, 91.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Rules

2 488×	`lower-fma.f64`
2 488×	`lower-fma.f32`
1 796×	`lower-*.f32`
1 790×	`lower-*.f64`
974×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	224
0	47	224
1	76	220
2	120	220
3	215	220
4	372	220
5	667	220
6	1376	220
7	3114	220
8	3781	220
9	4025	220
10	4104	220
11	4119	220
12	4133	220
13	4738	220
14	5133	220
15	5281	220
16	5365	220
17	5421	220
18	5437	220
19	5445	220
20	5445	220
21	5653	220
22	5842	220
23	5846	220
24	5846	220
0	5846	216

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize214.0ms (2.9%)

Memory

-2.5MiB live, 121.4MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.17578125	(/.f64 #s(literal 1 binary64) #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 z)) y)))
accuracy	0.1875	(/.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 z)) y)
accuracy	0.26171875	(/.f64 #s(literal 2 binary64) (sqrt.f64 z))
accuracy	33.17091095101119	#s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 z)) y))
accuracy	0	(sqrt.f64 z)
accuracy	0.17578125	(/.f64 #s(literal 1 binary64) #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 z))))
accuracy	0.26400375976844204	(/.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 z))
accuracy	33.17091095101119	#s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 z)))
accuracy	0	(*.f64 y z)
accuracy	0	(sqrt.f64 z)
accuracy	7.736968805197177	(/.f64 (*.f64 y z) (sqrt.f64 z))
accuracy	33.0592613530402	#s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z)))
accuracy	0	(sqrt.f64 z)
accuracy	0.2578125	(/.f64 y (sqrt.f64 z))
accuracy	8.30684820686544	(*.f64 (/.f64 y (sqrt.f64 z)) z)
accuracy	33.0592613530402	#s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z))

Samples

95.0ms

256×

valid

Compiler

Compiled 170 to 29 computations (82.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 81.0ms

ival-div: 47.0ms (58.3% of total)

ival-mult: 26.0ms (32.2% of total)

ival-add: 2.0ms (2.5% of total)

ival-sqrt: 2.0ms (2.5% of total)

ival-sub: 1.0ms (1.2% of total)

ival-neg: 1.0ms (1.2% of total)

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

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

exact: 0.0ms (0% of total)

series35.0ms (0.5%)

Memory

19.1MiB live, 57.6MiB allocated

Counts

17 → 468

Calls

Call 1

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

Outputs
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (.f64 #s(approx (+ ( (sqrt z) y) x) (.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (.f64 #s(approx (+ ( (sqrt z) y) x) (.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (.f64 #s(approx (+ ( (sqrt z) y) x) (.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (.f64 #s(approx (+ ( (sqrt z) y) x) (.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ (* (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (.f64 (/.f64 y (sqrt.f64 z)) z)) (patch #s(approx (+ ( (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #<representation:binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (.f64 (/.f64 y (sqrt.f64 z)) z)) (patch #s(approx (+ ( (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #<representation:binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (.f64 (/.f64 y (sqrt.f64 z)) z)) (patch #s(approx (+ ( (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #<representation:binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (.f64 (/.f64 y (sqrt.f64 z)) z)) (patch #s(approx (+ ( (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (.f64 (/.f64 y (sqrt.f64 z)) z) (patch (.f64 (/.f64 y (sqrt.f64 z)) z) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (.f64 (/.f64 y (sqrt.f64 z)) z) (patch (.f64 (/.f64 y (sqrt.f64 z)) z) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (.f64 (/.f64 y (sqrt.f64 z)) z) (patch (.f64 (/.f64 y (sqrt.f64 z)) z) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (.f64 (/.f64 y (sqrt.f64 z)) z) (patch (.f64 (/.f64 y (sqrt.f64 z)) z) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt (/ 1 z))) (taylor 0 z) (#s(alt (/.f64 y (sqrt.f64 z)) (patch (/.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt (/ 1 z))) (taylor 0 z) (#s(alt (/.f64 y (sqrt.f64 z)) (patch (/.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt (/ 1 z))) (taylor 0 z) (#s(alt (/.f64 y (sqrt.f64 z)) (patch (/.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt (/ 1 z))) (taylor 0 z) (#s(alt (/.f64 y (sqrt.f64 z)) (patch (/.f64 y (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (.f64 #s(approx (+ ( (sqrt z) y) x) (/.f64 (.f64 y z) (sqrt.f64 z))) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (.f64 #s(approx (+ ( (sqrt z) y) x) (/.f64 (.f64 y z) (sqrt.f64 z))) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (.f64 #s(approx (+ ( (sqrt z) y) x) (/.f64 (.f64 y z) (sqrt.f64 z))) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (* 1/2 (+ x (* y (sqrt z)))) (taylor 0 z) (#s(alt (.f64 #s(approx (+ ( (sqrt z) y) x) (/.f64 (.f64 y z) (sqrt.f64 z))) #s(literal 1/2 binary64)) (patch (.f64 #s(approx (+ (* (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) #s(literal 1/2 binary64)) #<representation:binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 (.f64 y z) (sqrt.f64 z))) (patch #s(approx (+ ( (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 (.f64 y z) (sqrt.f64 z))) (patch #s(approx (+ ( (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 (.f64 y z) (sqrt.f64 z))) (patch #s(approx (+ ( (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (+ x (* y (sqrt z))) (taylor 0 z) (#s(alt #s(approx (+ (* (sqrt z) y) x) (/.f64 (.f64 y z) (sqrt.f64 z))) (patch #s(approx (+ ( (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (/.f64 (.f64 y z) (sqrt.f64 z)) (patch (/.f64 (.f64 y z) (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (/.f64 (.f64 y z) (sqrt.f64 z)) (patch (/.f64 (.f64 y z) (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (/.f64 (.f64 y z) (sqrt.f64 z)) (patch (/.f64 (.f64 y z) (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y (sqrt z)) (taylor 0 z) (#s(alt (/.f64 (.f64 y z) (sqrt.f64 z)) (patch (/.f64 (.f64 y z) (sqrt.f64 z)) #<representation:binary64>) () ())) ())
#s(alt (* y z) (taylor 0 z) (#s(alt (.f64 y z) (patch (.f64 y z) #<representation:binary64>) () ())) ())
#s(alt (* y z) (taylor 0 z) (#s(alt (.f64 y z) (patch (.f64 y z) #<representation:binary64>) () ())) ())
#s(alt (* y z) (taylor 0 z) (#s(alt (.f64 y z) (patch (.f64 y z) #<representation:binary64>) () ())) ())
#s(alt (* y z) (taylor 0 z) (#s(alt (.f64 y z) (patch (.f64 y z) #<representation:binary64>) () ())) ())
#s(alt (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (taylor 0 z) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 z)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x)))) (taylor 0 z) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 z)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x)))) (taylor 0 z) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 z)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (+ (* -1/2 (/ (pow x 2) (- (* y (sqrt z)) x))) (* 1/2 (/ (* (pow y 2) z) (- (* y (sqrt z)) x)))) (taylor 0 z) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 z)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 z)))) #<representation:binary64>) () ())) ())
#s(alt (* -2 (/ (- (* y (sqrt z)) x) (pow x 2))) (taylor 0 z) (#s(alt #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 z))) (patch #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) y) (sqrt.f64 z))) #<representation:binary64>) () ())) ())
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#s(alt (* -1 (* x (- (* -1/2 (* (/ y x) (sqrt z))) 1/2))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 z)) y))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 z)) y))) #<representation:binary64>) () ())) ())
#s(alt (/ 2 x) (taylor -inf x) (#s(alt #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 z)) y)) (patch #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 z)) y)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (/ (- (* 2 (* (/ y x) (sqrt z))) 2) x)) (taylor -inf x) (#s(alt #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 z)) y)) (patch #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 z)) y)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (+ (* -2 (* y (sqrt z))) (* 2 (/ (* (pow y 2) z) x))) x)) 2) x)) (taylor -inf x) (#s(alt #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 z)) y)) (patch #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 z)) y)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (+ (* -2 (* y (sqrt z))) (* -1 (/ (+ (* -2 (* (pow y 2) z)) (* 2 (* (/ (pow y 3) x) (sqrt (pow z 3))))) x))) x)) 2) x)) (taylor -inf x) (#s(alt #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 z)) y)) (patch #s(approx (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 z)) y)) #<representation:binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
4.0ms	y	@	0	((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (/ y (sqrt z)) z) (/ y (sqrt z)) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* y z) (sqrt z)) (* y z) (/ 1 (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2))) (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/ (/ 2 y) (sqrt z)) (/ 2 y) (/ 1 (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2))) (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/ (/ 2 (sqrt z)) y) (/ 2 (sqrt z)) (sqrt z))
4.0ms	z	@	-inf	((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (/ y (sqrt z)) z) (/ y (sqrt z)) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* y z) (sqrt z)) (* y z) (/ 1 (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2))) (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/ (/ 2 y) (sqrt z)) (/ 2 y) (/ 1 (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2))) (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/ (/ 2 (sqrt z)) y) (/ 2 (sqrt z)) (sqrt z))
2.0ms	y	@	-inf	((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (/ y (sqrt z)) z) (/ y (sqrt z)) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* y z) (sqrt z)) (* y z) (/ 1 (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2))) (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/ (/ 2 y) (sqrt z)) (/ 2 y) (/ 1 (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2))) (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/ (/ 2 (sqrt z)) y) (/ 2 (sqrt z)) (sqrt z))
2.0ms	z	@	0	((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (/ y (sqrt z)) z) (/ y (sqrt z)) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* y z) (sqrt z)) (* y z) (/ 1 (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2))) (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/ (/ 2 y) (sqrt z)) (/ 2 y) (/ 1 (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2))) (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/ (/ 2 (sqrt z)) y) (/ 2 (sqrt z)) (sqrt z))
2.0ms	y	@	inf	((* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (* (/ y (sqrt z)) z) (/ y (sqrt z)) (* (+ (* (sqrt z) y) x) 1/2) (+ (* (sqrt z) y) x) (/ (* y z) (sqrt z)) (* y z) (/ 1 (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2))) (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/ (/ 2 y) (sqrt z)) (/ 2 y) (/ 1 (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2))) (/ (- (* (sqrt z) y) x) (* (+ (* (* z y) y) (* (neg x) x)) 1/2)) (/ (/ 2 (sqrt z)) y) (/ 2 (sqrt z)) (sqrt z))

simplify694.0ms (9.5%)

Memory

-7.9MiB live, 225.6MiB allocated

Algorithm

1×	egg-herbie

Rules

8 248×	`lower-fma.f64`
8 248×	`lower-fma.f32`
6 354×	`lower-*.f64`
6 354×	`lower-*.f32`
4 390×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	370	5854
1	1166	5460
2	4053	5230
0	8944	5006

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 462

Calls

Call 1

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

rewrite234.0ms (3.2%)

Memory

11.9MiB live, 251.8MiB allocated

Rules

9 356×	`lower-fma.f64`
9 356×	`lower-fma.f32`
5 830×	`lower-*.f32`
5 824×	`lower-*.f64`
3 720×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	204
0	47	204
1	158	200
2	907	148
0	9037	140

Stop Event

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

Counts

17 → 407

Calls

Call 1

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

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

eval219.0ms (3%)

Memory: -0.8MiB live, 234.2MiB allocated
Compiler: Compiled 12 247 to 1 437 computations (88.3% saved)

prune59.0ms (0.8%)

Memory

-8.7MiB live, 99.0MiB allocated

Pruning

9 alts after pruning (3 fresh and 6 done)

	Pruned	Kept	Total
New	950	3	953
Fresh	0	0	0
Picked	2	2	4
Done	1	4	5
Total	953	9	962

Accuracy

100.0%

Counts

962 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
✓	42.3%	(.f64 #s(approx (+ ( (sqrt z) y) x) (/.f64 (*.f64 y z) (sqrt.f64 z))) #s(literal 1/2 binary64))
	48.2%	(.f64 #s(approx (+ ( (sqrt z) y) x) (/.f64 y (/.f64 (sqrt.f64 z) z))) #s(literal 1/2 binary64))
	48.1%	(.f64 #s(approx (+ ( (sqrt z) y) x) (*.f64 (/.f64 z (sqrt.f64 z)) y)) #s(literal 1/2 binary64))
✓	41.5%	(.f64 #s(approx (+ ( (sqrt z) y) x) (*.f64 (/.f64 y (sqrt.f64 z)) z)) #s(literal 1/2 binary64))
✓	48.2%	(.f64 #s(approx (+ ( (sqrt z) y) x) (*.f64 (sqrt.f64 z) y)) #s(literal 1/2 binary64))
	41.5%	(.f64 #s(approx (+ ( (sqrt z) y) x) (.f64 #s(approx (/ y (sqrt z)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) y)) z)) #s(literal 1/2 binary64))
✓	99.8%	(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (sqrt.f64 z))))
✓	53.5%	#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 353 to 178 computations (49.6% saved)

regimes60.0ms (0.8%)

Memory

18.8MiB live, 138.3MiB allocated

Counts

24 → 1

Calls

Call 1

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

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

Calls

7 calls:

13.0ms	(*.f64 y (sqrt.f64 z))
9.0ms	y
9.0ms	(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z))))
7.0ms	x
7.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`y`
99.8%	1	`z`
99.8%	1	`(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z))))`
99.8%	1	`(+.f64 x (*.f64 y (sqrt.f64 z)))`
99.8%	1	`(*.f64 y (sqrt.f64 z))`
99.8%	1	`(sqrt.f64 z)`

Compiler

Compiled 25 to 34 computations (-36% saved)

regimes16.0ms (0.2%)

Memory

-2.7MiB live, 36.5MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

7 calls:

3.0ms	(*.f64 y (sqrt.f64 z))
2.0ms	(sqrt.f64 z)
2.0ms	(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z))))
2.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))
2.0ms	z

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`y`
99.8%	1	`z`
99.8%	1	`(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z))))`
99.8%	1	`(+.f64 x (*.f64 y (sqrt.f64 z)))`
99.8%	1	`(*.f64 y (sqrt.f64 z))`
99.8%	1	`(sqrt.f64 z)`

Compiler

Compiled 25 to 34 computations (-36% saved)

regimes76.0ms (1%)

Memory

-77.1MiB live, 19.7MiB allocated

Counts

3 → 3

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

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

Calls

7 calls:

64.0ms	y
2.0ms	x
2.0ms	(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z))))
2.0ms	z
2.0ms	(sqrt.f64 z)

Results

Accuracy	Segments	Branch
75.6%	3	`x`
78.4%	3	`y`
62.9%	2	`z`
59.9%	3	`(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z))))`
59.9%	3	`(+.f64 x (*.f64 y (sqrt.f64 z)))`
78.8%	3	`(*.f64 y (sqrt.f64 z))`
62.9%	2	`(sqrt.f64 z)`

Compiler

Compiled 25 to 34 computations (-36% saved)

regimes9.0ms (0.1%)

Memory

10.5MiB live, 10.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

7 calls:

1.0ms	(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z))))
1.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))
1.0ms	(*.f64 y (sqrt.f64 z))
1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
53.5%	1	`(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x (.f64 y (sqrt.f64 z))))`
53.5%	1	`(+.f64 x (*.f64 y (sqrt.f64 z)))`
53.5%	1	`z`
53.5%	1	`(sqrt.f64 z)`
53.5%	1	`x`
53.5%	1	`y`
53.5%	1	`(*.f64 y (sqrt.f64 z))`

Compiler

Compiled 25 to 34 computations (-36% saved)

bsearch1.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	2931626420611.5063	1.0326817820731973e+27
0.0ms	-1.068973048285371e-17	-3.034914161772606e-23

Compiler

Compiled 13 to 16 computations (-23.1% saved)

simplify33.0ms (0.4%)

Memory

5.7MiB live, 44.9MiB allocated

Algorithm

1×	egg-herbie

Rules

10×	`-commutative-binary64-.f64`
2×	`1-exp-binary32-exp.f32`
2×	`1-exp-binary64-exp.f64`
2×	`+-commutative-binary64-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	83
1	38	83

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (sqrt.f64 z))))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(if (<=.f64 (.f64 y (sqrt.f64 z)) #s(literal -6490371073168535/649037107316853453566312041152512 binary64)) #s(approx ( (/ 1 2) (+ x (* y (sqrt z)))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 z) y))) (if (<=.f64 (.f64 y (sqrt.f64 z)) #s(literal 5000000000000 binary64)) #s(approx ( (/ 1 2) (+ x (* y (sqrt z)))) (.f64 #s(literal 1/2 binary64) x)) #s(approx ( (/ 1 2) (+ x (* y (sqrt z)))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 z) y)))))
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))

Outputs
(.f64 #s(literal 1/2 binary64) (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 (+.f64 (.f64 (sqrt.f64 z) y) x) #s(literal 1/2 binary64))
(*.f64 (fma.f64 (sqrt.f64 z) y x) #s(literal 1/2 binary64))
(if (<=.f64 (.f64 y (sqrt.f64 z)) #s(literal -6490371073168535/649037107316853453566312041152512 binary64)) #s(approx ( (/ 1 2) (+ x (* y (sqrt z)))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 z) y))) (if (<=.f64 (.f64 y (sqrt.f64 z)) #s(literal 5000000000000 binary64)) #s(approx ( (/ 1 2) (+ x (* y (sqrt z)))) (.f64 #s(literal 1/2 binary64) x)) #s(approx ( (/ 1 2) (+ x (* y (sqrt z)))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 z) y)))))
(if (<=.f64 (.f64 (sqrt.f64 z) y) #s(literal -6490371073168535/649037107316853453566312041152512 binary64)) #s(approx ( (/ 1 2) (+ x (* y (sqrt z)))) (.f64 (.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64))) (if (<=.f64 (.f64 (sqrt.f64 z) y) #s(literal 5000000000000 binary64)) #s(approx ( (/ 1 2) (+ x (* y (sqrt z)))) (.f64 x #s(literal 1/2 binary64))) #s(approx ( (/ 1 2) (+ x (* y (sqrt z)))) (.f64 (.f64 (sqrt.f64 z) y) #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (* (/ 1 2) (+ x (* y (sqrt z)))) (*.f64 x #s(literal 1/2 binary64)))

soundness401.0ms (5.5%)

Memory

-7.8MiB live, 266.8MiB allocated

Rules

7 460×	`lower-fma.f64`
7 460×	`lower-fma.f32`
5 642×	`lower-fma.f64`
5 642×	`lower-fma.f32`
4 298×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
0	16	21
1	41	21
2	234	21
3	2001	21
0	8162	19
0	75	646
1	251	646
2	797	646
3	2298	622
4	5069	622
5	7549	622
0	8141	566

Stop Event

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

Compiler

Compiled 117 to 64 computations (45.3% saved)

preprocess30.0ms (0.4%)

Memory: 18.6MiB live, 56.7MiB allocated
Compiler: Compiled 122 to 60 computations (50.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze55.0ms (0.8%)

sample1.4s (18.5%)

explain180.0ms (2.5%)

preprocess71.0ms (1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.1%)

localize29.0ms (0.4%)

series10.0ms (0.1%)

simplify160.0ms (2.2%)

rewrite184.0ms (2.5%)

eval44.0ms (0.6%)

prune41.0ms (0.6%)

simplify439.0ms (6%)

localize75.0ms (1%)

series50.0ms (0.7%)

simplify518.0ms (7.1%)

rewrite333.0ms (4.5%)

eval336.0ms (4.6%)

prune48.0ms (0.7%)

simplify148.0ms (2%)

localize102.0ms (1.4%)

series53.0ms (0.7%)

simplify202.0ms (2.8%)

rewrite233.0ms (3.2%)

eval272.0ms (3.7%)

prune54.0ms (0.7%)

simplify261.0ms (3.6%)

localize214.0ms (2.9%)

series35.0ms (0.5%)

simplify694.0ms (9.5%)

rewrite234.0ms (3.2%)

eval219.0ms (3%)

prune59.0ms (0.8%)

regimes60.0ms (0.8%)

regimes16.0ms (0.2%)

regimes76.0ms (1%)

regimes9.0ms (0.1%)

bsearch1.0ms (0%)

simplify33.0ms (0.4%)

soundness401.0ms (5.5%)

preprocess30.0ms (0.4%)

end0.0ms (0%)

Profiling